I

15th International Stellarator Workshop

Programme CommitteeChairman: H. Yamada NIFS (Japan)

J.H.Harris ANU (Australia), ORNL (USA)T.Klinger IPP Greifswald (Germany)O.Motojima NIFS (Japan)L.M.Kovrizhnykh GPI (Russia)E.Ascasíbar CIEMAT (Spain)V.I.Lapshin IPP Kharkov (Ukraine)M.C.Zarnstorff PPPL (USA)

Local Organising CommitteeChairman: E. Ascasíbar CIEMAT (Spain)Scientific Secretary: K. McCarthy CIEMAT (Spain)

F. Castejón CIEMAT (Spain)B. van Milligen CIEMAT (Spain)A. Suárez CIEMAT (Spain)

IAEA Technical Meeting on Innovative Concepts and Theory of Stellarators

Programme CommitteeChairman: L. García Universidad Carlos III (Spain)

F. Castejón CIEMAT (Spain)G. Mank IAEAH. Maassberg IPP Greifswald (Germany)N. Nakajima NIFS (Japan)M. Gryaznevich UKAEA (UK)J. Sarff Univ. of Wisconsin (USA)

Local Organising CommitteeChairman: F. Castejón CIEMAT (Spain)

K. McCarthy CIEMAT (Spain)E. Ascasíbar CIEMAT (Spain)B. van Milligen CIEMAT (Spain)A. Suárez CIEMAT (Spain)

II

Contents of the Book of Abstracts

Index of Contributed Abstracts to the Stellarator Workshop

Contents of Monday, October 3 IIIContents of Tuesday October 4 IVContents of Wednesday, October 5 VIIContents of Thursday, October 6 IXContents of Friday, October 7 X

Stellarator Workshop Programme 1

Contributed Abstracts to the Stellarator Workshop

Monday, October 3 3Tuesday October 4 47Wednesday, October 5 89Thursday, October 6 131Friday, October 7 139

IAEA Technical Meeting Programme 151

Contributed Abstracts to the IAEA Technical Meeting 153

III

Contents of Monday, October 3

Invited TalksTitle First author Page

IT-01 Electron internal transport barriers and magnetic topologyin the TJ-II stellarator

Estrada 5

IT-02 Status of construction and assembly of W7-X Hartmann 6IT-03 Optimization of the ARIES-CS compact stellarator reactor

parametersLyon 7

IT-04 Improved confinement and related physics study in CHS Okamura 8IT-05 Effects of Quasi-symmetry on Particle and Thermal

Transport in HSXCanik

9IT-06 Recent results from the H-1 Heliac Blackwell 10IT-07 Recent progress of MHD study in high-beta plasmas of

LHDSakakibara 11

OralsOr-01 First results from the Columbia Non-Neutral Torus (CNT) Pedersen 12Or-02 Review of L-2M Stellarator Recent Results Shchepetov 13Or-03 Hot Cathode Biasing Experiment in Compact Helical

System Takahashi 14

Or-04 Novel physics involved in interpretation of Alfvenicactivity accompanied by thermal crashes in W7-AS Kolesnichenko 15

Poster Session P1P1-01 Transport Analysis of High Beta Plasmas on LHD Funaba 16P1-02 Application of the Integrated Transport Code for Helical

Plasmas to LHDFunaba 17

P1-03 Flows and Diffusions driven by Neoclassical Viscositiesin Helical Plasmas

Nishimura 18

P1-04 Active Neutral Particle Diagnostics on LHD by LocallyEnhanced Charge Exchange on an Impurity PelletAblation Cloud

Goncharov 19

P1-05 Reheat mode discharges in high density regime ofCompact Helical System

Isobe 20

P1-06 Progress on Electron Cyclotron Heating Experiments inLHD

Shimozuma 21

P1-07 Observation of Equilibria with a Double Magnetic Axis inLHD

Yamada 22

P1-08 Effect of Neoclassical Transport Optimization on ElectronHeat Transport in the Low-collisionality LHD plasma

Murakami 23

P1-09 Using e-beam mapping to detect coil misalignment inNCSX

Fredrickson 24

P1-10 New method of determining coil misalignments in theITER tokamak on the base of sensitive vacuum magneticmeasurements

Georgiyevskiy 25

P1-11 Impurity Ion Transport under Drift Wave Electric Field inHelical Plasma

Antufyev 26

P1-12 The Equilibrium β Limit in W7-AS Reiman 27

IV

P1-13 Derivatives of the local ballooning growth rate withrespect to surface label, field line label and ballooningparameter

Hudson 28

P1-14 SVD Methods for Magnetic Diagnostics Design in NCSX Pomphrey 29P1-15 The Design of magnetic Diagnostics for Reconstructing of

NCSX Stellarator EquilibriaLazarus 30

P1-16 Equilibrium Reconstruction in Stellarators: V3FIT Hanson 31P1-17 Field–mapping and initial experiments in the Compact

Toroidal Hybrid (CTH) ExperimentKnowlton 32

P1-18 Recent Developments in the Quasi-Poloidal StellaratorProject

Lyon 33

P1-19 Coil Development for the Quasi-Poloidal StellaratorProject

Nelson 34

P1-20 Bootstrap Current in Quasi-Symmetric Stellarators Ware 35P1-21 Ballooning Stability in Quasi-symmetric Stellarators Sanchez 36P1-22 Overview of recent results from HSX and the Planned

Experimental ProgramAnderson 37

P1-23 Structure of Edge Turbulence in the HSX Stellarator Lechte 38

P1-24 Quasisymmetry-breaking and increased parallel viscousdamping near magnetic islands in HSX

Talmadge 39

P1-25 Evidence for Fast-electron-Driven Alfvenic Modes in theHSX Stellarator

Brower 40

P1-26 Stability Properties of Anisotropic Pressure StellaratorPlasmas with Fluid and Non-interacting Energetic ParticleModels

Cooper 41

P1-27 Electron Cyclotron Current Drive Compensation of theBootstrap Current in Quasi-symmetric Reactor Devices

Ferrando 42

P1-28 3D Full Wave Propagation Code for Warm Plasma Mellet 43P1-29 VENUS+df - A Bootstrap Current Calculation Module for

3D ConfigurationsIsaev 44

P1-30 The First Electron Plasmas in the Columbia Non-neutralTorus

Kremer 45

P1-31 Field Line Mapping Results in the CNT Stellarator Sarasola 46

V

Contents of Tuesday, October 4

Review TalkRT-01 Overview of progress of LHD experiment Komori 49

Invited TalksIT-08 Progress in NCSX and QPS design and construction Reiersen 50IT-09 Configuration control for the confinement improvement in

Heliotron JMizuuchi 51

IT-10 New approach of statistical analysis and modelling ofturbulent processes in plasma

Skvortsova 52

IT-11 Statistical description of transport van Milligen 53IT-12 Effect of magnetic configuration on density fluctuation

and particle transport in LHDTanaka 54

IT-13 Materials for the Plasma-Facing Components of SteadyState Stellarators

Bolt 55

OralsOr-05 Potential Ternary Compounds for First Wall Fusion

ApplicationsO'Connor 56

Or-06 Recent results of LID experiments on LHD Morisaki 57Or-07 Recycling and impurity retention in high-density,

improved-confinement plasmas in W7-ASSardei 58

Or-08 Critical design issues of Wendelstein 7-X Gasparotto 59

Poster Session P2P2-01 Validation of Wendelstein 7-X assembly stages by

magnetic field calculationsAndreeva 60

P2-02 Implications of the Quasi-Neutrality Condition forNeoclassical Transport in Stellarators

Beidler 61

P2-03 Experimental Design: Case studies of DiagnosticsOptimization for W7-X

Dreier 62

P2-04 H-mode edge rotation in W7-AS Hirsch 63P2-05 Transition to improved confinement mode of operation

triggered by strong gas fuellingIgitkhanov 64

P2-06 Magnetic field accuracy and Correction Coils inWendelstein 7-X

Kisslinger 65

P2-07 Optimization of ECE diagnostic for W7-X stellarator Marushchenko 66P2-08 The microwave heating systems at the WEGA stellarator -

status and prospectsSchubert 67

P2-09 Statistical Analysis of the equilibrium configurations ofthe W7-X stellarator using Function Parameterization

McCarthY, P 68

P2-10 Feasibility study for Heavy Ion Beam Probing (HIBP)project on stellarator W7-X

Krupnik 69

P2-11 Development of Heavy Ion Beam Probing (HIBP)diagnostic for stellarator WEGA

Krupnik 70

P2-12 Impurity transport in drift optimized stellarator ergodicand non-ergodic plasma configurations

Shyshkin 71

P2-13 Kinetic modelling of the nonlinear ECRH in stellarators Kasilov 72

VI

P2-14 Additional criteria for optimization of trapped particleconfinement in stellarators

Nemov 73

P2-15 Computation of neoclassical transport in stellarators withfinite collisionality

Kernbichler 74

P2-16 Study of neoclassical transport in the 1/n regime for aresearch fusion reactor

Kalyuzhnyj 75

P2-17 Observation of Ion Bernstein Waves during Alfven WavePlasma Heating in Uragan-3M Torsatron

Pavlichenko 76

P2-18 Transport barriers in helical systems Volkov 77P2-19 Magnetic Islands and Plasma Transport in Helical Devices Shishkin 78P2-20 Surface flute modes in the bumpy magnetic field Girka 79P2-21 Optimization of energy confinement in Uragan-2M Seiwald 80P2-22 Optimization Studies of TJ-II Stellarator Seiwald 81P2-23 Fast ion dynamics of NBI plasmas in Heliotron J Kaneko 82P2-24 Dependence of Toroidal Current on Magnetic Field

Configuration in Heliotron JMotojima 83

P2-25 Effect of the Bumpy Field Component on the BootstrapCurrent

Nakamura 84

P2-26 Formation and Confinement of High Energy Ions inHeliotron J

Okada 85

P2-27 Studies of MHD Stability in Heliotron J Plasmas Yamamoto 86P2-28 On the in-out asymmetry of divertor plasma flows in

heliotron/torsatron devicesVoitsenya 87

P2-29 35 years since the start up and the first plasma of thestellarator-torsatron "Saturn". Main results for one decadeof operation

Voitsenya 88

VII

Contents of Wednesday, October 5

Review TalkRT-02 Critical issues and comparison of different optimized

stellaratorsNührenberg 91

Invited TalksIT-14 Properties of ballooning modes in the heliotron

configurationsNakajima 92

IT-15 Equations and applications of perturbed plasma equilibria Boozer 93IT-16 Sheared plasma flow generation- a new measure for

stellarator optimizationSpong 94

OralsOr-09 Heavy Ion Beam Probe investigations of plasma potential

in ECRH and NBI in the TJ-II stellaratorA. Melnikov 95

Or-10 Current control by ECCD for W7-X Y. Turkin 96Or-11 Quasi-isodynamic Configuration with large number of

periodsM. Mikhailov 97

Or-12 Development of integrated simulation system for helicalplasmas

Y. Nakamura 98

Poster Session P3P3-01 High-speed turbulence imaging and wavelet-based

analysis during edge shear flow development in TJ-IIAlonso 99

P3-02 Ion Temperature Profiles on TJ-II Stellarator During NBIPlasma Heating

Balbín 100

P3-03 Microwave Reflectrometry in TJ-II Blanco 101P3-04 Exp. evidence of coupling between density tails and

turbulent transport in the scrape-off layer region of TJ-IIplasmas

Calderon 102

P3-05 Ion temperature and flow measurements using a combinedforce-Mach-Langmuir probe

Calderon 103

P3-06 Experimental dependence of ECRH plasma breakdown onwave polarization in the TJ-II stellarator

Cappa 104

P3-07 A study of central impurity ion temperatures during ECRand NBI heating phases in TJ-II

Carmona 105

P3-08 Ion orbits and ion confinement studies on ECRH plasmasin TJ-II stellarator

Castejon 106

P3-09 The quest for the divertor effect in the TJ-II stellarator Garcia-Cortés 107P3-10 Impact of gas puffing location on density control and

plasma parameters in TJ-IITabares 108

P3-11 Influence of the stray light on the recorded Thomsonelectronic distribution function

Herranz 109

P3-12 Electromagnetic Instabilities in Strongly MHD Stable TJ-II Heliac

Jimenez 110

P3-13 Analysis of MHD instabilities in TJ-II plasmas Jimenez-Gómez

111

P3-14 Recent results with NBI plasmas in the TJ-II stellarator Liniers 112

VIII

P3-15 Up-down and in-out asymmetries monitoring based onbroadband radiation detectors

Ochando 113

P3-16 On the influence of EXB sheared flows in the statisticproperties of turbulence in the plasma boundary of TJ-IIplasmas

Orozco 114

P3-17 Experimental investigation of edge sheared flowdevelopment and configuration effects in TJ-II plasmas

Pedrosa 115

P3-18 Transport and fluctuations during electrode biasing on TJ-II

Silva 116

P3-19 A simulation code to estimate / deduce local toroidalrotation profiles in TJ-II from chord-integratedmeasurements

Rapisarda 117

P3-20 Local transport in density and rational transform scans inTJ-II ECRH discharges

Vargas 118

P3-21 TJ-II operation tracking from Cadarache Vega 119P3-22 Comparison of Impurity Poloidal Rotation in ECRH and

NBI Discharges of the TJ-II HeliacZurro 120

P3-23 Characterisation of the quasi-coherent oscillations byHIBP diagnostic in the TJ-II stellarator

Krupnik 121

P3-24 Design and Testing of an Electron Bernstein WaveEmission Radiometer for the TJ-II Stellarator

Caughman 122

P3-25 Influence of plasma biasing on turbulence in the torsatronTJ-K

Ramisch 123

P3-26 High Density Plasma Productions by Hydrogen StorageElectrode in the Tohoku heliac

Utoh 124

P3-27 Plasma Energy Balance at ECRH in the L-2M Stellarator Fedyanin 125P3-28 Unexpected Transport Phenomena in low-b Plasmas of L-

2M StellaratorShchepetov 126

P3-29 Modification of the Electron Temp. Profile Depending onthe Heating Power and Plasma Parameters

Voronov 127

P3-30 Results of Measurements of the Ion Temperature Profileof ECR Heated Plasmas in the L-2M Stellarator

Voronov 128

P3-31 Recent Results of Studies of Plasma Fluctuations inStellarators by Microwave Scattering Technique

Skvortsova 129

Panel Discussion TalkPD-01 Keeping the options open for a reactor: issues in the

stellarator roadmapSánchez 130

IX

Contents of Thursday, October 6

Review TalkRT-03 Internal transport barrier physics in helical systems M. Yokoyama 133

Invited TalksIT-17 Effect of ripple-induced transport on H-mode

performance in tokamaksV. Parail 134

IT-18 Study of magnetic Fourier components effect on ionviscosity in the Tohoku University Heliac

S. Kitajima 135

IT-19 Overview and Future Plan of Helical Divertor Study inLHD

S. Masuzaki 136

IT-20 The steady state ECRH-system at Wendelstein 7-X H. Laqua 137IT-21 Long pulse plasma discharge experiment by ICRF heating

in LHDT. Seki 138

X

Contents of Friday, October 7

Review TalkRT-04 Significance of MHD effects in stellarator confinement A. Weller 141

Invited TalksIT-22 Suppression of large edge localized modes with edge

resonant magnetic fields in high confinement DIII-Dplasmas

P. Thomas 142

IT-23 Assessment of Global Stellarator Confinement: Status ofthe International Stellarator Confinement Scaling Database

A. Dinklage 143

IT-24 Self-sustained detachment observed in LHD J. Miyazawa 144IT-25 New classes of quasi-axisymmetric configurations L.P. Ku 145IT-26 Nonlinear Evolution of MHD instability in LHD H.Miura 146IT-27 On the role of turbulence on momentum redistribution in

fusion devicesC. Hidalgo 147

Oct.3 Oct.4 Oct.5 Oct.6 Oct.7Monday Tuesday Wednesday Thursday Friday

8:30-8:45 8:30 Komori (RT-01) 8:30 Nührenberg (RT-02) 8:30 Yokoyama (RT-03) 8.30 Weller (RT-04)8:45-9:00 8:45 Opening9:00-9:159:15-9:30 9:15 Estrada (IT-01) 9:15 Reiersen (IT-08) 9:15 Nakajima (IT-14) 9:15 Parail (IT-17) 9:15 Thomas (IT-22)9:30-9:45

9:45-10:00 9:45 Hartmann (IT-02) 9:45 Mizuuchi (IT-09) 9:45 Boozer (IT-15) 9:45 Kitajima (IT-18) 9:45 Dinklage (IT-23)10:00-10:1510:15-10:30 10:15 Lyon (IT-03) 10:15 coffee 10:15 coffee 10:15 coffee 10:15 Miyazawa (IT-24)10:30-10:4510:45-11:00 10:45 coffee 10:45 Skvortsova (IT-10) 10:45 Sánchez 10:45 Masuzaki (IT-19) 10:45 coffee11:00-11:15 11:10 Panel11:15-11:30 11:15 Okamura (IT-04) 11:15 van Milligen (IT-11) Discussion: 11:15 Laqua (IT-20)11:30-11:45 Stellarator11:45-12:00 11:45 Canik (IT-05) 11:45 Tanaka (IT-12) Research 11:46 Seki (IT-21) 11:45 Miura (IT-26)12:00-12:15 in the New Era12:15-12:30 12:15 Blackwell (IT-06) 12:15 lunch 12:15 lunch 12.15 Hidalgo (IT-27)12:30-12:45 12:30 lunch12:45-13:00 12:45 lunch 12.45 Close13:00-13:15 13.00 lunch13:15-13:3013:30-13:4513:45-14:0014:00-14:1514:15-14:30 Poster Session P1 Poster Session P2 Poster Session P314:30-14:4514:45-15:00 Excursion15:00-15:1515:15-15:3015:30-15:45 15.30 coffee 15.30 coffee 15.30 coffee15:45-16:0016:00-16:15 16:00 Sakakibara (IT-07) 16.00 Bolt (IT-13) 16:00 Spong (IT-16)16:15-16:3016:30-16:50 16:30 Pedersen (Or-01) 16:30 O'Connor (Or-05) 16:30 Melnikov (Or-09)16:50-17:10 16:50 Shchepetov (Or-02) 16:50 Morisaki (Or-06) 16:50 Turkin (Or-10)17:10-17:30 17:10 Takahashi (Or-03) 17:10 Sardei (Or-07) 17:10 Mikhailov (Or-11)17:30-17:50 17:30 Kolesnichenko (Or-04) 17:30 Gasparotto (Or-08) 17:30 Nakamura (Or-12)

18:00-19:30 Reception

20:00-23:00 Conf.Dinner

11:15 Ku (IT-25)

1

2

MONDAY

3rd October

3

4

Electron Internal Transport Barriers and Magnetic Topology in theStellarator TJ-II

T. Estrada, L. Krupnik*, A. Alonso, F. Castejón, A.A. Chmyga*, N. Dreval*, L.Eliseev**, C. Hidalgo, S.M. Khrebtov*, A.D. Komarov*, A.S. Kozachok*, A.V.

Melnikov**, J.L. de Pablos, V. Tereshin*

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain*Institute of Plasma Physics, NSC KIPT, 310108 Kharkov, Ukraine

**Institute of Nuclear Fusion, RNC Kurchatov Institute, Moscow, Russia

Electron Internal Transport Barriers (e-ITBs) are frequently observed in helical systems.e-ITBs are characterized by an increase in core electron temperature and plasmapotential as well as an improvement in core electron heat confinement. A comparativestudy of transport barriers in different helical devices will be presented by Yokoyama etal at this conference [1].In most helical systems, and in particular in TJ-II stellarator, the formation of e-ITBs isobserved in Electron Cyclotron Heated plasmas with high heating power density [2]. InTJ-II, e-ITBs are also formed in magnetic configurations having a low order rationalsurface close to the plasma core where the ECH power is deposited [3]. In suchconfigurations the key element to improve heat confinement, i.e. the strong radialelectric field, results from a synergistic effect between enhanced electron heat fluxesthrough the low order rational surface and pump-out mechanisms in the heat depositionzone [4,5].Recent experiments show a quasi-coherent mode associated with a rational surface thattriggers the formation of the e-ITB [6]. This quasi-coherent mode is observed by bothECE and HIBP diagnostics. The mode is found to be localized within the radial range ρ:0.0 - 0.4, with a maximum amplitude around ρ: 0.25 - 0.35, close to the foot of the e-ITB. The quasi-coherent mode evolves during the formation/annihilation of the e-ITBand vanishes as the barrier is fully developed. These observations indicate that thequasi-coherent modes are modified by the radial electric fields that develop at thetransitions, thereby showing the importance of ExB flows in the evolution of MHDinstabilities linked to low-order rational surfaces.Further studies are in progress to investigate the influence of the order of the lowrational surfaces (3/2, 5/3,…) in triggering core transitions.

[1] M. Yokoyama, H. Maassberg, T. Estrada et al. This conference[2] F. Castejón, V. Tribaldos, I. García-Cortes, et al. Nuclear Fusion 42 (2002) 271[3] T. Estrada, L. Krupnik, N. Dreval et al. Plasma Phys. Control. Fusion 46 (2004) 277[4] F. Castejón, D. López-Bruna, T. Estrada et al. Nuclear Fusion 44 (2004) 593.[5] M.A. Ochando and F. Medina Plasma Phys. Control. Fusion 45 (2003) 221.[6] T. Estrada et al, Submitted to Plasma Phys. Control. Fusion

IT-01

5

Status of Construction and Assembly of Wendelstein 7-X

D. A. Hartmann for the Wendelstein 7-X Team

Max-Planck Institut für Plasmaphysik, EURATOM-Assoc., Wendelsteinstraße 1, 17491Greifswald, Germany

Wendelstein 7-X (W7-X) is a low-shear stellarator with an optimized quasi-isodynamicconfiguration and five-fold symmetry that is presently under construction in Greifswald,Germany. The goal of the device is to investigate the fusion reactor capability of stellarators.Therefore the magnetic field will be generated using superconducting coils and all relevantcomponents (10 MW ECR heating system, divertor and wall protection elements) are designedfor 30 min. operation, which is equivalent to steady-state. The basic parameters of the device are:magnetic field up to 3 T on axis, major radius 5.5 m, average minor radius 0.55m.

The device consists of 50 non-planar and 20 planar coils, the coil support structure, 10plasma vessel half modules, 10 outer vessel half shells and 299 ports. Presently of the non-planar coils 38 winding packs have been produced, of which 25 have been embedded. Two ofthe coils have been successfully tested for their cryogenic and superconducting properties at thetest site at CEA Saclay and were delivered. Of the planar coils all 20 winding packs have beenproduced, 5 have been embedded. 6 of the plasma vessel half modules and about 180 of theports have been delivered. The first module of the coil support structure is being machined andwill be delivered in fall 2005.

The assembly of the device started last fall: diagnostic Mirnov coils were attached to theoutside of the plasma vessel, sections of the super-insulation were added, the first coil wasthreaded onto a section of a plasma vessel half module and a second section was welded onto thefirst catching the threaded coil in between. Presently the further progress of assembly is sloweddown by the required reworking of several coils. The inside of the plasma vessel will be fullylined by water cooled structures: divertor modules consisting of CFC elements brazed ontoCuCrZr substructures for areas with convective losses up to 10 MW/m2 and double-walledstainless steel panels for areas with radiative losses up to 100 kW/m2. Presently the targetelements, the panels and the support structures are being manufactured.

The ECR heating system will consist of 10 gyrotrons with an output power of 1 MWcw each, appropriate optical transmission lines and launching systems. The first two gyrotronshave been delivered and are being commissioned. One of them has already produced more than800 kW high frequency power for more than 30 minutes.

The assembly of the basic machine is expected to be completed in 2011, the finalinstallation of the periphery, diagnostics and heating systems are planned for the same year sothat commissioning can start and the first plasma is produced by the middle of 2012.

IT-02

6

Optimization of the ARIES-CS Compact Stellarator Reactor Parameters

J. F. Lyon1, L.P. Ku2, L. El-Guebaly3, L. Bromberg4 and the ARIES Team

1 Oak Ridge National Laboratory, PO Box 2008, MS-6169, Oak Ridge, TN 37831-61692 Princeton Plasma Physics Laboratory, PO Box 451, Princeton, NJ, 08543-0451

3University of Wisconsin, 1500 Engineering Drive, Madison, WI, 53706-16874Massachusetts Inst. of Technology, 167 Albany St., Cambridge, MA, 02139

Stellarators have the potential for an attractive, fully ignited reactor. They are inherentlysteady-state without a large plasma current, which reduces both the power needed to sustain theplasma and the risk of plasma disruptions. However, earlier studies led to large stellaratorreactor sizes; the most advanced concept had an average major radius R = 22 m. The ARIESStellarator Power Plant Study reactor with R = 14 m was a first step toward a smaller sizereactor. The recent development of the compact stellarator concept that takes advantage of quasi-symmetry to improve plasma confinement now allows reactors with major radius closer to thatof tokamak reactors.

Stellarator power plant studies are carried out in the U.S. as part of the advanced design(ARIES) program. The ARIES Team uses integrated physics, engineering, and systems studiesto assess the potential of different confinement concepts as attractive reactor candidates. Theseassessment capabilities have been applied in a number of tokamak reactor studies. The ARIESTeam is currently conducting a three-year study of the potential of compact stellarators asreactors. Their smaller plasma aspect ratio should lead to significant cost reductions throughreducing the mass of the most expensive parts of the fusion reactor core (the first wall, blanket,shielding, vacuum vessel, coils, structure and other components that scale approximately with theplasma surface area). Both two- and three-field-period concepts are being studied using updatedphysics and engineering assumptions to explore different blanket and shield concepts and bothport-through and field-period-disassembly maintenance approaches.

The most important factor determining stellarator reactor size is the distance neededbetween the edge of the plasma and the nonplanar magnetic field coils for the plasma scrapeoffregion, the first wall, the blanket and shield, manifolds, the coil case, and assembly gaps. Otherconsiderations in determining the optimum reactor size are the minimum distance between coils,neutron and radiative power flux to the wall, and the beta limit.

A reactor systems/optimization code is used to optimize the reactor parameters forminimum cost of electricity subject to a large number of physics, engineering, materials, andreactor component constraints. Different transport models, reactor component models, andcosting algorithms are used to test sensitivities to different models and assumptions. A 1-Dpower balance code is used to study the path to ignition and the effect of different plasma andconfinement assumptions including density and temperature profiles, impurity density levels andpeaking near the outside, confinement scaling, beta limits, alpha particle losses, etc. for eachplasma and coil configuration.

Variations on two different magnetic configurations were analyzed in detail: a three-field-period (M = 3) NCSX-based plasma with coils modified to allow a larger plasma-coilspacing, and an M = 2 plasma with coils that are closer to the plasma on the outboard side withless toroidal excursion. The reactors have major radii R in the 7-9 m range with an improvedblanket and shield concept and an advanced superconducting coil approach. The results showthat compact stellarator reactors should be cost competitive with tokamak reactors.

* Supported by USDOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

IT-03

7

Improved confinement and related physics studyin Compact Helical System

S. Okamura, T. Akiyama, A. Fujisawa, K. Ida, H. Iguchi, M. Isobe, S. Kado 3),T. Minami, K. Nagaoka, K. Nakamura, S. Nishimura, K. Matsuoka,

H. Matsushita, H. Nakano, S. Ohshima, T. Oishi 2), A. Shimizu, C. Suzuki,C. Takahashi, K. Toi, Y. Yoshimura, M. Yoshinuma and CHS group

National Institute for Fusion Science, Oroshi 322-6, Toki 509-5292, Japan

2) Department of Quantum Engineering and System Science, Graduate School of Engineering,

The University of Tokyo, Hongo 7-3-1, Tokyo 113-8656, Japan

3) High Temperature Plasma Center, The University of Tokyo, Yayoi 2-11-16,

Tokyo 113-8656, Japan

Recent experimental results in Compact Helical System (CHS) will be presentedfocusing on the improved confinement and physics study of electric field and turbulencein helical plasmas. Among various improved confinement modes found in CHS experi-ments, the edge transport barrier (ETB) formation is an important topic, which we havebeen studying intensively for these years. The discharges of CHS with ETB have char-acteristics very similar to H-mode discharges in tokamaks and W7-AS stellarator. Weobserve a sharp drop of Hα emission signal, increase of plasma density together with anincrease of local density gradient at the plasma edge, so we call our ETB discharges asH-mode. The power threshold for the transition is clearly observed which is againsimilar to standard H-mode discharges, i.e., the threshold increases with the density andmagnetic field. Unique feature of CHS H-mode is the dependence on the magnetic fieldconfiguration. We examined H-mode discharges for the configurations with magneticaxis shift and the magnetic quadupole control. The transition appeared for a wide rangeof configurations with the rotational transform at the plasma edge (iota(a)) below andabove unity. There is a general dependence of power threshold: higher power needed forthe inward shifted configuration (with lower value of iota(a)) and lower power for out-ward shift. The absolute power threshold of CHS H-mode for the outward shifted con-figuration is very close to the tokamak H-mode with a divertor configuration.

Other topics of confinement studies in CHS will be also presented. We have aunique diagnostic system of two heavy ion beam probes. It is unique in stellarator re-search and also for all toroidal confinement research including many tokamaks in theworld. As well as fruitful result of electric field measurements, that is one of key ele-ments for stellarator physics, this diagnostic measures turbulence in the plasma, whichgives essential information for the study of anomalous transport. The zonal flow mea-surement was one example of experimental observations from this diagnostics.

IT-04

8

Effects of Quasi-symmetry on Particle and Thermal Transport in HSX

J.M. Canik, D.T. Anderson, J.N. Talmadge, K. Zhai

HSX Plasma Lab, U. of Wisconsin-Madison

The density profile in the Quasi-Helically Symmetric (QHS) configuration is centrallypeaked for both on- and off-axis heating. In a magnetic configuration with the symmetrybroken (Mirror), the density profile is flat or slightly hollow with on-axis heating, where thetemperature profile is centrally peaked. When the ECH resonance is moved off-axis, thetemperature profile becomes flat inside the heating radius, and the density profile becomespeaked. This suggests that a thermodiffusive particle flux is the cause of the hollow profile inthe centrally heated case. In order to study the particle transport in more detail, experimentaldata from a set of absolutely calibrated H_ detectors has been coupled to simulations using theDEGAS1 neutral gas code. These calculations yield the particle source rate, which can beintegrated using the continuity equation to give the steady state radial particle flux. It is foundthat in QHS plasmas, the experimental particle flux is much larger than the neoclassical fluxacross the entire minor radius. In Mirror plasmas, however, the neoclassical flux iscomparable to experiment in the core (r/a < 0.4). In this region, the thermodiffusive flux isthe dominant term in the total neoclassical particle flux, suggesting that neoclassicalthermodiffusion is the cause of the hollow density profile. The peaked density profilesobserved in QHS plasmas indicate that, at present parameters, thermodiffusion is not asignificant part of the total particle balance.

The density and temperature profiles have been measured in fine time incrementsthrough the turn-off of the ECH power. By analyzing the evolution of the density andtemperature profiles, the absorbed power profile has been determined. This yields theelectron heat flux, which combined with the steady state plasma profiles gives the electronthermal diffusivity. It is found that, in a configuration without quasi-symmetry, the thermaldiffusivity is anomalous at the plasma edge, and close to neoclassical in the core. In the QHSconfiguration, the thermal diffusivity is also anomalous towards the edge, and nearly an orderof magnitude lower in the core, reflecting the reduction of neoclassical transport. At 50 kWof injected power, this reduced transport results in a core electron temperature that is ~200 eVlarger in QHS than in the non-symmetric configuration. This work is supported by DOEGrant DE-FG02-93ER54222.

1. Heifetz, D.B. et al, J. Comp. Phys. 46, (1982) 309

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Recent Results from the H-1 Heliac

Boyd Blackwell, J.H. Harris, J. Howard, S.M. Collis, D.G. Pretty, T.A. SanthoshKumar, F.J. Glass, D. Oliver, B. Powell, C.A. Michael, M.G. Shats, H. Punzmann,

G.G. Borg.Plasma Research Laboratory, Research School of Physical Sciences and Engineering

Australian National University, ACT 0200, AUSTRALIA.

The H-1 heliac is a current-free 3 period helical axis stellarator. The helicalcontrol winding (“flexible heliac[1]”) provides a wide range of transforms (0.9 < ι0 < 1.5for B0 <1T, �r� > 0.15-0.2 m) or a larger range (0.7 < ι0 < 2.2) at reduced performanceB0 ~ 0.5 T, �r� > 0.1 m. By varying currents in the two vertical field coil sets, flexibilityis enhanced to allow almost independent control of two of the three parameters: ι,magnetic well (–2% to +6%) and shear (∆ι/ιo = -0.05 to 0.15) , which can be positive(stellarator-type) negative (tokamak-like), or near zero. The coils are powered by twoprecision regulated computer controlled DC supplies keeping ripple is kept well below1A for precise control of configuration, and to avoid induction of plasma currents. At 0.5 tesla, RF (20 ~150kW, ω ~ ωcH) produces plasma in H:He and H:Dmixtures at densities up to <ne> ~ 2↔1018m-3, with temperatures initially limited to< 50eV by low-Z impurities. ECH (ω = 2ω ce) produces considerably highertemperatures and centrally-peaked density profiles. The operation of H-1 and powersystems has recently been automated using 4 programmable logic controllers and aflexible sequencing state machine. This allows rapid and highly detailed computercontrolled scans of parameters, in particular magnetic configuration. Several databasescontaining summary, log book and fluctuation characteristics enable datamining.Preprocessing and classification techniques including SVD and time-frequency analysiswill be discussed.

Analysis of configuration scans show a detailed dependence of plasma densityon rotational transform, which is more pronounced for RF production. Magneticfluctuations are also stronger in these plasmas, and their spectra depend on magneticconfiguration[2]. There are broad regions of low or zero density when central ι is near ι0~ 5/4 and 4/3, and other narrower, less clearly identifiable features. Alternatively, thepresence of a lower order rational at the edge (e.g. ιa = 7/5), or shear may be importantfactors. Both poloidally localised and globally coherent fluctuations have beenobserved, which may suggest the presence of distinct ballooning and interchangeinstabilities. Large amplitude m=3 modes have been associated with low order rationalιa values. Evidence suggesting the existence of Alfvén eigenmodes will be discussed.

Two novel magnetic surface mapping techniques have been demonstrated–rotating wire electron beam tomography, and visible ion emission tomography[3].Investigations of magnetic island mapping comparing both techniques will be presented.

Pulsed supersonic beams of neutral helium have been used to spectroscopicallyprobe the plasma with good localisation. Results will be presented for helium ion andneutral lines in ECH and RF discharges.

1 Harris, J.H., Cantrell, J.L. Hender, T.C., Carreras, B.A. and Morris, R.N. Nucl. Fusion 25, 623 (1985).2 Harris J.H., Shats M.G., Blackwell B.D., Solomon W.M., Pretty D.G, et al Nucl. Fusion 44 (2004) 279-286.3 Glass F, Howard J, Blackwell B. IEEE Transactions on Plasma Science (33) 2, pp.472-3 (2005)

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Recent Progress of MHD Study in High-Beta Plasmas of LHD

S.Sakakibara, K.Y.Watanabe, H.Yamada, Y.Narushima, H.Funaba, K.Toi, S.Ohdachi,

T.Yamaguchi1, S.Inagaki, K.Narihara, K.Tanaka, T.Tokuzawa, K.Ida, K.Kawahata, A.Komori

and LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292, Japan 1 Dep. of Fusion Science, Graduate Univ. for Advanced Studies, Toki 509-5292, Japan

Characterization of pressure-driven modes and the control of them in the high-β regime are one of crucial issues towards for a helical fusion reactor. Since the heliotron configuration has a magnetic hill in the peripheral region and weak magnetic shear in the plasma core, violation of stability of ideal and resistive interchange modes are concerned. To investigate configuration dependence of MHD activities and to optimize the magnetic configuration for production of high-beta plasmas, the control of rotational transform profile by external coils has been done in Large Helical Device (LHD). The central rotational transform ι0/2π can be changed from 0.4 to 0.73 at the same magnetic axis position. While the increase in ι0/2π has a disadvantage on MHD stability because it leads to restraint of Shafranov shift restricting spontaneous magnetic well formation in addition to the reduction of magnetic shear, a degradation of particle confinement due to an increment of helical ripples with the plasma outward-shift expects to be avoided. As results, average beta <βdia> of 4.3 % was achieved in the configuration with Rax = 3.6 m, Bt = 0.45 T and ι0/2π = 0.52. While several MHD modes excited in peripheral region are dominantly observed and enhanced with increasing <βdia>, they saturate and/or intermittently observed when <βdia> exceeds about 3 %. Also, the dependence of magnetic Reynolds number, S, on MHD modes have been found out, and about 10 % of degradation of plasma stored energy due to peripheral MHD modes has been observed in density ramp-up operation with temporal reduction of S. The linear theory suggests that the growth rate of resistive interchange mode is increased by an increment of S, and it is qualitatively consistent with characteristics of observed MHD activities. On the other hand, the achieved beta gradually decreases with the increase in ι0/2π by external coil control and/or positive plasma current. The minor collapse of plasma due to m/n = 1/1 mode was observed in the highest ι0/2π configuration (0.73). Also, even if the vacuum ι0/2π is relatively small, the large plasma current increasing ι0/2π causes the similar collapse. The growth of m/n = 1/1 island, which was identified as profile flattening of Te near the resonant surface at ρ ~ 0.5, was observed just before the minor collapse in both cases, and it decreases <βdia> by more than 50 %. Then the peripheral plasma pressure with strong magnetic shear was still maintained before and after the collapse. These phenomena may be caused by the reduction of magnetic shear at the m/n = 1/1 resonance in magnetic hill configuration.

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First results from the Columbia Non-neutral Torus

T. Sunn Pedersen, A. H. Boozer, J. P. Kremer, R. G. Lefrancois, Q. Marksteiner, X. Sarasola*

Dept. of Applied Physics and Applied Math, Columbia University, New York, NY 10025, USA

* Currently at CIEMAT, Madrid, Spain

Harry Mynick, Neil Pomphrey

Princeton Plasma Physics Laboratory, Princeton, NJ, USA

The Columbia Non-neutral Torus started operation in November 2004. CNT is anultralow aspect ratio stellarator designed to study the physics of non-neutral plasmas confinedon magnetic surfaces. It is created from a unique and simple coil set consisting of two pairs ofplanar circular coils. Hence, its coil set is simpler than that of any other stellarator, or anytokamak. The first results from CNT include detailed magnetic surface mappings, and initialpure electron plasma experiments.

The magnetic surface mapping experiments confirm the existence of large high qualitymagnetic surfaces with last closed flux surface aspect ratios as low as <1.9. These experimentswere performed at magnetic field strengths up to 0.1 Tesla, and are in very good agreement withthe numerical calculations (Figure 1). This makes CNT by far the lowest aspect ratio stellaratorever built. A significant, but smaller, volume of good magnetic surfaces is found even at very lowmagnetic fields, B=3 milliTesla. Detailed field line mapping results will be presented.

Figure 1. Experimentally obtained drift surfaces for a beam energy of 100 eV and amagnetic field of 0.1 Tesla (left) and numerically calculated magnetic surfaces (right).

A stationary electron emitter has been inserted into the confinement region to create pureelectron plasmas. Measurements show that up to 1011 electrons fill the volume of the magneticsurfaces, and that the electron confinement time can be more than 10 milliseconds, despite themodest magnetic field strength (B<0.1 T), the lack of quasi-symmetry, and the presence of amacroscopic material object in the plasma (the emitter rod). Since the estimated drift escape timeis less than 1 msec, the much longer confinement time is experimental evidence that anequilibrium exists for a pure electron plasma in a stellarator, as predicted from theory1. Theconfinement time is observed to decrease with increasing neutral pressure, and decreasingmagnetic field strength. We will report on these first experiments, and discuss the results ofupcoming experiments that will provide more detailed information.

1. T. Sunn Pedersen and A. H. Boozer, PRL 88, 205002, 2002.

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Or-02

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Hot Cathode Biasing Experiment in Compact Helical System

H. Takahashia, H. Utoha, S. Kitajimaa, M. Isobeb, C. Suzukib, M. Takeuchic, R. Ikedac, Y. Tanakaa, M. Yokoyamab, K. Toib, S. Okamurab and M. Sasaoa

aDepartment of Quantum Science and Energy Engineering, Tohoku University, Sendai, Japan bNational Institute for Fusion Science, Toki, Japan

cDepartment of Energy Engineering and Science, Nagoya University, Nagoya, Japan

Electrode biasing experiments were carried out in Compact Helical System (CHS).

CHS is the m = 8/l = 2 helical device with major radius ~ 1 m, minor radius ~ 0.2 m and maximum magnetic field strength is 2 T. The hot cathode of LaB6 (diameter is 10 mm, length is 17 mm) was inserted from low magnetic field side. The tip of the hot cathode was located at plasma edge (ρ ~ 0.8) and the hot cathode was biased negatively against the vacuum vessel of CHS by using current control power supply. The formation of negative radial electric field is expected from the attainment of a new equilibrium state between ions and electrons by the electron injection from the hot cathode.

In a preliminary experiment at low magnetic field, where the target plasma was produced by 2.45 GHz electron cyclotron heating (input power ~ 30 kW) for a He gas, we observed following results; (i) the improvement of electron density by the factor of 3, (ii) the increase of electron stored energy, (iii) the formation of steep gradient in electron density and electron pressure profiles, (iv) the transition of plasma space potential from positive to negative, (v) the formation of negative radial electric field (~ -250 V/m). These results implied that the plasma confinement was improved.

The experiment will be extended to a low collisional and/or high temperature plasma at high toroidal field in order to clarify the role of the ion viscosity for the transition to the enhanced confinement mode. In this paper, we show the dependence of (i) plasma parameters on input power from the electrode, (ii) the structure of the radial electric field on the position of the electrode, (iii) the critical electrode current required for the transition on the magnetic axis positions, and investigate the consistency between the experimental results and the calculations predicted from the transition mechanism based on the neoclassical theory. 1-3 1. V. Rozhansky and M. Tendler: Phys. Fluids B 4, 1877 (1992). 2. K. C. Shaing: Phys Rev. Lett. 76, 4364 (1996). 3. M. Yokoyama, et al.: NIFS-519 (1997).

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Novel physics involved in interpretation of Alfvénic activity accompanied by thermal crashes in W7-AS

Ya.I. Kolesnichenko1, V.V. Lutsenko1, A. Weller2, A. Werner2, H. Wobig2,

Yu.V. Yakovenko1, J. Geiger2, A.V. Tykhyy1, and S. Zegenhagen2

1Institute for Nuclear Research, 03680 Kyiv, Ukraine 2Max-Planck-Institut für Plasmaphysik, D-17489 Greifswald, Germany

Alfvén instabilities driven by fast ions have been observed in many experiments on

tokamaks and stellarators. In tokamaks, they can strongly affect the fast ion confinement but not the bulk plasma. In contrast to this, experiments on the Wendelstein 7-AS (W7-AS) stellarator have shown that Alfvénic activity can strongly deteriorate the global energy confinement time: strong thermal crashes (the temperature dropped by up to 30%) were reported in Ref. [1] and observed also in the last series of experiments in 2002. To explain this phenomenon, recently a new mechanism of anomalous electron heat conductivity associated with Kinetic Alfvén Waves (KAW) was suggested [2].

In this work, we further develop theory required for the interpretation of experimental observations of Alfvénic activity in W7-AS and analyse a particular shot (No. 34723) where strong drops of the plasma energy content took place in details.

As a result, (i) we identified the instability observed in the mentioned W7-AS shot as Non-conventional Global Alfvén Eigenmode (NGAE), (ii) suggested an explanation of the frequency chirping (from ~70 kHz to ~45 kHz) during the instability bursts, (iii) showed why the instability was most strong at the end of the bursts when thermal crashes occurred, (iv) considered two possible mechanisms of thermal crashes (anomalous heat conductivity [2] and instability-induced-loss of the injected ions), (v) made a modelling of oscillations of the plasma energy content.

An important role of the finite orbit width of fast ions was revealed: it was found that finite orbits actually trigger the instability at 70≤ω kHz and weaken the mode destabilization at the end of the instability bursts (when 40≥ω kHz). It was concluded that the observed frequency chirping can be explained by the expulsion of fast ions from the plasma core and a concomitant local change of the rotational transform. In order to identify the instability, the Alfvén continuum and Alfvén eigenmodes were calculated by the codes COBRA and BOA, respectively. The orbits of the injected ions were studied by the code ORBIS; it was found that particles with non-standard orbits, “semi-trapped” particles, constituted a considerable fraction of fast ions in the region where NGAE was localized and contributed noticeably to the instability growth rate. It was shown that core-localized NGAE was transformed into KAW, which considerably extended the region affected by the instability and generated the perturbed longitudinal electric field leading to anomalous electron thermal transport.

A new code, GAMMA-O, calculating the instability growth rate with taking into account finite orbits of fast ions in stellarators was developed. The radial structure of Alfvén gap modes in low-shear systems was determined.

1. A. Weller et al., Phys. Plasmas 8 (2001) 931. 2. Ya.I. Kolesnichenko et al., Phys. Rev. Lett. 94 (2005) 165004.

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Transport Analysis of High Beta Plasmas on LHD

H.Funaba, K.Y.Watanabe, S.Sakakibara, S.Murakami1, I.Yamada, K.Tanaka,

T.Tokuzawa, M.Osakabe, Y.Narushima, N.Nakajima, M.Yokoyama,

H.Yamada, O.Kaneko, K.Kawahata and the LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292, Japan1Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan

High beta plasmas with over4% of the volume averaged beta,⟨β⟩, are obtained in the LHD

experiments1 . Then it becomes possible to investigate transport characteristics of plasmas in

the relevant beta region to reactors which have almost5% of ⟨β⟩. According to the results of

recent analysis with respect to the global confinement property based on the empirical scaling

ISS952 , no disruptive degradation was found up to⟨β⟩ ∼ 4%, while gradual degradation of

confinement efficiency was observed. The improvement factor of the energy confinement time

compared with ISS95,HISS95 , showed decrement by about30% when⟨β⟩ increased from2% to

4% 3 . Local transport analysis has been made in order to clarify the causes of such degradation.

The analysis is carried out using the gyro-reduced Bohm (GRB) type model as reference. The

dependence of ISS95 on the parameters is almost similar to that of the GRB model. The ratio of

the effective thermal transport coefficient,χeff , which is evaluated from the experiment, to the

transport coefficient by the GRB model,χGRB , is studied at various radial positions. It is found

that degradation of transport at the peripheral region is large. At the normalized minor radius,

ρ = 0.9, χeff /χGRB becomes large in the highβ regime by some factors of5 ∼ 10 . On the other

hand, the degradation ofχeff /χGRB is weak aroundρ ∼ 0.5.

As some possible reasons for this degradation, following causes can be considered. (1)

Effects of the pressure-driven MHD modes : In LHD, which is a heliotron type device, it is

predicted that the pressure-driven MHD modes become unstable in the highβ regime at the pe-

ripheral region. (2) Degradation of confinement property at the high density or high collisionality

regime : At the high collisionality regime even in lowβ cases, confinement degradation, which

is compared with the GRB type model or the ISS95 model, was also observed4 although the

reason is not clear. On LHD, highβ was achieved in the density region near the density limit. (3)

Increment in ergodicity of magnetic flux surfaces in the peripheral region with the increment in

β : From the results of the 3-dimensional MHD equilibrium code which does not assume nested

flux surfaces a priori, it is shown that a stochastic region at the edge begins to penetrate to the

core region whenβ increases5 . In order to study the effect of the pressure-driven MHD modes

which is listed as (1) above, comparison between the experiment and the anomalous transport

model by the resistive g-mode6 will be carried out.

1. O. Motojima,et al., Proc. of 20th IAEA Fusion Energy Conf., OV/1-4, (Vilamoura, 2004) .2. U. Stroth, M. Murakamiet al., Nucl. Fusion,36 (1996) 1063.3. K.Y. Watabnabe,et al., Proc. of 20th IAEA Fusion Energy Conf., EX/3-3, (Vilamoura, 2004) .4. J. Miyazawaet al., Plasma Phys. Control. Fusion (to be submitted).5. N. Nakajima,et al., Proc. of 20th IAEA Fusion Energy Conf., TH/5-6, (Vilamoura, 2004) .6. B.A. Carreras and P.H. Diamond, Phys. Fluids B1 (1989) 1011.

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Application of the Integrated Transport Code

for Helical Plasmas to LHD

H.Funaba, K.Y.Watanabe, N.Nakajima, A.Fukuyama1, H.Yamada, M.Yokoyama,

K.Narihara, I.Yamada, K.Tanaka, T.Tokuzawa, S.Murakami1, M.Osakabe,

Yuji Nakamura2, K.Kawahata and the LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292, Japan1Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan2Graduate School of Energy Science, Kyoto University, Uji 611-0011, Japan

The integrated transport simulation system for helical plasmas is developed1 by extending

the 1-dimensional transport code TASK (Transport Analyzing System for tokamaK)2 into treat-

ing 3-dimensional MHD equilibrium. In this study, it is aimed to evaluate the transport property

of the LHD plasmas by using this new system. The TASK code is characterized by the combined

simulation with modular structure. One of the modules is TASK/PL which works as a platform of

the whole code. The interfaces for 3-dimensional MHD equilibrium and the experimental profile

data are included in TASK/PL. The input data form for TASK is the UFILE format, which is

adopted in the ITER profile database3 . Therefore, profile data from the LHD experiments are

converted to the UFILE format.

As a preliminary analysis, the effective thermal transport coefficients,χeff , in the LHD plas-

mas will be evaluated based on the power balance of steady state using the transport analysis

module for tokamaks, TASK/TR. Model simulations can be made by TASK with various trans-

port models, such as the drift wave models, the current-diffusivity driven model, theory based

ITG/TEM and ETG models and so on. It is expected that this will be helpful to understand

the transport behaviour on LHD. The derivedχeff will also be compared with the results from

another transport analysis by using PROCTR4 , which is a transport code for helical plasmas.

A new module for transport analysis of helical plasmas, TASK/HT (Helical Transport), will be

installed in this integrated simulation system and results with this module will also be reported.

1. Yuji Nakamuraet al., (in this conference).2. A. Fukuyamaet al., Proc. of 20th IAEA Fusion Energy Conf., IAEA-CSP-25/TH/P2-3,

(Vilamoura, 2004).3. The ITER 1D Modelling Working Group, Nucl. Fusion,40, (2000) 1955.4. H.C. Howe, ORNL/TM-11521 (1990).

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Flows and Diffusions driven by Neoclassical Viscosities in Helical Plasmas

S.Nishimura, H.Sugama, and Y.Nakamura*)

National Institute for Fusion Science, Toki 509-5292, Japan

*) Graduate School of Energy Science, Kyoto University, Kyoto 606-8501, Japan

In a previously formulated full neoclassical transport matrix for general non-symmetrictoroidal plasmas, full neoclassical characteristics of magnetic configurations are described bythe three mono-energetic viscosity coefficients M*(parallel viscosity against flows),N*(driving force for bootstrap currents), and L*(radial diffusion)[1]. Here we discuss onanalytical expressions for these mono-energetic coefficients. Although this previousformulation has been applied to some recently designed devices[2] to date, these applicationswere based on a direct numerical calculation of the linearized drift kinetic equation(LDKE).For the calculations requiring many iterative processes such as configuration optimizationstudies and the equilibrium calculations including the "self-consistent bootstrap currents",however, the analytical expressions are indispensable. To derive the expressions, the radial drift term in the LDKE is divided into two partscorresponding to the effects of local and global structures of the magnetic field. Theadvantages provided by this method separating the contributions of two types of trapped orbits(banana-trapped and ripple-trapped) are as follows; (1) Effects of non-bounce-averagedparticle motions can be approximated by connecting results of only three types of conventionalasymptotic expansions of the divided equations, i.e., banana-, plateau-, and Pfirsch-Schlueter-regime expansions, (2) N* obtained by adding the results of divided equations preciselypredicts the directions of bootstrap currents and Ware pinch depending on the collisionality, (3)L* predicts n regime of the diffusion due to the non-bounce-averaged particle motions, and soon. A simple analytical expression is derived for the ripple-trapped/untrappd boundary layereffect to the parallel viscosity force (N*) in the 1/n regime. An existing expression of theboundary layer solution is applied to obtain the moments of the LDKE with the pitch-angle-scattering collision operator, and the obtained moments can be easily converted to the parallelviscosity force following our previous formulation [1]. Furthermore, a minor modification isproposed for the circulating/trapped boundary condition in the velocity space in a previousbanana regime theory [3] to extend the applications to configurations having a kind of quasi-symmetry [2]. Calculation results in Heliotron-J are shown as examples of this problem. Themono-energetic viscosity coefficients given by these analytical methods approximatelyreproduce results of a direct numerical calculation of the LDKE in various types of non-symmetric toroidal configurations. A physical insight into the viscosity driven neoclassicalflows will be useful also for other advanced studies related to interactions between flows andturbulences in helical plasmas.

[1] H.Sugama and S.Nishimura, Phys.Plasmas 9, 4637 (2002)

[2] D.A.Spong, Phys.Plasmas 12, 056114 (2005)

[3] K.C.Shaing, E.C.Crume, Jr., J.S.Tolliver, et al., Phys.Fluids B1, 148 (1989)

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Active Neutral Particle Diagnostics on LHD by Locally Enhanced Charge Exchange on an Impurity Pellet Ablation Cloud

P.R. Goncharov1, T. Ozaki1, S. Sudo1, N. Tamura1, D.V. Kalinina2, E.A. Veshchev2,

TESPEL Group1 and LHD Experimental Group1

1) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan 2) Graduate University for Advanced Studies, Hayama, Kanagawa, 240-0193, Japan

Production, confinement and thermalization of high-energy particles are the

fundamental issues in fusion plasma ion kinetics. The ion distribution function and its evolution under the ion cyclotron heating and neutral beam injection are studied by energy resolved charge exchange neutral flux measurements. For helical systems, such as LHD, local diagnostics are required due to the complex 3D magnetic field. In passive methods one needs to analyze the integral relation between the plasma ion distribution function and the observed neutral flux, which is a superposition along the diagnostic sightline, taking into account the charge exchange target density profile. In active measurements either a diagnostic neutral beam or a solid pellet injection are used to enhance the charge exchange locally. An impurity pellet ablation cloud rcloud << rplasma provides a localized charge exchange target scanning the plasma radially. Pellet-induced neutral fluxes were previously measured on LHD with a natural diamond detector. However, obtaining the energy spectra from these data in the main energy range of interest (101-102 keV in the present experiments) is complicated due to the high operating speed, i.e. the spatial resolution requirement [1].

A new diagnostic based on a compact neutral particle analyser (CNPA) [2] has been installed on LHD for measurements in the H0 energy range 1 - 170 keV. CNPA employs a thin 50 Å diamond-like carbon stripping film instead of a traditional gas stripping cell, a high-field-strength permanent analysing magnet and an array of 40 channel electron multipliers (CEMs) for particle detection. CEMs can be used in both counting and current modes to be able to process high neutral particle fluxes from the charge exchange on the dense pellet cloud. Thus, the system is suitable for both passive measurements and the active probing with a diagnostic pellet. Pneumatically accelerated polystyrene (-C8H8-)n balls are injected transversally; typical Dpel = 500-900 mm, vpel = 300-400 m/s. The angle between the analyser sight line and the pellet injection axis is 2° on the horizontal midplane projection and 1° in the poloidal plane. The values of the local v7/v for the observable particles are in the range -0.25 to +0.25 along the average pellet flight length.

The neutral flux is determined by the local ion distribution function in the plasma, the neutralization fraction F(E) in the pellet ablation cloud and the attenuation of the neutral flux in the plasma on the way out to the periphery. F(E) can be calculated from the ionization-recombination balance in the cloud. The knowledge of the cloud density and the dominating ion charge states in the cloud during the pellet flight is required as well as the experimental data or theoretical estimations of the relevant charge exchange cross-sections.

A clear response to the pellet injection has been observed on the neutral fluxes in the discharges with different heating scenarios. The pellet-induced spectra from ECRF/tangential NBI heated plasmas and from ICRF plasmas were measured. The initial data analysis (with 16 of 40 energy channels available) and the interpretation of these neutral spectra using the estimated carbon/hydrogen ablation cloud neutralization fraction will be discussed. [1] P.R. Goncharov, T. Ozaki et al., Rev. Sci. Instrum., 75 (2004), 3613 [2] F.V. Chernyshev, V.I. Afanasyev, A.V. Detch et al., Instr. and Exp. Tech., 47 (2004), 214

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Reheat mode discharges in high density regimeof Compact Helical System

M.Isobe, K.Nagaoka, Y.Yoshimura, C.Suzuki, T.Minami, T.Akiyama, S.Nishimura,K.Nakamura, H.Iguchi, A.Shimizu, 1)H.Matsushita, 2)S.Murakami, A.Fujisawa, C.Takahashi,

K.Matsuoka, S.Okamura and CHS group

1)National Institute for Fusion Science, Toki-shi 509-5292 Japan2)The Graduate University for Advanced Studies, Toki-shi 509-5292 Japan

3)Graduate School of Engineering, Kyoto University, Kyoto-shi, 606-8501 Japan

The large increment of plasma stored energy has been observed in the high densityregime of CHS after the intense gas puffing is terminated[1]. This is called 'reheat mode'.Currently, the reheat mode experiment is being conducted under the maximum neutral beamheating power and the highest magnetic field strength of CHS to explore improvedconfinement regime in high density helical plasmas. In a low density region(ne<4_1019m-3),the stored energy linearly increases as electron density increases with gas puffing. However,the stored energy tends to saturate in the density range over 4_1019m-3 and begins to dropwhen the density reaches 8_1019m-3 due to significant radiation loss. After the gas puffing isturned off, the total radiation loss is largely suppressed and the recovery of stored energy isseen. The remarkable differences between the gas puffing and the reheat phases are in thedensity profile and edge electron temperature. The Thomson scattering diagnostic indicatesexcessively hollowed density profile in the gas puffing phase while the density is peaked inthe reheat phase. The Langmuir probe located near the last closed flux surface shows largeincrease of electron temperature, by about double, compared with gas puffing phase. Atpresent, the reheat mode spontaneously terminates. Judging from fan-array measurementusing absolute extreme ultraviolet photodiodes, we suppose that this is due to inward impurityaccumulation while the reheat mode is maintained. In addition to report on characteristics ofthe reheat mode in high Bt operation, comparison of confinement property in the reheat phasebetween high and low Bt will be presented.

[1] S.Morita et al., in Plasma Physics and Controlled Nuclear Fusion Research 1992 (Proc.14th Int. Conf. Würzburg, 1992), Vol.2, IAEA, Vienna (1993) 515.

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20

Progress on Electron Cyclotron Heating Experiments in LHD

T. Shimozuma, S. Kubo, Y. Yoshimura, H. Igami, K. Nagasaki1, T. Notake,S. Inagaki, S. Ito, S. Kobayashi, Y. Mizuno, Y. Takita, K. Ohkubo, K. Saito, T. Seki,

R. Kumazawa, T. Watari, T. Mutoh and LHD Experimental group

National Institute for Fusion Science, 322-6 Oroshi-Cho Toki-City, Gifu 509-5292, Japan1) Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

In the last experimental campaign, nine gyrotrons (two 82.7GHz/0.5MW/2sec, two

84GHz/0.8MW/3sec, one 84GHz/0.2MW/CW and four 168GHz/0.5MW /1sec) were welloperated and over 2MW power could be injected into LHD. The transmission lines consist of

two evacuated corrugated waveguide systems of a 31.75mm inner diameter and six non-

evacuated ones of an 88.9mm diameter. One narrow waveguide line was used for both pulse

and CW power transmission of 84GHz and was enforced the evacuation and cooling.

Several kinds of ECH experiments were performed by using these flexible ECH

systems.(1) Analyses of ECH power deposition and electron heat transport were experimentally

performed by the modulated ECH (MECH) method. The heat transport property in high

electron temperature plasmas with an internal transport barrier was investigated with respect

to the existence of lower order rational surfaces and islands. Electron Bernstein Wave (EBW)

heating was tried for the first time in LHD by the fundamental X-mode injection from the

high field side. The wave absorption position and profile were discussed on the basis of theFourier analysis of the modulated temperature response.

(2) Electron cyclotron current drive (ECCD) experiments were performed by the fundamental

O-mode and the second X-mode injection into the ICRF sustained plasmas and ECR plasmas

in order to minimize the initial plasma current (Bootstrap and NBI beam driven currents) of

the target plasmas. The current of 5kA was driven by obliquely injected ECH pulse

(84GHz/0.4MW/0.8s) in the ICRF sustained plasma. The direction of the driven toroidalcurrent obviously depended on N// of injected EC waves in the ECR target plasma case.

(3) The 84GHz CW gyrotron and improved transmission system enabled to achieve over 1

hour plasma sustainment. The plasma with 1.5keV electron temperature and 1.5_1018 m-3 line-

averaged electron density was successfully sustained for 65min by the injection of 110kW

power and the control of gas puff. The discharge was manually terminated and there is no

limitation in the discharge period except the temperature increase of non-cooled waveguidehorn antenna so far.

For further high-power and reliable system, power up of a gyrotron and evacuation

of the transmission line are proceeded and evaluation works are also in progress, such as

direct measurement of the injected power and the actual focusing position and beam size from

the antennas in the vacuum vessel.

P1-06

21

Observation of Equilibria with a Double Magnetic Axis in LHD

H.Yamada, Y.Suzuki, K.Ida, M.Yoshinuma, T.Kobuchi, K.Y.Watanabe, K.Tanaka

and LHD Experimental Group

National Institute for Fusion Science

Toki, Gifu 509-5292, Japan

Plasma shape control is a major knob to investigate confinement as well as MHD

characteristics of magnetically confined plasmas. LHD has a large flexibility to explore a

configuration effect by using 6 independent coil systems. Elongation can be controlled by a

quadrupole field. Experimental observation of moderate elongation has shown that

confinement is degraded gradually in both prolate (vertically elongated) and oblate

(horizontally elongated) configurations. Since the rotational transform is weaker in the core

region than in the periphery in LHD, a theoretical analysis suggests that excess quadrupole

field results in split of the magnetic axis. Then the internal separatrix like petals emerges.

Further application of quadrupole field eventually realizes a doublet configuration with a

double magnetic axis bounded by this separatrix. An analytics1) suggests that split of the

magnetic axis starts beyond elongation κ of 1.6 in the prolate case. The role of separatrix is

attracting interest in effect on confinement performance as well as physics of unstable

manifold, which has motivated strong shaping experiment in LHD. Both shaping of prolate

and oblate directions has been explored for NBI heated plasmas. In the strongly prolate case,

the doublet image has been observed by a tangential soft X-ray camera. Available profile

measurements of temperature and density have not provided the 2-dimensional profile,

however, assumption of concentric surfaces with a single magnetic axis seems to contradict

with experimental observations in the 1-dimensional measurements in the case with strong

shaping. This suggests the existence of doublet magnetic surfaces. These complex equilibria

cannot be treated by the numerical code, ex.VMEC, with an assumption of nested flux

surfaces with a single magnetic axis. Characteristics of these eccentric equilibria have been

investigated by the HINT code which does not assume existence of nested flux surfaces.

Experimental and computational results are discussed with emphasis on split of magnetic axis

in the prolate case, and large Shafranov shift and consequent equilibrium beta limit in the

oblate case.

1 Pustovitov, V.D., Review of Plasma Physics (2000, Kluwer Academic/Plenum

Publisher) Vol.21, pp.138.

P1-07

22

Effect of Neoclassical Transport Optimization on Electron Heat Transport in the Low-collisionality LHD plasma

S. Murakami, H. Yamada1), A. Wakasa2), H. Inagaki1), K. Tanaka1), K. Narihara1),

S. Kubo1), T. Shimozuma, H. Funaba1), J.Miyazawa1), S. Morita1), K. Ida1), K.Y. Watanabe1), M. Yokoyama1), H. Maassberg5), C.D. Beidler5),

and LHD Experimental Group

Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan 1)National Institute for Fusion Science, Oroshi, Toki, Gifu 509-5292, Japan

2)Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan 3)Max-Planck-Institut fuer Plasmaphysik, D-17491 Greifswald, Germany

Recent numerical studies of neoclassical transport in the LHD configuration have shown an optimum configuration with respect to 1/ν transport when the magnetic axis has a major radius of 3.53m1. In this case, the effective helical ripple is very small, remaining below 2% inside 4/5 of the plasma radius. Also, in this configuration, the deviation of trapped particle orbit from magnetic surfaces is very small and a good confinement of alpha-particle is obtained for a time longer than the energy slow-down time in the reactor scaled device2. These facts indicate that a strong inward shift of the magnetic axis can optimize the LHD configuration to a level typical of so-called "advanced stellarators''. Therefore it is an important issue for the LHD experiment to clarify the effect of configuration optimization on the plasma confinement in a helical system. In this paper the electron heat transport in the low-collisonality plasma ( n

e! 1.0 "10

19m-3 ) is analyzed to clarify the effect of configuration optimization on

the thermal plasma transport in the LHD. Typical five configurations of LHD are considered; i.e. Rax=3.45m, 3.53m, 3.6m, 3.75m and 3.9m. We set the magnetic field strength to 1.5T at the magnetic axis so that the ECH (f~84GHz, P~880kw) heat deposition profiles are distributed inside of r/a =0.3 in the these configurations. It is found that the global confinement times of the configurations near the optimized point; Rax=3.53m and 3.6m are not so much different, and that these values are about 1.5 to 2.0 times larger than that of the other non-optimized configurations (Rax=3.45m, 3.75m and 3.9m) in the low-collisonality plasma. Also no clear difference in the temperature profiles (ECE and Thomson) in the region 0.4<r/a<0.8 can be seen between the 3.53m and 3.6m configurations, and significant differences can be seen between the optimized and non-optimized configurations. The electron heat transport coefficients are estimated and compared with the neoclassical transport predictions by DCOM3. The characteristics of the electron heat transport and the role of neoclassical transport are discussed in the low-collisionality LHD plasma. 1. S. Murakami, et al., Nuclear Fusion 42 (2002) L19. 2. S. Murakami, et al., Fusion Sci. Technl. 46 (2004) 241. 3. A. Wakasa, et al., J. Plasma Fusion Res. SERIES, Vol. 6 (2004) 203.

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23

Using e-beam mapping to detect coil misalignment in NCSX

E. Fredrickson1, A. Georgiyevskiy1, V. Rudakov2, M. C. Zarnstorff1

1Princeton Plasma Physics Laboratory, Princeton, NJ,2 Institute of Plasma Physics, National Science Center

“Kharkov Insitute of Physics and Technology”,Kharkov, Ukraine.

The primary object of the e-beam mapping simulation program on NCSX is to developrequirements for the hardware and machine capabilities necessary for the actual e-beammapping experiments. The magnetic flux surface configuration was constructed using anumerical code, based on the Biot-Savart law, to calculate the magnetic field components andtrace the field line trajectory many times around the torus. Magnetic surfaces are then mappedby recording the field line intersections with toroidal cross-sections of the magnetic system,much as in an actual e-beam mapping experiment. In the course of these calculations, a catalogof many hundreds of vacuum magnetic configurations was compiled, each with varyingsensitivity to the coil displacements. The NCSX coils were designed to provide good magneticsurfaces at high beta with significant bootstrap current. The coil set includes separatelypowered modular, toroidal field, and poloidal field coils, and can produce a wide range ofmagnetic configurations. Many of the vacuum field configurations with low order rationalsurfaces have finite, stellarator-symmetric islands present. Nevertheless, despite the presence ofthese islands, configurations have been found which will allow, we believe, the identification ofmodular and poloidal field coil displacements of < 0.5 mm. There was generally less sensitivityto toroidal field coil displacement, and a novel approach of energizing a subset of the toroidalfield coils at higher current is proposed. By using half of the toroidal field coils, at twice thecurrent, it is possible to detect alignment errors of less than approximately 1 mm. These resultsassume that the spatial resolution of the e-beam mapping apparatus is of order 5 mm, apreviously achieved result for the luminescent rod method1. We have also investigated thepossibility of performing the initial e-beam mapping (and possibly start-up) studies in NCSXusing two or fewer power supplies for the coils in the magnetic system (18 MC + 6 PFC + 18TFC). There is a potential advantage of minimizing the complexity and cost of the initialmapping phase. More importantly, reducing the number of power supplies reducesuncertainties in the field mapping from current regulation or measurement of the currents. Wefind that a single source powering all modular coils in series produces good magnetic surfaces,however, without the most sensitive ι = 0.5 rational surface. With the addition of current in thetoroidal field coils, the ι = 0.5 resonance can be introduced and the previous sensitivity to coildisplacements of order 1 mm is recovered. Future work will focus on developing methods toidentify specific types of coil misalignments.

1. Bykov V.E., Voitsenya V.S., Volkov E.D., Georgievskiy A.V., Schworer K, Hailer H. etal.–In: VANT Ser. Termonuclear Fussion, M: ZNII Atominform. 1990, Vol.III, p. 12.G.G. Lesnyakov, E.D. Volkov, A. V. Georgievskij, et al., Nuclear Fusion 32 (1992) 2157.

P1-09

24

New method of determining coil misalignments in the ITER tokamak on thebase of sensitive vacuum magnetic measurements with the use of a “Saw

Tooth” coil providing the creation of stellarator resonance magneticsurfaces

A.V. Georgiyevskiy, consultant of the Princeton Plasma Physics Laboratory, Princeton, NJ.V.A. Rudakov, Institute of Plasma Physics, National Science Center

“Kharkov Institute of Physics and Technology”, Kharkov, Ukraine.

The paper presents a new highly sensitive “e-beam” method of determiningmisalignments of elements in the ITER magnetic system on the base of magneticmeasurements (MM). For the period of MM experiments it is suggested to make a “tokamak-stellarator” hybrid (ITER-S) by means of addition to the ITER magnetic system of a new, nothelical Saw Tooth-shaped Coil1 (STC) in order to provide the creation of “resonance”magnetic surfaces with the angles of rotational transform t = n/m = 1/2 or t = 1/3. In one ofvariants the STC parts can be introduced into the vacuum vessel through the largest port andassembled into a single coil.

We propose a highly sensitive “e-beam” method using the luminescent rod, i.e. the fastestand most accurate method giving a direct pictures of magnetic surface structure. In themethod proposed the basic component of the equipment is a small (∅≈1.5mm ) metal rodcoated with a thin phosphor layer. In other poloidal cross-section the electron gun, movablealong the minor radius of the torus, is placed. The pictures of many “magnetic surfaces” areobtained by photographing the light emitted by phosphor due to electrons striking the rod.Experiments on the Uragan-3M torsatron have shown that up to 15 contours of “magneticsurfaces” can be registered. The typical resolution δr along the minor radius is of the order ofδr ≈ (3 –5)mm.

The calculations of the ITER-S magnetic configuration show that due to the turn of thepoloidal field coil PF3 (radius Rc = 12.01 m) around the axis X direction at an angle αααα = 1’the resonance structure is formed with t = 1/2 and the maximum island width δδδδo ≈≈≈≈50 mm.Under this tilt the maximum misalignment of coil elements from the design position ∆∆∆∆αααα isonly 3.5 mm. The vertical and horizontal magnetic field components in the resonance regionare changing by the value bj ≈ (0.5 – 0.6) G, that corresponds approximately to the relative

value of perturbation bj/Bo ≈≈≈≈ 1*10-5. Generally in similar cases one uses the estimation forthe transversal island dimension: δo = 4 (bmn Ro/ m Bo t’)1/2 , where Ro is the major radius,t’ =dt/dr at the rational surface. For the resonance structure m=2, n=1 with the maximumisland width δδδδo ≈≈≈≈50 mm be created it is necessary to have a perturbing field with an harmonicamplitude bmn ≈ 0.3 G. The calculations show that the decrease of the coil tilt angle up toα=1⁄4′ results in the proportional decrease of the bj components and approximately in the 2-

fold decrease of δo in the island structure (δδδδo ≈≈≈≈ 25 mm). Remind, the value of “resolution”(δr) given by the proposed method of MM is equal to δδδδr ∼∼∼∼(3 – 5)mm (i.e. δδδδr << δδδδo).

So, we have found the means for identification of misalignments in the case ofmagnetic system elements deviation from the design position to the values ∆∆∆∆αααα ∼∼∼∼ 1 mm thatleads to the relative values of perturbing fields bj/Bo ≈≈≈≈ 3 10 –6.

1 The STC winding was proposed and investigated for the first time by A.V.Georgiyevskiy and V.A.Rudakovtogether with the scientists of Wiskonsin University in 1995.

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25

Impurity Ion Transport under the Drift Wave Electrtic Field in Helical Plasma

Oleksandr Yu. Antufyev1, Alexander A. Shishkin2, Zhanna S. Kononenko1 1 Kharkov V.N. Karazin National University, Kharkov, Ukraine

2 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology, Kharkov, Ukraine

Heavy impurity ion transport is considered in the vicinity of two adjacent rational magnetic surfaces with the rotational transforms mnr mn /)( 2

, =ι and mnr mn ′′=′′ /)( 2,ι in

the helical plasma under the drift-wave-like potential, which is written in the form ])(exp[),(

~~tiMNi ωϑφϑρ −−Φ=Φ , where 0rr −=ρ is the radial distance from the

rational magnetic surface with the rotational transform mn /=ι .1 The trajectories of the passing particles can form the rational drift surfaces. If there are some adjacent rational drift surfaces with the drift rotational transform mn /* =ι , mn ′′= /*ι , mn ′′′′= /*ι , then the magnetic perturbations with the wave numbers ( nm, ), ( nm ′′, ), ( ), nm ′′′′ can lead to some families of drift islands. Overlapping of the adjacent resonance structure is the reason for the stochasticity of the particle trajectories. If a particle trajectory passes through the set of perturbations this test particle can escape from the center of the confinement volume to the periphery. The helically trapped particles with the orbits of the helical banana-type can be transferred into the “toroidally trapped” particles under the effect of this electromagnetic field. It is shown, that passing impurity particle becomes trapped under the drift wave electric field. Similarly to the estafette of drift resonances 2 the impurity ion feels the drift wave electric field sequentially and moves outside of the confinement volume and escapes. The investigation of integral transport properties is carried out. Although the backward impurity transition from the trapped state into the passing one is possible, the penetration of the impurity into the core plasma is not expected. It is important to understand the conclusive result of impurity transport. The numerical simulation is carried out with the use of Newton-Poisson equation system. As the test particle the tungsten ion is taken.

This work is partly supported by the Science and Technology Center in Ukraine in the framework of the Project N 2313.

1. Hyoung-Bin Park, Eun-Gi Heo, Wendell Horton and Duk-In Choi, Physics of Plasmas Physics of Plasmas v. 4 (1997) pages 3273-3281.

2. Alexander A. Shishkin, Nuclear Fusion v.42 (2002), pages 344-353.

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26

The Equilibrium ββββ Limit in W7-AS

A. Reiman1, M. Zarnstorff1, D. Monticello1, A. Weller2, J. Geiger2

and the W7-AS Team1Princeton Plasma Physics Laboratory, Princeton, NJ 08543 USA

2Max-Planck Institute for Plasma Physics, D-17491, Greifswald, Germany

The PIES three-dimensional MHD equilibrium code has been modified to allow the

imposition of an experimentally determined pressure profile. When run in this mode,

the code does not flatten the pressure profile in islands or stochastic regions, unless

this is indicated by the diagnostic measurements. To model the equilibrium in the

W7-AS experiment, the pressure profile has been determined by the data from the

Thomson scattering system and from the set of magnetic diagnostics. PIES

equilibrium calculations with the imposed profile and varying β indicate that a

stochastic region appears at the plasma edge above a threshold value of β, and that the

width of the stochastic region progressively increases as β is further increased. The

threshold value for the appearance of the stochastic region and the width of the

stochastic region depend on the magnitude of the current in the divertor control coils,

Icc. The maximum achievable β in the experiment also depends on the value of Icc,

and the achievable β correlates with the width of the stochastic region calculated by

PIES. In each case calculated, the highest achievable β corresponds to a stochastic

region enveloping approximately the outer 1/3 of the plasma. The value of Icc has

little effect on the shift of the magnetic axis, indicating that the equilibrium β limit is

not adequately characterized by the often invoked rule of thumb that assumes that the

equilibrium β limit corresponds to a magnetic axis shift of approximately _ the minor

radius. The pressure gradient in the stochastic region is found to play an important

role in determining the width of that region. If, instead of imposing the

experimentally determined pressure profile in the stochastic region, the pressure

gradient is flattened there, the stochastic region is calculated to widen progressively as

the code iterates, and the equilibrium solution is lost. Further PIES calculations for

modeling the W7-AS equilibria are focusing on the effects of the current profile, with

zero net current.

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27

Derivatives of the local ballooning growth rate with respect to

surface label, field line label and ballooning parameter

S.R.Hudson

Princeton Plasma Physics Laboratory, P.O. Box 451,Princeton NJ 08543, USA.

For comprehensive ballooning analysis in three-dimensional (stellarator) systems, anextensive set of ballooning eigenvalue calculations is generally required. For several ap-plications, it is convenient to know how the local ballooning stability will change as afunction of the surface label ψ, the field line label α and the angle-like ballooning pa-rameter ηk. A particularly important application is in the ray tracing problem [Dewar& Glasser 1983], when results from the local ballooning analysis are extended to makepredictions regarding global stability. This article presents an explicit method for calcu-lating the derivatives of the ballooning eigenvalue with respect to (ψ, α, ηk). The requiredderivatives satisfy

δλ =∂λ

∂ψ

∣∣∣α,ηk

δψ +∂λ

∂α

∣∣∣ψ,ηk

δα+∂λ

∂ηk

∣∣∣ψ,αδηk, (1)

for infinitesimal variations δψ, δα and δηk. The method is an application of eigenvalueperturbation analysis. The ballooning equation, with eigenvalue λ and eigenfunction ξ,may be written

∂ηP∂η ξ +Qξ = λR ξ, (2)

A small change in (ψ, α, ηk) induces a change in the ballooning coefficients, and a corre-sponding variation in the ballooning eigenvalue. The eigenvalue derivatives are calculated

∂λ

∂ψ

∣∣∣α,ζ

=〈ξ|∂ηδPψ∂ + δQψ − λδRψ|ξ〉

〈ξ|R|ξ〉 . (3)

where Pψ, Qψ, and Rψ are the changes in the coefficients due to a small change in ψ, withsimilar expressions for ∂λ/∂α and ∂λ/∂ηk. Preliminary results of ray-tracing calculationswill be presented.

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28

SVD Methods for Magnetic Diagnostics Design in NCSX

N. Pomphrey1 and E.A. Lazarus2

1 Princeton University Plasma Physics Laboratory, Princeton, New Jersey 08543, USA

2 Oak Ridge National Laboratory, Oak Ridge, Tennessee 37382, USA In this companion presentation to [1], we describe details of a Singular Value Decomposition (SVD) method for designing magnetic diagnostics (MD’s) in NCSX. A variety of external MD’s will be installed on NCSX and used for between-shot equilibrium reconstruction, and possibly used for real-time plasma shape control. Signals from a large database of candidate equilibria (~2500) are analyzed by candidate “supersets” of MD’s which include diamagnetic loops, Rogowski coils, saddle loops arrayed on the vacuum vessel (VV) structure, poloidal and toroidal flux loops on the VV, triple-axis magnetic probes, and flux loops co-wound on modular and poloidal field coil casings. SVD analysis of the matrix of signals formed by the ensemble of equilibria provides information (through the number of significant eigenvalues) on how much equilibrium information is accessible to the external MD’s. The SVD eigenfunctions determine which diagnostics are most important for recovering the equilibrium information. Two recently developed recursive SVD algorithms for ranking the candidate diagnostics will be discussed. The algorithms improve the methods discussed in [2]. Starting with a superset of ~ 450 MD’s per half-period (including ~100 VV saddle loops and 3 x 100 triple-axis B-probes), a least squares regression of the MD signals is performed on the magnetic field values from the plasma and coils at a mesh of points on the surface of a close-fitting toroidal surface in the vacuum region surrounding all of the equilibria. The first algorithm is a “rejection” procedure where examination of the eigenfunction corresponding to the smallest SVD eigenvalue leads to the rejection of a single diagnostic from the superset. The rank of the signal matrix is then reduced by eliminating the row corresponding to the rejected diagnostic and an SVD of the reduced matrix is performed. The procedure is repeated, rejecting one diagnostic after each SVD until the Total Least Squares (TLS) regression fitting error exceeds a tolerable minimum, leaving a minimal set of acceptable diagnostics. The second method is a “retention” algorithm. A Truncated SVD regression analysis identifies the top few (4-8) “most important” diagnostics in the superset. These diagnostics are placed in a reserved pool and SVD regression is performed on the reduced matrix formed by eliminating columns of the diagnostics signal matrix corresponding to the reserved diagnostics. The procedure is repeated until the TLS regression fitting error exceeds the tolerable minimum. Results from applying the diagnostics ranking procedures will be discussed in the context of reserved port allocations. [1] E.A. Lazarus and N. Pomphrey, “The design of Magnetic Diagnostics for Reconstructing NCSX Equilibria” (companion presentation, these Proceedings). [2] N. Pomphrey, et al., Proceedings of the Twentieth International Conference on Plasma Physics and Controlled Nuclear Fusion Research (Vilamoura, Portugal, October 2004) (International Atomic Energy Agency, Vienna, Austria, 2004), Paper IC/P6-45.

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1

The Design of Magnetic Diagnostics for Reconstructing of NCSX

Stellarator Equilibria E.A. Lazarus and N. Pomphrey

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37381, USA

Princeton Plasma Physics Laboratory, Princeton, New Jersy 08543, USA

In previous work [1] we have demonstrated that NCSX (National Compact Stellaraator Experiment) will require active control of the helical and poloidal field coils in order to remain on a stable trajectory to high beta while retaining quasi-axisymmetry. We require a set of magnetic diagnostics that will be sensitive to changes in the equilibrium that represent departures from such a trajectory. That is, we will need to control features of the plasma boundary shape to a specification; that specification itself will vary with the current and pressure profiles. We need to determine a satisfactory set of magnetic sensors for this task

To address this we have postulated a diagnostic set of 443 sensors that we believe is overly complete. A data base of ~2500 free-boundary equilibria is created with variation of coil currents, plasma pressure and toroidal current profiles, plasma size, total pressure and total current. The signals expected on this array of diagnostics are calculated using a response function formalism[2]. These are used in a linear regression to predict the magnetic field on a smallest vacuum surface that encompasses all the equilibria in the database. We have extended a standard “variable selection” method of multivariate statistics to determine a complete ranking of the sensors. The ranking scheme is based on properties of the null space of the matrix of diagnostic signals for all equilibria in the database.

Subsets are chosen according to this ranking and we judge adequacy by our ability to reconstruct the equilibrium with STELLOPT [3]. While the ability to reconstruct the equilibrium in free boundary does not yield information on optimal control algorithms, it does show whether a particular set of sensors contains the necessary information to allow control of the plasma. Results will be reported. It is yet to be determined just how much information about the profiles can be known from external measurements. We will present results of a study that addresses this issue.

References: [1] E.A. LAZARUS, et al., Fusion Science & Tech. 46 (2004) 213. [2] S.P. HIRSHMAN, E.A. LAZARUS, J.D. HANSON, S.F. KNOWLTON, L.L. LAO,

Phys. Plasmas 11 (2004) 595. [3] S. P. Hirshman, et al., Phys. Plasmas, 6 (1999)1858.

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Equilibrium Reconstruction in Stellarators: V3FIT

J. D. Hanson, J. Shields, S. F. Knowlton Auburn University, Auburn, Alabama 3684, USA

S. P. Hirshman, E. A. Lazarus

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA

L. Lao General Atomics, San Diego, California 92121, USA

Input parameters to an MHD equilibrium code include the radial pressure and current

profiles. These input parameters are not directly measurable in an experiment. Equilibrium Reconstruction (ER) refers to the process of determining (or reconstructing) the input parameters (current and pressure profiles) by making observed diagnostic signals as consistent as possible with signals computed from the equilibrium. ER is an example of a broad class of procedures called data assimilation, or parameter estimation procedures.

The EFIT1 code, the most widely used tool for axisymmetric equilibrium reconstruction, has proven invaluable for equilibrium control, and for comparisons with MHD stability and confinement predictions. The V3FIT code, currently under construction, will perform fast, accurate reconstruction for stellarators. To be most useful for experiments, the V3FIT code will need to a) run rapidly, b) be flexible, and c) be extensible. V3FIT is written in Fortran 95, and makes extensive use of the modern features (modules, derived types, and pointers) of the language.

The broad outline of the reconstruction algorithm is clear: a function minimization in the space of equilibrium parameters, with the function to be minimized being a measure of the mismatch between observed and model-derived diagnostic signals. However, for the ER to be rapid, the evolution of the equilibrium parameters toward their true values will need to be tightly coupled to the iterative equilibrium solution. There are many possible algorithms for this tight coupling, and the best algorithm is not known. The code is being written in a structured, modular way, with clear and consistent data flow. Thus, modifying old algorithms and implementing and testing new algorithms will be easy. The modular code structure makes adding signal types straightforward. (Magnetic diagnostics2 and microwave interferometry/polarimetry signal types have been implemented.) Changing the equilibrium solver (currently VMEC3) is also possible. ------------- Work supported by the U. S. Department of Energy. 1 L.L. Lao, et al, Nucl. Fusion 25, 1611 (1985). 2 S. P. Hirshman, E. A. Lazarus, J. D. Hanson, S. F. Knowlton, and L. L. Lao, Phys. Plasmas

11, 595 (2004). 3 S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983).

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31

Field–mapping and initial experiments in the Compact Toroidal Hybrid (CTH)Experiment.

S. F. Knowlton, G. J. Hartwell, C. M Montgomery, R. Kelly, J. Peterson, B. A.. Stevenson, and

J. Hanson

Physics Department, Auburn University, Auburn, AL 36849 USA

The Compact Toroidal Hybrid (CTH) is a low-aspect ratio torsatron with adjustablevacuum rotational transform and shear that operates with ohmic plasma current to investigatethe equilibrium and stability of current-carrying helical plasmas. Equilibrium reconstruction ofexperimental stellarator plasmas for optimization of stability and transport has become moreimportant in recent years because of the finite levels of pressure-driven currents now achievedin high β helical plasmas, and also because the NCSX and QPS stellarators will make use ofbootstrap and/or driven plasma current to generate a non-negligible fraction of the plasmarotational transform. A new computational scheme to reconstruct equilibrium flux surfaces instellarators (V3FIT) is under development,1 and will be tested in CTH with external andinternal magnetic diagnostics in strongly current-driven plasmas. Moreover, issues of current-driven MHD instability and the potential for disruptions in stellarators are also of paramountinterest in such hybrid configurations. In this regard, CTH will investigate the onset ofresistive and ideal current-driven instabilities in magnetic equilibria in which key parameters(global shear, vertical elongation, vacuum rotational transform, fraction of current-drivenrotational transform) are varied in order to assess the potential for passive disruption controlin current-carrying stellarators.

The CTH device is a five-field period, L = 2 torsatron (R0 = 0.75 m; aVessel = 0.3 m)with toroidal field coils for control of the vacuum rotational transform, and three independentsets of poloidal field coils for equilibrium control, and an ohmic transformer to produce anexpected maximum current of 50 kA. In addition, a set of 15 error-correction coils has beeninstalled to minimize static islands in vacuum and plasma configurations, and may also be usedto influence rotating islands. The minimum plasma aspect ratio in vacuum magneticconfigurations is Ap = 4. The maximum magnetic field on axis is Bo ≤ 0.7 T with zerosupplementary toroidal field (ι a( ) ≅ 0 18. ), though most initial work is carried out at Bo = 0.33

T to make use of 2nd harmonic ECH at 18 GHz.ECH plasmas in CTH were first attained in Feb. 2005. Current efforts center on field-

mapping and precision alignment of the multiple coil sets to achieve low aspect ratio vacuumconfigurations with minimal islands over a range of vacuum rotational transforms. Results of thefield-mapping and the use of the flexible error-correction coil set will be presented.

Supported by US DoE Grant DE-FG02-00ER54610

1. S. P. Hirshman, E.A. Lazarus. J. D. Hanson, S.F. Knowlton and L. Lao, Phys. Plasmas 11,(2004) 595

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Recent Developments in the Quasi-Poloidal Stellarator Project

J. F. Lyon1, B. E. Nelson1, R. D. Benson2, L. A. Berry1, M. Cole1, P. Fogarty1, K. Freudenberg1, P. Goranson3, P. Heitzenroeder4, S. P. Hirshman1, A. Lumsdaine2, M. Madhukar2,

P. K. Mioduszeski1, G. H. Neilson4, R. Sanchez5, T. Shannon2, D. A. Spong1, D. J. Strickler1,A. S. Ware6, D. Williamson1

1Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA2University of Tennessee, Knoxville, TN 37996, USA

4Princeton Plasma Physics Laboratory, Princeton, NJ 08502, USA3DevTech, Oak Ridge, TN 37830, USA

5Universidad de Carlos III de Madrid, Madrid, Spain6Department of Physics and Astronomy, University of Montana, Missoula MT 59812, USA

The Quasi-Poloidal Stellarator (QPS), currently in the R&D and prototyping stage, is alow-aspect-ratio (R/a ≥ 2.3), compact stellarator experiment with a magnetic field that is non-axisymmetric and whose magnitude is nearly poloidally symmetric in magnetic coordinates.The quasi-poloidal symmetry and reduced effective field ripple lead to large reductions in:neoclassical transport at low collisionality; the bootstrap current; and poloidal viscosity, whichallows large E x B poloidal flows for suppression of anomalous transport. The magneticconfiguration is stable to finite-n ballooning modes, external kink modes, and vertical instabilityto <beta> ~ 5%. Recent QPS-related physics studies have focused on fluid-moments self-consistent evaluations of viscosities and neoclassical transport coefficients, momentum transportand flow damping features, the impact of the bootstrap current on the equilibrium and stabilityproperties, global ballooning stability, reduction of beta limits for experimental tests,minimization of magnetic islands by minimizing the residues of the dominant island chains,measures of poloidal symmetry deviation using electron beam mapping, optimization of viewingsightlines, diverted flux patterns for control of recycling, and control of the plasma and neutraldensities as a function of fueling rate, divertor baffling, wall adsorption, and particle exhaust.

The QPS design parameters are <R> = 0.95 m, <a> = 0.3-0.4 m, B = 1 T, and a 1.5-spulse length with 3-5 MW of ECH and ICRF heating power. The most challenging componentfor engineering design and fabrication is the set of 20 nonplanar modular coils located inside theQPS vacuum tank. Stainless steel winding forms are machined to the required high toleranceand stranded copper cable conductor is wound on the winding forms to the highly precise shaperequired (to an accuracy of less than 1 mm). The windings are enclosed in a welded, stainlesssteel cover with stiffeners for compatibility with the QPS vacuum requirements, and the cans arethen vacuum pressure impregnated with cyanate ester resin to form the finished coil windingpack. An R&D program is underway that includes extensive conductor characterization andtesting, vacuum canning studies, and fabrication of a full scale-prototype modular coil. The coilwinding form has been cast and is being machined to the required tolerance prior to windingwith conductor. One of the most critical design issues is the cooling of the winding pack. Twocooling concepts are being evaluated: (1) an internally cooled conductor having a copper tubefilled with a Pb-Bi filler imbedded in the conductor cable to avoid crimping during winding, and(2) an externally cooled winding pack using copper cladding inboard and copper chill platesoutboard of the pack. The issues being studied are the effect of the increased conductorstiffness on winding the coil, evacuating the filler material in the coolant tube after the initialpotting step, and separating the cooling tube from the conductor at the electrical connectioninterface. Four-turn test coils are being tested for mechanical properties (cyclic loading forfatigue properties), thermal properties (conductivity), and tensile properties (stiffness andstrength).

* Supported by USDOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

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Coil Development for the Quasi-Poloidal Stellarator Project

B. E. Nelson1, R. D. Benson2, L. A. Berry1, M. J. Cole1, F. Dahlgren3, P. J. Fogarty1, K. Freudenberg1, P. Goranson4, T. Hargrove4, P. Heitzenroeder3, S. P. Hirshman1, G. Jones5, G. Lovett6, A. Lumsdaine2, J. F. Lyon1, M. Madhukar2, G. H. Neilson3,

M. Parang2, T. Shannon2, D. A. Spong1, D. J. Strickler1, D. Williamson1

1Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA2University of Tennessee, Knoxville, TN 37996, USA

3Princeton Plasma Physics Laboratory, Princeton, NJ 08502, USA4DevTech, Oak Ridge, TN 37830, USA

5BWXT Y-12, Oak Ridge, TN 37831, USA6MK Technologies, Knoxville, TN 37930, USA

The Quasi-Poloidal Stellarator (QPS), currently in the R&D and prototyping stage, is alow-aspect-ratio (R/a ≥ 2.3), compact stellarator experiment with a non-axisymmetric, near-poloidally-symmetric magnetic field. The QPS design parameters are <R> = 0.95 m, <a> = 0.3-0.4 m, B = 1 T, and a 1.5-s pulse length with 3-5 MW of ECH and ICRF heating power. Themost challenging component to design and fabricate is the set of 20 nonplanar modular coilslocated inside the QPS vacuum tank. There are five distinct coil winding shapes, but only threetypes of winding forms are needed because each supports two distinct windings and bothwindings on the most complex coil form are the same shape. The stainless steel winding formsare machined to the required high tolerance and stranded copper cable conductor is wound onthe winding forms to the highly precise shape required (to an accuracy of less than 1 mm). Thewindings are enclosed in a welded, stainless steel cover with stiffeners for compatibility with theQPS vacuum requirements, and the cans are then vacuum pressure impregnated with cynate esterresin to form the finished coil winding pack. Computer modeling and experimentalmeasurements of the welding process indicate that distortion and thermal stress should beacceptable. A prototype coil using the most complex of the three winding forms is beingfabricated. The coil winding form has been cast and is being machined to the required toleranceprior to winding with conductor. The machined modular coil forms will be shipped to thewinding facility mounted on carts, which provide a work platform for preparing, winding,welding, and potting of the coils. The carts allow rotating the coils for optimum positioningduring winding and fabrication. An overhead fixture allows supporting the spools of conductorand feeding the conductor in the correct orientation, groupings, and tensioning.

An R&D program is underway that includes extensive conductor characterization andtesting, vacuum canning studies, and fabrication of a full scale-prototype modular coil. One ofthe most critical issues is the cooling of the winding pack because of space constraints, variableconductor behavior, coolant effectiveness, complex electrical circuits, impregnation issues,vacuum can conductance, possibility of welding/brazing damage, and the extremely complexconductor leads interface and connection. Two possible conductor cooling concepts are beingevaluated: (1) an internally cooled conductor having a copper tube filled with a Pb-Bi fillerimbedded in the conductor cable to avoid crimping during winding, and (2) an externally cooledwinding pack using copper cladding inboard and copper chill plates outboard of the pack. Theinternally cooled conductor concept is attractive due to a much more effective, active cooling ofthe conductor than the copper cladding/chill plates allow, resulting in up to a factor of 5 fastercooldown between shots. Issues being studied are the effect of the increased conductor stiffnesson winding the coil, evacuating the filler material in the coolant tube after the initial potting step,and separating the cooling tube from the conductor at the electrical connection interface. Four-turn test coils are being tested for mechanical properties (cyclic loading for fatigue properties),thermal properties (conductivity), and tensile properties (stiffness and strength).

* Supported by USDOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

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Bootstrap Current in Quasi-Symmetric Stellarators

A.S. Ware,1 D.A. Spong,2 L. A. Berry,2 S.P. Hirshman,2 J. F. Lyon2

1Department of Physics and Astronomy, University of Montana, Missoula MT 59812, USA 2Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge TN 37831-8070, USA

This work examines bootstrap current in quasi-symmetric stellarators with a focus on the impact of bootstrap current on the equilibrium and stability properties of the Quasi-Poloidal Stellarator (QPS) [1]. In the design of QPS, a code was used to predict the bootstrap current based on a calculation in an asymptotically collisionless limit [2]. This calculation is believed to be a good approximation of the bootstrap current for a low density, high electron temperature (n ~ 3×1019 m-3, Te ~ 1 keV, Ti ~ 0.2 keV), ECH heated plasmas in QPS but is expected to be much higher than the actual bootstrap current for more collisional (n ~ 8×1019 m-3, Te ~ 0.4 keV, Ti ~ 0.4 keV), ICH heated plasmas in QPS. Recently, a fluid moments approach has been developed to self-consistently calculate viscosities and neoclassical transport coefficients [3]. The viscosities and transport coefficients can be used to calculate the bootstrap current (in addition to neoclassical flows) for arbitrary collisionality and arbitrary magnetic geometry. The predictions from the asymptotic collisionless formula agree qualitatively with the bootstrap current predicted by the fluid moments calculation for the low density, ECH plasmas in QPS. For the high density, ICH heated plasmas, the shape of the predicted profiles are similar but the asymptotic collisionless formula predicts a magnitude of current 4 ~ 5 times larger than the prediction from the fluid moments code. Bootstrap currents in NCSX and HSX plasmas are also calculated. The effect of degrading quasi-symmetry on the bootstrap current is examined. [1] D. J. Strickler, S. P. Hirshman, D. A. Spong, et al., Fusion Sci. Tech. 45, 15 (2004). [2] K. C. Shaing, E. C. Crume, Jr., J. S. Tolliver, S. P. Hirshman, W. I. van Rij, Phys. Fluids B 1, 148 (1989). [3] D. A. Spong, Phys. Plasmas 12, 056114 (2005). ________________________________ Work supported by U.S. Department of Energy under Grant DE-FG02-03ER54699 at the University of Montana and Contract DE-AC05-00OR22725 at ORNL with UT-Battelle, LLC.

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Ballooning Stability in Quasi-symmetric Stellarators

R. Sánchez,1 A. S. Ware,2 E. Mondloch,2 D. del-Castillo-Negrete,3 D.A. Spong3

1Universidad de Carlos III de Madrid, Madrid. Spain 2Department of Physics and Astronomy, University of Montana, Missoula MT 59812, USA

3Oak Ridge National Laboratory, P.O. Box 2009, Oak Ridge TN 37831-8070, USA In this work, global ballooning stability is examined for three different quasi-symmetric stellarator equilibria: the quasi-poloidally symmetric QPS [1], the quasi-helically symmetric HSX [2], and the quasi-axisymmetric NCSX [3]. Previous work on ideal MHD ballooning stability of the Quasi-Poloidal Stellarator (QPS) focused on local calculations of stability [4]. In this work, theoretical calculations of global ballooning mode stability in QPS, HSX, and NCSX are done using the results of infinite-n ballooning theory and the ray tracing techniques introduced by Dewar and Glasser [5]. Comparison of the Dewar-Glasser formalism and the results from the finite-n TERPSICHORE code has been undertaken by Cooper et al. [6] for a large-aspect ratio, ten-field period stellarator. More recent work using the ray tracing technique has included testing ballooning stability in the LHD [7], Heliotron J [8], and NCSX [9] stellarators. Here, the mode structure of cylindrical and spherical ballooning surfaces in the different devices is examined to try to ascertain the role they play in allowing or impeding access to second ballooning stability regimes. These results will be compared to local calculations of second stability in these devices [10]. [1] D. J. Strickler, S. P. Hirshman, D. A. Spong, et al., Fusion Sci. Tech. 45, 15 (2004). [2] F. S. B. Anderson, et al., Fusion Technol. 27, 273 (1995). [3] G. H. Neilson, et al., Phys. Plasmas, 7, 1911 (2000). [4] A. S. Ware, D. Westerly, E. Barcikowski, et al., Phys. Plasmas 11, 2453 (2004). [5] R. L. Dewar and A. Glasser, Phys. Fluids 26, 3038 (1983). [6] W. A. Cooper, D. B. Singleton, and R. L. Dewar, Phys. Plasmas 3, 275 (1996). [7] P. Cuthbert, J. L. V. Lewandowski, H. J. Gardner, et al., Phys. Plasmas 5, 2921 (1998). [8] O. Yamagishi, Y. Nakamura, and K. Kondo, Phys. Plasmas 8, 2750 (2001). [9] M. H. Redi, J. L. Johnson, S. Klasky, et al., Phys. Plasmas 9, 1990 (2002). [10] S. R. Hudson, C. C. Hegna, R. Torasso and A. Ware, Plasma Phys. Control. Fusion 46, 869 (2004). ________________________________ Work supported by U.S. Department of Energy under Grant DE-FG02-03ER54699 at the University of Montana and Contract DE-AC05-00OR22725 at ORNL with UT-Battelle, LLC.

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Overview of Recent Results from HSX and the Planned ExperimentalProgram

D.T. Anderson, A. Abdou, A.F. Almagri, F.S.B. Anderson, D.L. Brower1, J. Canik,C. Deng1, S.P. Gerhardt2, W. Guttenfelder, C. Lechte, K.M. Likin, H. Lu, S. Oh,

P.H. Probert, J. Radder, V. Sakaguchi, J. Schmitt, J.N. Talmadge, K. Zhai

HSX Plasma Laboratory, University of Wisconsin-Madison1University of California at Los Angeles

2Present address: Princeton Plasma Physics Laboratory

Up to now HSX has demonstrated that the quasihelical symmetry (QHS) does indeedimprove single-particle confinement over a non-optimized 3-D configuration, as predicted.Some neoclassical differences have been observed under the present operating conditions.Using flows induced with a biased electrode we have demonstrated that quasisymmetry leadsto reduced parallel viscous damping. The flow in the QHS configuration rises and dampsmore slowly than in the Mirror (quasihelical symmetry intentionally broken) and attainsapproximately twice the flow velocity for the same drive. This work is being extended to lookat flow damping in the presence of islands that locally break the quasihelical symmetry. Thedensity profile is broader and not as peaked in the Mirror compared to the QHSconfiguration. We have concluded, by making comparisons of on-axis to off-axis heating,that thermodiffusion may account for the difference, with low thermodiffusion in the QHScase. We do not yet see large, conclusive differences in the temperature profiles between thetwo configurations consistent with the expected dominant role for anomalous transport underpresent operating conditions.

We have used the 1-D transport code, ASTRA to help point the way to understand therelative role of anomalous versus neoclassical transport so that we can move to a regimewhere the neoclassical differences would be emphasized. Our goals are to increase thedensity, the magnetic field and heating power. By this fall we will raise the magnetic field to1.0 T. Ordinary-mode heating with our 28 GHz gyrotron will be employed using a newquasioptical transmission line to deliver the full 200kW (minus losses in the line) to the torus.This will allow us to raise the density by a factor of 2, decrease anomalous transport, reducethe contribution of the nonthermal population to the global stored energy and raise theconfinement time. Over the next 1 _ years, another 200 kW gyrotron will be brought intooperation, making available 400 kW total microwave power. Power modulation of the 2nd

gyrotron will permit a determination of the thermal conductivity by heat wave analysis thatcan be compared to steady-state measurements. A steerable launcher will give some controlover Te profiles for thermal conductivity and thermodiffusion studies.

Empirical stellarator database studies suggest that global confinement improves withdecreasing effective ripple, even when the plasma collisionality is relatively high. Byenergizing all of the main HSX coils except for those of Type 3 (of 6 types), a magneticconfiguration is made which has a high effective ripple (nearly a factor of four over ourMirror mode), but similar volume, transform and well depth to the QHS configuration.Variation of the coil-3 current with respect to the rest of the modular coils will allowcomparisons of confinement over a wide range of effective ripple in a single device.

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Structure of Edge Turbulence in the HSX Stellarator

C. Lechte, W. Guttenfelder, J.N. Talmadge, D.T. Anderson

HSX Plasma Laboratory, University of Wisconsin-Madison

The magnetic field of HSX has a unique helical quasisymmetry, which can bemodified by an auxiliary coil set to alter the magnetic field spectrum, as well as increaseor decrease the magnetic well depth. Hydrogen plasmas, produced by up to 130 kW ofECRH power at 5 kG, exhibit turbulent behavior which is diagnosed by Langmuir probearrays at the plasma edge (r/a > 0.6). The main probe has 16 pins, all located on the sameflux surface. A reference probe can be positioned to intercept a magnetic field lineoriginating from the multipin probe. The multipin probe is advanced radially, while thereference probe stays fixed.

Measurements of plasma density and potential are processed with correlationanalysis and conditional sampling to find the structure of particle transport events("blobs") at the plasma edge. The influence of the different magnetic configurations onturbulent transport is investigated. Furthermore, the density-potential crossphases areused to classify the underlying instabilities (i.e. drift wave vs. interchange.)

First results from inside the separatrix show blobs moving mostly in the poloidaldirection with their speed being consistent with the overall plasma rotation. Thecrossphase is small, hinting at drift wave dynamics. While the blob diameter ofapproximately 2 cm does not vary greatly with the different magnetic configurations, it isexpected to scale with the drift radius ρs = cs/ωci (sound speed over ion cyclotronfrequency).

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Quasisymmetry-Breaking and Increased Parallel Viscous Damping nearMagnetic Islands in HSX

J.N. Talmadge, J. Schmitt, S.P. Gerhardt+ and D.T. Anderson

HSX Plasma Laboratory, University of Wisconsin-Madison+ Present address: Princeton Plasma Physics Laboratory

The standard quasihelically symmetric (QHS) configuration in HSX has a singledominant [n,m] = [4,1] component in the magnetic field spectrum. One mechanism bywhich the quasisymmetry can be broken is with the introduction of a magnetic island intothe topology.1 A set of auxiliary coils is to vary the rotational transform and the magneticwell depth and also to introduce natural magnetic islands into the plasma. These islandshave toroidal mode numbers that are multiples of the number of field periods (four) inHSX. One striking example of an island structure that can be formed is when thetransform for the QHS configuration, which is 1.05 at the center rising to 1.12 at theedge, is lowered to 1.0 at the half-radius and a large n = 4, m = 4 island appears. For thiscase, spectral components such as the [8,5] and the [0,3] terms appear that break thequasisymmetry. These components arise because of the interaction of the main helicalcomponent [4,1] with the island perturbation [4,4].

To quantify the increase in parallel viscous damping due to the additional spectralcomponents, we solve two momentum balance equations in Hamada coordinates on aflux surface to obtain the slow and fast decay times.2 Both decay rates sharply increase inthe vicinity of the islands due to the distortion of the magnetic surfaces.

We have attempted to measure this increase in the parallel viscous damping in thevicinity of natural islands formed in HSX. We use an electrode inserted inside the lastclosed flux surface to draw a radial current and exert a torque on the plasma. The flow ismeasured with a 6-tipped Mach probe. A multi-parameter fit to the flow evolution is usedto extract the two decay rates. We have some initial experimental data for a configurationin which we raise the rotational transform so that an n = 8 m= 7 island appears interior tothe separatrix. The data shows a localized increase in the slow damping rate in thevicinity of the island.

1 S.P. Gerhardt, D.T. Anderson and J.N. Talmadge, Phys. Plasmas 12, 012504 (2005).2 M. Coronado and J.N. Talmadge, Phys. Fluids B5, 1200 (1993).

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Evidence for Fast-Electron-Driven Alfvenic Modes in the HSX Stellarator

D.L. Brower1, C. Deng1, D.A. Spong2, A. Abdou3, A.F. Almagri3, D.T. Anderson3,F.S.B. Anderson3, W. Guttenfelder3, K. Likin3, S. Oh, V. Sakaguchi3, J.N. Talmadge3, K.

Zhai3

1University of California at Los Angeles, Los Angeles, California USA2Oak Ridge National Laboratory, Oak Ridge, Tennessee USA3University of Wisconsin-Madison, Madison, Wisconsin USA

The helically-symmetric experiment (HSX) stellarator device is the first of a newgeneration of stellarators that exploit the concept of quasi-symmetric magnetic fields. InHSX, the plasma is both produced and heated by use of electron cyclotron resonance heating(ECRH) at the 2nd harmonic X-mode resonance. This heating configuration generates anonthermal energetic electron population. Herein, we report on the first experimentalevidence for fast-electron-driven Global Alfven Eigenmodes (GAE). This mode haspreviously been observed in both tokamaks and stellarators but it was always driven byenergetic ions, not electrons. Evidence for this instability is obtained from quasi-helicallysymmetric HSX plasmas. Potential consequences of these measurements are twofold; (1) fastelectrons can drive the GAE instability, and (2) quasi-symmetry makes a difference by betterconfining the particles that drive the instability as compared to the conventional stellaratorconfiguration.

We report on several features of this fluctuation. It is a coherent mode that isexperimentally observed in the plasma core and edge by external magnetic coils,interferometry, ECE and Langmuir probes diagnostics. Fluctuations are observed in thefrequency range of 20-120 kHz and scale with ion mass density according to expectations forAlfvenic modes. The mode is observed to be global with odd poloidal mode number (inferredfrom interferometry, possibly m=1) and is present in quasi-helically symmetric HSXplasmas. When quasi-helical symmetry is broken, the mode is no longer observed. Theorypredicts a GAE mode in the gap below the Alfven continua can be excited in the frequencyrange of the measured fluctuations. By employing a biased electrode inserted deep into theplasma, flows can be generated. Under these conditions, the Alfvenic mode amplitude canincrease and the fluctuation is even observed in the conventional stellarator configuration.Shifts in the measured frequency can be used to determine the core radial electric field andplasma flow dynamics. Issues related to mode structure, growth rates, flows. and magneticconfiguration dependence are unresolved and remain active research topics. Supported byU.S.D.O.E.

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]DegG¤Ä�}lÅÆegGZÇ@fSCZ{1ICF|ÈegWFYÉW d[egf@GÊX�GZ~­egfSbFe6Ë�Ì�ÍlÎÐÏFÑ W¥{aINGZÇ@WZ{nfzXgGJÇÓÒÔ`aC�~$GJY�{Õ~$GJ|gYfz{nf@GZYVC Ö˳×PØZÍÙÏ�Ú¨ÛZÜuKÞݾT�J�ß�����1���N��àH¢ámÕâVfÓ{1eÕegfSbFeaEÁCLâlGJIáÛ¥ÜQãåä {1W |gbFGJ|n{nf@WFÇ�|$GJcß{nINWFÇgvHGJW `æf@|jç�GJd�{nf@C |Y�ÒÁYè{1GJ`�{negWZ{¨EgIC�~$cgdJGZYÕGZ|gGJIbFG�{nf@d¨fSCF|gY¤CFÖÔÛ¥éFÜQêgë1ì­=1K)íîcgI�{negGJI`aCFINGZ\AÖ©CFIïÛ¯Ú8Û¥ÜuKÞÝNðòñ máó˳×PØZͤó�ÏôÚåÛZÜuKÞÝLðòñ m�\ {negGôGJ|$GJINb G�{1fSd-EgWFIè{1fSdJÇSGJY¤fS|g~gcgdZG-WáYNfSbF|gfSõgdJW |1{¨E$INGJYYNcgIG-WF|gfSYNCZ{nINCFEnÒâVfÓ{1e�ö�÷ùøÙö�úÉ=Lh9<ÙGte$W[XgG¯`aC�~gf@õ$GJ~Â{negG2{negINGZG�ûL~gf@`aGZ|gYNfSCF|gWFÇùü�ÏFÅ�ý�þ�ÿ���B#dJC�~gG2{nC¶`aC�~gGJÇWF|-GZ|gGJIbFG�{nf@dsYNEHGJdZf@GZY�âVfz{ne¨WlX�WFIf@W |1{�CFÖ�W¤vgfzûLÿ�W��uâlGJÇSÇ@fSWF|¨~gf@Yè{1If@vgcj{1fSCF|�Ö©cg|gd�{nf@C |¤{negWZ{sYWZ{1fSY�ûõgGZY�{negG2dJCF|gYè{1IWFf@|n{������ ���åÜtm7WF|g~ÕegWLX�G_G��u{1GZ|g~gGZ~t{1egG2ÏFÅ ]����_R�p�� BD}lq����ÔYè{1WFvgfSÇSfz{ ÒdJC�~gG2{1CôfS|nX�GJYè{1fSbFWZ{nGl{1egGtG��HGJd�{nYÉCFÖ�EgIGJYYNcgIG¤WF|gfSYNCZ{nINCFEnÒòf@|Õ{ âÉC-ÇSf@`afÓ{1Y=�]DegG¯ÇSCLâÉGZIÉÇSf@`afÓ{af@YvgWFYGJ~òCF|­W¨EgcgIGJÇÓÒ��$cgf@~òysINcgYrjW ÇzûLqVvHGJI`aWF|òGZ|gGJIbZÒ EgINfS|gdZf@EgÇSGî�8ü�fSbF|gC INfS|gba{negGÕY�{1W vgf@ÇSfSYNfS|gbruf@|$G�{1fSd9fS|n{1GZbFINWFÇSýÕWF|g~�{negG¨cgEgEHGJIÕÇ@fS`afz{9f@YÕCFvß{nWFfS|gGJ~ Ö©INCF` WF|)GJ|$GJINb¥Ò E$INfS|gdJfSEgÇSG9fS|�âVegfSd[e{1e$G�egCZ{ÈE$WFI�{nf@dZÇ@GáEgIGJYYNcgIG�W |g~ dJcgIINGZ|1{�~$GJ|gYfz{ Ò8IGJÖ©IWFf@| Ö©ICF` f@|n{1GZINWFdÊ{1fS|gb�âVfz{ne {1egG�~jÒ�û|gWF`afSdJY2CFÖg{1e$G�f@|gYè{1WFv$f@ÇSfz{ ÒávÁGZdJWFcgYGù{1egGZf@ID~gfSWF`aWFbF|$G�{1fSds~gINfSÖ {sÖ©IG��ucgGJ|$d�Ò�fSYDdJCF|gYf@~$GJINGZ~9`tcgd[eÇSWFINbFGZI�{1e$WF|¯{1egGl~gCF`af@|$WF|n{VbFINCLâD{1e�IWZ{1GZ=��-<�G�egWLXgG�YNEHGJdJfSõgdZWFÇ@ÇÓÒÈfS|nX�GJYè{1fSbFWZ{nGJ~Õ{negGÉfS|gY�{nWFvgfSÇzûfÓ{ Ò­E$INCFEHGJIè{1fSGJY_CFÖ�WÕ}lGJÇSfSCZ{1ICF|9~gGÊXÁf@dZGAâVfz{ne�WÕ`ÕWjç�CFIAIWF~gfScgY�Ï �"!Jð WF|g~a{1CZ{nWFǶ˳Ì�Í$#>Ï �%! Ñ \âVegGZINGù{1egG�GZ|gGJIbFG�{nf@dsEgW I�{1fSdJÇSG�dJC |1{nINfSvgcß{nf@CF|Ð˳Ì&�QÍ�X$W INfSGJYDÖ©INC ` ÜÈ{nCïÛ��SÏ Ñ Ö©CFI¤ö ÷(' ö�ú)�+*�=,ùCZ{neò`aC�~gGJÇSYs~gGJ`aCF|$Y�{1IWZ{1GÕW�YNfSbF|gfSõgdJW |1{¶Y�{nWFvgfSÇ@fSYNW¥{1fSCF|­CFÖ�W�bFÇSCFvgWFÇ�ð ' ×-�.* '0/ `aC�~gGaWFY˳Ì&�QÍ ' Ë�Ì�ͤWFEgE$INCFWFd[e$GJY9Û ' Ï�\ßâVfÓ{1el{negGD|gCF|ßûLf@|n{nGJINW d�{1fS|gb�egC¥{2EgWFIè{1fSdJÇSGD`ÕC�~gGZÇjXÁf@Iè{1cgW Ç@ÇÓÒ-IGJWFd[eßûfS|gbÕ{negGÂEHCFfS|n{¶C Ö�`aWFINb f@|gW Ç�Yè{1WFv$f@ÇSfz{ ÒÈâVegGZ| ˳Ì&�FÍ ' Ë�Ì�Í�# Û ' *�=�?åX�WFIf@WZ{nf@C |òCFÖ�ö ÷(' ö�ú&WZ{õ1�ÁGJ~ Ë�Ì&�QÍ ' Ë Ì�Í�� Û ' ÏïYNegCLâVY¯W¨|gCZ{nf@dZGJWFv$Ç@GÕ~gGJdZINGZWFYNGÂf@|�{1egGaWFvgYCFÇScß{1GÕ`aWFbF|gfÓ{1cg~$GÂCFÖ�{1egGcg|gYè{1WFv$Ç@G�GZf@bFGZ|nX$W Ç@cgGsfS|�{1egGÉIWF|gbFG ÛDó�ö�÷ ' ö�ú�ó / f@|¯{negG2�gcgfS~�yVIcgYNroWFÇÓû[qsvHGJI`ÕW |-`ÕC�~gGZÇ@=]DegG7|gCF|ßûLf@|n{1GZINWFdÊ{1fS|gb­GZ|gGJIbFG�{nf@d7EgWFIè{1fSdJÇSG7`aC�~gGJÇ2INGZ`aWFf@|$Y¶|gGZWFIÂ`aWFIbFfS|gWFÇSfz{ Ò!fS|�{negG7IWF|gbFGÛDó�ö�÷ ' ö�ú�ó+*�=

3547684 924:<;�=>;�?@;�ACBED>FHGJILK@MONP�QSRUTWVYX>QSD>TZX�D[GUTY\^]ZD�X>_JTYRUIa`cbZd�egf5h5h�iZjkf�iZ4f54 l�4�9m;5n�;�o5p@qsr@tOD�F&GUIuKOvHwxRyX�`7zU{UP|F@}~vHVW� RUT|�>`�RUT�v~I�GJP��[G[vH_U��P�`S�&�ORUTY\URJTY�@}�� ���1RUIa`��U�U��egf5h5h�iZj�H� 4�35h5�54�547�14 � 4&�c��;g�5B���D>F~GUIuK vH_J��P|`���D>��`��ZD�F�F�`¡ Zb�egf5h5h5h5jk35f5h�iZ4iZ47¢£4�¤�4&6c�¥pZ�¥¦;5§C;�?@¨ª©�4�«m4�¬cACB���n�;�?@K7vH_U��P�`HM IaNQ­\JP$®Eeg35¯ �5° jkf5� � 4� 47�14�±&4���²5rZ?Y�¥²5?@K�«k4�¢�476³p@§ �¥�¥p@¨´;�?@¨ª684�µH40:WBJt�n�B���K vHIaGUP|�¶G·v~_U��P�`�®Z®Eeg35¯5¸5¯5j�iZ¸5�54

P1-26

41

Electron Cyclotron Current Drive Compensation of the BootstrapCurrent in Quasi-symmetric Reactor Devices

S. Ferrando i Margalet1, W.A. Cooper1, F. Volpe2, F. Castejon3

1Centre de Recherches en Physique des Plasmas, EURATOM-Confederation Suisse, EPFL, 1015Lausanne, Switzerland

2UKAEA Fusion, Experim. Dept. D3 Culham, Oxfordshire OX14 3DB, United Kingdom3Laboratorio Nacional de Fusion, EURATOM-CIEMAT, 28040 Madrid, Spain

Previous results have shown that the bootstrap current (BC) can considerably affect the equi-librium and stability of some reactor-size stellarator configurations through its alteration of therotational transform profile1. This suggests that a way to externally compensate the effects ofthe BC may be needed in order to keep the ι within MHD stable values.

The present work is devoted to model the current driven (CD) by an electromagnetic wavein the region where the BC profile needs to be locally altered. The simulations are carried outwith the 3D ray-tracing code ART in which an interface with a current drive module based onthe solution of the Langevin equations has been implemented. The ensemble calculates thecurrent drive density at each magnetic surface pierced by the ray. The method allows to inves-tigate different launching scenarios (position, wave frequency, input power, polarization, etc.)depending on the amount, localization and magnitude of the current to be induced.

Two contrasting configurations have been considered, a 3-period quasi-axisymmetric (QAS)and a 4-period quasi helically-symmetric (QHS), in which the BC affects the rotational trans-form in opposite ways.

In the QAS case, the goal is to induce a counter-current in the vicinity of ρ = 0.76 wherethe ι approaches the resonant value ιc = 2/3 value, at β = 6.4%. A second harmonic X-modewave launched from a high field region, with 385 GHz of frequency (the configuration hasB0 = 4.9 Tesla) and 1.5 MWatt of power has been modeled which drives a current opposite tothe BC in the desired location. Both currents together lead to an equilibrium in which the ι isheld well beneath the ιc = 2/3 value ensuring that the configuration is stable.

In contrast, for the QHS case studied, the idea is to create a current in the same directionas the BC to further decrease the ι near the axis at β = 3%, pushing it away from the ιc = 1rational value. This has been obtained with a 3rd harmonic X-polarized electromagnetic wavewith 500 GHz of frequency (B0 = 5.6 Tesla) launched from the top of the plasma. In this case10 KWatt of input power was sufficient to maintain the ι below unity. Higher power would altertoo drastically the ι making the convergence to an equilibrium more difficult.

The use of electron Bernstein waves to drive the current near the axis for the QHS case isalso studied in order to investigate other means of current drive with lower input frequency.

1. S. Ferrando i Margalet et al, FS&T 46 (2004), 44

P1-27

42

3D Full Wave Propagation Code for Warm Plasma

N. Mellet, W. A. Cooper, P. Popovich, L.Villard, S. Brunner

Centre de Recherches en Physique des plasmas,

Association EURATOM – Confédération Suisse, EPFL, 1015 Lausanne, Switzerland

Simulations of wave propagation in the low-frequency range are made using the three-

dimensional code LEMan. This permits to study wave heating and fast ion destabilisation.

This code solves a wave equation derived from the linearised Maxwell equations. Until now,

all the calculations have been performed within a cold formulation. A warm model is now

under development. The methodology is unchanged but the dielectric tensor has now finite

temperature effects. It is calculated from the Vlasov equation but it does not take into account

finite Larmor Radius terms. Nevertheless, effects in the direction parallel to the equilibrium

magnetic field are retained and the parallel vector is computed exactly. This last component

has a particularly simple form thanks to the Fourier decomposition in toroidal and poloidal

angles.

From the previous version of LEMan, a numerical effort has been made to parallelise

the code with MPI. This permits to improve the efficiency of computing and run cases

needing more memory. It is particularly interesting for 3D warm model cases which require

increased cpu and memory limit for the calculation of the dielectric tensor. But it is useful in

the cold model, too. For instance, in the ICRF domain, you have to take a great number of

Fourier modes into account when the wavelengths become small compared with the plasma

dimensions.

P1-28

43

VENUS+Æf -

A BOOTSTRAP CURRENT CALCULATIONMODULE FOR 3D CONFIGURATIONS

M. Yu. Isaev 1, S. Brunner2, W.A. Cooper2, T. M. Tran2,

A.Bergmann3, C.D.Beidler4, J.Geiger4, H. Maassberg4,

J.N�uhrenberg4, M. Schmidt4

1 Nuclear Fusion Institute, RRC "Kurchatov Institute",

Moscow, Russia2 Centre de Recherches en Physique des Plasmas, EPFL,

Lausanne, Switzerland3 Max-Planck-Institut f�ur Plasmaphysik, Garching, FRG4 Max-Planck-Institut f�ur Plasmaphysik, Greifswald, FRG

We present a new 3D code - VENUS+Æf - for neoclassical transport calcula-

tions in nonaxisymmetric toroidal systems. Numerical drift orbits from the original

VENUS code [1] and the Æf method for tokamak transport calculations [2], [3] are

combined. The �rst results obtained with VENUS+Æf are compared with neoclas-

sical theory for di�erent collisional regimes in a JT-60 tokamak test case with mo-

noenergetic particles and with a Maxwellian distribution. Benchmarks with DKES

code results for the bootstrap current in the W7X con�guration [4] as well as further

VENUS+Æf developments are discussed.

References

[1] O.Fischer, W. A. Cooper, M. Isaev, L. Villard, Nucl. Fusion, v. 42, 817(2002).

[2] Z.Lin, W.Tang, W.Lee, Phys. Plasmas, v. 2, 2975(1995).

[3] A. Bergmann, A.G. Peeters, S. D. Pinches, Phys. Plasmas, v. 8, 5192(2001).

[4] C.D.Beidler, S.V.Kasilov, W.Kernbichler et al. Proc. of the 14th Int. Stell. Workshop,Greifswald, FRG, 2003.

P1-29

44

The First Electron Plasmas in the Columbia Non-neutral Torus

J. P. Kremer, R. G. Lefrancois, T. Sunn Pedersen, Q. Marksteiner, X. Sarasola*

Dept. of Applied Physics and Applied Math, Columbia University, New York, NY 10025, USA

* Currently at CIEMAT, Madrid, Spain

The Columbia Non-neutral Torus (CNT) started operation in November 2004. Thisultra-low aspect ratio stellarator was designed to study the equilibrium, stability, and confinementof non-neutral plasmas confined on magnetic surfaces. CNT features a unique and simple coilset consisting of two pairs of planar circular coils, a configuration that is simpler than that of anyother stellarator or tokamak.

A detailed field line mapping of CNT has been performed and an aspect ratio of <1.9has been confirmed. The first electron plasma experiments are presently being carried out. Afirst generation four segment tungsten electron emitter has been inserted into the confinementregion to make and diagnose pure electron plasmas. The presence of at least 1011 electrons inthe confining region with a confinement time of 10 milliseconds has been measured, thusconfirming that an equilibrium exists. The emission rate of electrons and the potential profilehave been measured for a range of magnetic field strengths, neutral pressures and radialpositions of the emitter segments. As expected, confinement improves with increased magneticfield and decreases with neutral pressure. At higher neutral pressure, confinement time is seento degrade linearly in time during the life of the plasma. The rate of this degradation increaseswith neutral pressure. We hypothesize that this is due to ion contamination. When electrons areemitted close to the magnetic axis, a hyperbolic-like radial potential profile results. Whenemitted closer to the edge of the plasma a hollow radial potential profile results although there issome electron transport towards the axis. As expected, electrons emitted closer to the magneticaxis have a longer confinement time than those emitted closer to the edge. Detailed results ofthese experiments will be presented.

The next set of experiments (currently underway) will investigate the perturbative effectsof insulated rods, like those of the electron emitter and the internal diagnostics, in the plasma.Once these are completed, a new probe array consisting of four emissive probes and eightLangmuir probes will be used to measure the potential, density, and temperature profiles of theelectron plasmas. The degree of ion contamination will be determined by measuring the ionsaturation current, if any, on the Langmuir probes. These measurements will allow for theoptimization of pure electron plasmas for small Debye length. The results and progress onthese experiments will be presented.

Another probe array consisting of emissive probes is currently being constructed andwill be mounted on a rotatable arm. This will allow the measurement of the potential on a largesection of a single toroidal cross-section. A second generation electron emitter, consisting ofeight separate segments, is also being constructed. Also under construction is a set of coppermeshes which will be used to surround the confining region. Theory predicts that the presenceof a conforming electrostatic boundary will improve confinement. These meshes will also beused as a set of capacitive diagnostics and, when biased, as a means of pushing on the plasma.Progress on these construction projects will be presented.

P1-30

45

Field Line Mapping Results in the CNT Stellarator

X. Sarasola*, T. Sunn Pedersen, J. P. Kremer, R. G. Lefrancois, Q. Marksteiner

Dept. of Applied Physics and Applied Math, Columbia University, New York, NY 10025, USA * Currently at Laboratorio Nacional de Fusion, CIEMAT, 28040 Madrid, Spain

N.Ahmad

UC Berkeley, Berkeley, CA, USA

The Columbia Non-neutral Torus (CNT), located at Columbia University, is a toroidal, ultra-high vacuum stellarator designed to confine pure electron and other nonneutral plasmas. Its coil configuration is the simplest of any stellarator constructed, since it consists only of two pairs of circular planar copper coils. CNT started operation in November 2004. During its first months of operation a detailed mapping of the nested magnetic surfaces has been developed using the fluorescent method.

An electron beam was emitted along a field line by a small moveable electron gun. Different beam energies (ranging from 50 to 200 eV) were used to perform the field line mapping. The e-beam emitted by the electron gun followed the field lines around the torus and hit two moveable ZnO coated aluminum rods that emit visible light when struck by the e-beam. For each position of the e-gun, the phosphor rods scanned the cross-section of the torus allowing a standard digital camera to record a single magnetic surface in a five second exposure. Multiple photos were taken and then manipulated and superposed using IDL software to create composite images of the nested magnetic surfaces. Detailed mapping of the magnetic flux surfaces was completed at a variety of magnetic configurations and at pressures in the 10-8 Torr range.

The experimental results were compared with numerical calculations demonstrating that the obtained measurements agree very well with numerical predictions. In particular, the current configuration has an ultralow aspect ratio (A≤1.9) and excellent magnetic surface quality with no detectable island structures or stochastic regions, except at the edge of the plasma where a predicted island chain is present. These experimental results will be presented along with details of the field line mapping system.

P1-31

46

TUESDAY

4th October

47

48

Overview of Progress of LHD Experiment

A. Komori, S. Sakakibara, T. Mutoh, N. Ohyabu, K. Kawahata, O. Kaneko, Y. Nagayama,

H. Yamada, S. Kubo, K. Ida, S. Sudo, O. Motojima and LHD experimental Group

National Institute for Fusion Science, Toki 509-5292, Japan

Recently remarkable progress has been made, especially, in high-beta and steady-state

experiments on the Large Helical Device (LHD), which is a large heliotron with a major

radius of 3.6 m and a minor radius of 0.6 m. LHD offers a great opportunity to study

currentless plasmas, and full steady-state operation is expected, using superconducting

coils.

The optimization of rotational transform has been made for high-beta plasma

production from a viewpoint of particle transport and MHD stability. While an increment of

rotational transform restricts the Shafranov shift, which increases the ripple loss of

particles, it restrains the formation of a magnetic well in the core region, and a magnetic hill

in the peripheral region is enhanced. In the recent experiments, the configuration optimized

for these two subjects has been found out, and hence the average beta of 4.3 % was

achieved. The peripheral MHD activities were almost saturated and/or suppressed with an

increase in beta. Accordingly, they are not fatal subjects for high-beta plasma production.

Steady-state discharges were also successfully performed for more than 30 min by

using the magnetic-axis swing technique. The heat load along the divertor legs was largely

redistributed by the small temporal change of axis position of 3 cm, and the experimental

observation of heat load was well explained by analytic calculation. The plasma was heated

and sustained by ICRF heating, and additional EC and NBI heating. The central ion

temperature was around 2 keV, and the line-averaged electron density was around 0.7 ~ 0.8

× 1019 m–3. The average input power was 680 kW and the plasma duration was 31 min 45

sec. The total input energy to the plasma reached 1.3 GJ, which is the largest energy to high

temperature plasmas at the keV levels among magnetic confinement devices, including

tokamaks and helical devices. This successful long operation shows that the heliotron

configuration has a high potential as a steady-state fusion reactor.

These recent LHD achievements make helical fusion reactors more realistic. The design

activity for a steady state fusion reactor without disruption is advancing apace assuming

LHD configurations.

RT-01

49

PROGRESS IN NCSX AND QPS DESIGN AND CONSTRUCTION

W. Reiersen1, P Heitzenroeder1, G.H. Neilson1, B. Nelson2, M. Zarnstorff1, T. Brown1,M. Cole2, J. Chrzanowski1, P. Fogarty2, P. Goranson2, J. Lyon2, J. Schmidt1, R. Strykowsky1,

M. Viola1, and D. Williamson2

1Princeton Plasma Physics Laboratory, PO Box 451, MS-40, Princeton, NJ 085432Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831-6169

The National Compact Stellarator Experiment (NCSX) is being constructed at thePrinceton Plasma Physics Laboratory (PPPL) in partnership with the Oak Ridge NationalLaboratory (ORNL). The stellarator core is designed to produce a compact 3-D plasmathat combines stellarator and tokamak physics advantages. The engineering challenges ofNCSX stem from its complex geometry. From the project’s start in April, 2003 toSeptember, 2004, the fabrication specifications for the project’s two long-leadcomponents, the modular coil winding forms and the vacuum vessel, were developed. Anindustrial manufacturing R&D program refined the processes for their fabrication as wellas production cost and schedule estimates. The project passed a series of reviews andestablished its performance baseline with the Department of Energy. In September, 2004,fabrication was approved and contracts for these components were awarded. Thesuppliers have completed the engineering and tooling preparations and are in production.Meanwhile, the project completed preparations for winding the coils at PPPL by installinga coil manufacturing facility and developing all necessary processes through R&D. Themain activities for the next two years will be component manufacture, coil winding, andsub-assembly of the vacuum vessel and coil subsets. Machine sector sub-assembly,machine assembly, and testing will follow, leading to First Plasma in July, 2009.

The Quasi-Poloidal Stellarator Experiment (QPS) is an experiment to explore thequasi-poloidal approach to compact stellarators. It will be constructed at ORNL and is apartnership between PPPL, ORNL, and the University of Tennessee. The coil design isvery similar to NCSX, but QPS has a smaller aspect ratio and will have an external vacuumvessel. Activities for the next year will focus on R&D, including completion of aprototype modular coil. Detailed design will start in 2007 and the first plasma is expectedby 2011.

Research supported by the U.S. DOE under Contract No. DE-AC02-76CH03073with Princeton University and No. DE-AC05-00OR22725 with UT-Battelle, LLC.

IT-08

50

Configuration control for the confinement improvement in Heliotron J

T. Mizuuchi, F. Sano, K. Kondo1), K. Nagasaki, H. Okada, S. Kobayashi, S. Yamamoto, Y. Torii, K. Hanatani, Y. Nakamura1), Y. Suzuki1), M. Kaneko1), H. Arimoto1), J. Arakawa1),

T. Azuma1), T. Hamagami1), M. Kikutake1), G. Motojima1), K. Ohashi1), N. Shimazaki1), M. Yamada1), H. Yamazaki1), H. Kitagawa1), H. Nakamura1), T. Tsuji1), S. Watanabe1),

Y. Ijiri, T. Senju, K. Yaguchi, K. Sakamoto, K. Toshi, M. Shibano

Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, Japan. 1) Graduate School of Energy Science, Kyoto University, Gokasho, Uji 611-0011, Japan.

The Heliotron J device is a flexible concept-exploration facility for the helical-axis

heliotron concept, which is one of the advanced helical configurations based on the quasi-isodynamic approach. In this configuration, in addition to the toroidicity and the helicity, the bumpiness of the Fourier components in the Boozer-coordinate is introduced as the third knob to control the neo-classical transport. Besides the neoclassical viewpoint, the suppression of anomalous transport (or the formation of transport barrier) is another important issue in this study. One of the main objectives of the Heliotron J experiment is to study the configuration (Fourier components of the confinement field, the rational surfaces, the magnetic shear and/or magnetic well, the distance to the plasma facing materials, etc.) effects on the plasma performance.

The Heliotron J experiments have revealed the existence of the spontaneous transition to improved confinement modes similar to the H-mode. Although the transition is observed almost all ι(a)/2π configurations under a level of heating power, the ι(a)/2π-ranges where the peak values of HISS95 ≡ τE

exp/τEISS95 reach to ~1.8 are observed only near the major natural

resonances. One of the key factors for the H-mode quality might be the reduction of the poloidal viscous damping rate in the outer plasma region. According to preliminarily calculations based on the vacuum field, there seems to be some coincidence between the enhancement of HISS95-factor and the numerical reduction of the poloidal viscous damping rate coefficient. However, effects of the deformation of the edge magnetic flux surfaces due to the rationales or plasma current, and effects of the wall contact should be also considered.

In order to investigate the effect of the bumpiness (B04/B00) of the magnetic field component on the particle confinement, studies of fast ions produced by NBI or ICRF in low density (0.6-0.8×1019 m-3) plasmas have been performed in the range of 0.02 < B04/B00 < 0.16 at ρ = 0.5. Here Bmn is the poloidal/toroidal mode numbers of magnetic field strength. The decay time of the charge-exchange neutral flux for the tangentially injected beam ions increases with the bumpiness. In the ICRF minority heating experiment, the higher energetic tail components have been observed in the higher bumpiness configuration. These observations suggest that the configuration with higher bumpiness is favorable for the confinement of the passing/trapped particles.

In this paper, reporting the results from the recent experimental studies in Heliotron J, the configuration control and its effects on the plasma performance will be discussed.

IT-09

51

New Approach of Statistical Analysis and Modeling of Turbulent Processesin Plasma

N. N. Skvortsova*, V. Yu. Korolev**, G. M. Batanov*, A. E. Petrov*,K. A. Sarksyan*, N. K. Kharchev*, J. Sanchez***, and S. Kubo****

* General Physics, Russian Academy of Sciences, Moscow, 119991 Russia**Moscow State University, Moscow, 119899 Russia

***EURATOM-CIEMAT, 28040, Madrid, Spain****National Institute for Fusion Research, Toki, Japan

Experiments in ECRH plasma in three stellarators have shown the occurrence ofsteady-state low-frequency strong structural turbulence throughout the entire plasma column.A key feature of strong structural turbulence is the presence of stochastic plasma structures[1]. A new mathematical model is proposed for the probability distributions of thecharacteristics of the processes observed in turbulent plasmas. The model is based on formaltheoretical considerations related to probabilistic limit theorems for a nonhomogeneousrandom walk [2] and has the form of a finite mixture of Gaussian distributions [3].

The reliability of the model is confirmed by the results of a statistical analysis of theexperimental data on density and turbulent flux fluctuations in plasmas of the L-2M, LHD,and TJ-II stellarators with the use of the estimation–maximization algorithm [4]. It is shownthat low-frequency structural turbulence in a magnetized plasma of all these stellarators isrelated to non-Brownian transport, which is determined by the characteristic temporal andspatial scales of the ensembles of stochastic plasma structures. A new physical concept of theintermittence of plasma turbulent pulsations is developed on the basis of the statisticalseparation of mixtures in terms of the model proposed. The intermittence of plasma pulsationsis shown to be associated with the generation of plasma structures (solitons and vortices) andtheir nonlinear interaction, as well as with their damping and drift.

1. G. M. Batanov, V. E. Bening, V. Yu. Korolev, et al., JETP Lett. 78, (2003) 502.2. V. Bening and V. Korolev. Generalized Poisson Models and their Applications in insurance and finance.

VSP, Utrecht, The Netherlands, 2002.3. N. N. Skvortsova, V. Yu. Korolev, T. A. Maravina et al. Plasma Physics Reports, 31(2005). 57.4. S. A. Avazyan, V. M. Bukhshtaber, I. S. Enyukov, and L. D. Meshalkin, Applied Statistics: Classification

and Reduction of Dimensions (Finansy i Statistika, Moscow, 1989).

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A statistical approach to strange diffusion phenomenaB. Ph. van Milligen1, B.A. Carreras2 and R. Sánchez3

1 Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain2 Fusion Energy Division, Oak Ridge National Laboratory, P.O. Box 2001, Oak Ridge

TN 37831-2001, USA3 Departamento de Física, Universidad Carlos III, Avda. de la Universidad 30, 28911

Leganés, Spain

The study of particle (and heat) transport in fusion plasmas has revealed the existence ofwhat might be called “unusual” transport phenomena. Such phenomena are: unexpected scalingof the confinement time with system size, power degradation (i.e. sub-linear scaling of energycontent with power input), profile stiffness (also known as profile consistency), rapid transienttransport phenomena such as cold and heat pulses (travelling much faster than the diffusivetimescale would allow), non-local behaviour and central profile peaking during off-axis heating,associated with unexplained inward pinches. The standard modelling framework, essentiallyequal to Fick’s Law plus extensions, has great difficulty in providing an all-encompassing andsatisfactory explanation of all these phenomena.

This difficulty has motivated us to reconsider the basics of the modelling of diffusivephenomena. Diffusion is based on the well-known random walk. The random walk is capturedin all its generality in the Continuous Time Random Walk (CTRW) formalism. The CTRWformalism is directly related to the well-known Generalized Master Equation, which describesthe behaviour of tracer particle diffusion on a very fundamental level, and from which thephenomenological Fick’s Law can be derived under some specific assumptions. We show thatthese assumptions are not necessarily satisfied under fusion plasma conditions, in which caseother equations (such as the Fokker-Planck diffusion law or the Master Equation itself) providea better description of the phenomena. This fact may explain part of the observed “strange”phenomena (namely, the inward pinch)1,2.

To show how the remaining phenomena mentioned above may perhaps find anexplanation in the proposed alternative modelling framework, we have designed a toy model3,4

that incorporates a critical gradient mechanism, switching between rapid (super-diffusive) andnormal diffusive transport as a function of the local gradient5,6. It is then demonstrated that thistoy model, characterized by both criticality and non-locality, indeed produces the citedphenomena in a natural fashion.

1. B.Ph. van Milligen, P.D. Bons, B.A. Carreras and R. Sánchez, Eur. J. Phys. 26 (2005) 9132. B.Ph. van Milligen, B.A. Carreras and R. Sánchez, The foundations of diffision revisited, Tobe published in Plasma Physics and Controlled Fusion (2005)3. B.Ph. Van Milligen, R. Sánchez, and B.A. Carreras, Physics of Plasmas 11, 5 (2004) 22724. B.Ph. Van Milligen, B.A. Carreras, and R. Sánchez, Physics of Plasmas 11, 8 (2004) 37875. R. Sánchez, B.A. Carreras, and B.Ph. van Milligen, Phys. Rev. E 71 (2005) 0111116. R. Sánchez, B.Ph. van Milligen, and B.A. Carreras, Phys. Plasmas 12 (2005) 056105

IT-11

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Effect of magnetic configuration on density fluctuation and particle transport in LHD

K.Tanaka, C.Michael, LN.Vyacheslavov1*, A.L.Sanin*, O.Yamagishi, K.Ida, H.Yamada, M.Yoshinuma,

M.Yokoyama, J. Miyazawa, S,Morita, K.Kawahata, T.Tokzawa, M.Shoji

National Institute for Fusion Science, 322-6 Oroshi, Toki, 509-5292, Japan *Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia

The study of fluctuations and particle transport is important issue in heliotron and

stellarator devices as well as in tokamaks. A two dimensional phase contrast

interferometer (2D PCI) was developed to investigate fluctuation characteristics, which

play role in confinement. The current 2D PCI can detect fluctuations for which

0.3<k<1.5mm-1 and 5<f<500kHz. With the use of magnetic shear and the 2D detector,

the spatial resolution around 20% of averaged minor radius is possible presently. The

strongest fluctuations are localized in the plasma edge, where density gradients are

negative, but fluctuations also exist in the positive density gradient region of the hollow

density profile. The phase velocity of fluctuations in the positive gradient region is close

to plasma Er×Bt rotation. On the other hand, fluctuations in the negative density

gradient region propagate in the ion diamagnetic direction in the plasma frame and do

not follow Er×Bt rotation. This suggests there is a different nature of the fluctuations in

the positive and negative density gradient regions.

A particle transport was studied by means of density modulation experiments. The

systematic study was done at Rax=3.6m, which is so-called standard configuration [1].

The density profiles vary from peaked to hollow with increasing heating power. It was

also found that particle diffusion and convection are functions of electron temperature

and its gradient respectively. The magnetic configuration is another parameter, which

characterizes particle confinement. At more outward shifted configurations, helical

ripple becomes larger and the ergodic region becomes thicker, then neoclassical transport

becomes larger. However estimated diffusion coefficients are still around one order of

magnitude larger than neoclassical values in edge region, where ρ = 0.7 ~ 1.0 and they are

larger at more outward configurations. At the same time the convection velocity is found

to be comparable with neoclassical prediction at Rax=3.75, 3.9m and Rax=3.6m with low

power heating. Fluctuation level becomes larger at more outward configuration suggesting

correlation with particle diffusion. A comparison between observed fluctuation power and

theoretically computed linear growth rate of drift waves will be presented.

[1] K.Tanaka et al., to be published Nuclear Fusion

IT-12

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Materials for the Plasma-Facing Components of Steady State Stellarators

H. Bolt, J. Boscary, H. Greuner, P. Grigull, H. Maier, B. Streibl

Max-Planck-Institut für Plasmaphysik, Euratom AssociationGarching/Greifswald, Germany

The specific advantage of current-free stellarators is their inherent capability for fullsteady-state operation. This will lead to long discharges and the corresponding stationaryplasma exposure of the plasma-facing materials. Further to this, the absence of disruptionsrelaxes the requirements to the plasma-facing materials in terms of thermal shock stability,although ELM activity occurs also in stellarators and leads to fast transient surface loads onthe ms-time scale.

Another aspect regarding the plasma-material interactions in stellarators is thesensitivity to impurity accumulation in the core plasma. Thus, it is preferred to apply low-Zmaterials until operation scenarios are established which do not lead to this accumulationprocess. In the case of high-Z materials impurity accumulation will lead to a radiative plasmacollapse.

For the stellarator W7-X low-Z plasma-facing materials have been selected to protectthe divertor and the wall surfaces. Due to the stationary operation, the plasma-facing materialshave to be bonded or clamped to actively water-cooled substrates to remove the incident heatfluxes.The following materials have been selected to fulfil the operational requirements:1. A three directionally carbon fibre reinforced carbon composite (CFC) with very highthermal conductivity bonded to a water cooled CuCrZr heat sink for the divertor which will beexposed to heat fluxes up to 10MW/m2.2. Isotropic fine grain graphite tiles mechanically clamped to a CuCrZr heat sink which isbrazed to a stainless steel cooling tube for the areas of moderate heat fluxes up to 0.5 MW/m2

(baffles, inner wall).3. Thick boron carbide coating on water cooled steel panels for the outer wall surfaces withlow heat fluxes up to 0.2 MW/m2. This coating would be applied on most surfaces only afterthe initial operation.In the presentation the properties of these materials will be discussed with a view to theplasma-wall interaction in W7-X.

different. The long operation times of several years between refurbishment shut downs andthe low neutron irradiation resistance will most likely prevent the use of low-Z materials.Tungsten as a main candidate high-Z material is presently being intensely investigated. Theproperties of tungsten coatings and of massive tungsten as well as the related componenttechnology will be discussed in the presentation.

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Potential Ternary Compounds for First Wall Fusion Applications

D.J. O'Connor, E. Kisi, D. Riley, M. HealyUniversity of Newcastle, NSW 2308 Australia

The demands placed on a first wall in a fusion facility are both numerous anddemanding. In most cases up till now, the materials considered have largely been elemental ortwo component alloys but so far none have met the demanding benchmarks for a practicalsolution for long term applications.

A family of compounds, call MAX Phases, cover a broad range of elements and havevery promising synthesis properties as well as physical properties which indicate that they arewell placed to be considered as potential candidates. There are over 600 compounds in thisfamily though only 50 known have been synthesised so far, so it is not yet possible to claim athorough study has been undertaken of this class of material. An examination of the propertiesof just one compound, Ti3SiC2, shows the potential for this class of materials.

Consideration of Ti3SiC2 is based on the earlier work on TiC and SiC as potential firstwall materials. As a three element material Ti3SiC2 is essentially a machineable ceramic withexceptional properties and is suited to both mechanical and electrical applications. Ti3SiC,has the high temperature and chemical resistance of a ceramic combined with a degree ofductility and a higher electrical conductivity than pure Ti. Furthermore, the material has farhigher thermal conductivity than commercial stainless steel or Ti alloys, and although it has ahigh fracture toughness at high temperatures, it can be machined using conventional hardenedsteel tools. It exhibits excellent damage tolerance and good thermal shock resistance.

Ti3SiC2 has the advantage that there are a number of synthesis processes establishedwhich provide the opportunity to tailor the synthesis to meet specialist needs. One form ofmanufacture, called Self-Propagation High-Temperature Synthesis (SHS) promises to bothform large quantities relatively inexpensively but also, through the high temperaturesgenerated, will facilitate bonding to a variety of surfaces.

Preliminary experiments have been conducted on the native surface composition and responseto low energy (2keV) He bombardment to characterise the materials equilibrium compositionand effects associated with preferential sputtering and annealing.

Future pathways for this research will be outlined.

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Recent results of LID experiments on LHD

T. Morisaki, S. Masuzaki, M. Kobayashi, K. Narihara, K. Tanaka, R. Sakamoto, S. Inagaki,

Y. Feng1, N. Ohyabu, A. Komori, O. Motojima and LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292 Japan 1Max-Planck-Institute fuer Plasmaphysik, EURAROM Association,

D-17941, Greifswald, Germany

The Local Island Divertor (LID) experiment has been performed in the Large Helical

Device (LHD) to achieve the confinement improvement via its outstanding capability of edge

plasma control. It has been demonstrated that the LID is equipped with fundamental

divertor functions, i.e. efficient pumping capacity and screening effect for impurities.1

About 20% of confinement improvement from the ISS95 scaling raw has been demonstrated

in the outward shifted configuration until the last experimental campaign.2

Recently highly peaked electron density profiles are achieved with the hydrogen pellet

injection during LID discharges. The steep density gradient is formed in the internal region

near the rational surface of q=2 in the density decay phase after the pellet injection. In

these discharges, the height or shape of the edge pedestal does not change so much. The

plasma stored energy or central beta value increases and reaches its maximum as the density

decrease, which is a typical behavior of the reheat mode. It has been found that the

increase of the electron temperature mainly contributes the pressure rise at the center.

Because of this increase in central pressure, the large Shafranov is observed in electron

temperature and density profiles measured with the Thomson scattering system. On the

other hand, in the helical divertor (HD) configuration, peaking of the electron density profile

in the reheat mode after the pellet injection is mild, compared to that in the LID configuration.

These phenomena suggest the formation of internal transport barrier during the LID discharge.

In fact, an indication of the peaking in the electron temperature profile can also be seen in the

same region as the density profile, although it is much milder than that of the density profile.

In the workshop, results of the energy and particle transport analyses for the barrier will

be discussed in detail. An overview of the LID experiment for the last two years,

especially focused on the newly observed results from the modeling study with the

EMC3-EIRENE code, will also be presented.

1. T. Morisaki, et al., J. Nucl. Mater. 337-339 (2005) 154.

2. A. Komori, et al., to be published in Nucl. Fusion.

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Recycling and impurity retention in high-density, improved-confinement plasmas in W7-AS

Y. Fenga, F. Sardeia, P. Grigulla, F. Wagnera, J. Kisslingerb, K. McCormickb, D.Reiterc

a Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald, Euratom Association,Wendelsteinstr. 1, D-17491 Greifswald, Germanyb Max-Planck-Institut für Plasmaphysik, Euratom Association, D-85748 Garching,Germanyc Institut für Plasmaphysik, Forschungszentrum Jülich Gmbh, Euratom Association,Trilateral Euregio Cluster, D-52425 Jülich, Germany

In contrast to pre-divertor limiter operation, the island divertor in W7-AS enabledplasma density control even in the presence of a strong NBI-source, showing a significantimprovement of the recycling conditions. Impurity radiation could be kept within theisland SOL to enable a stable partial detachment without remarkable loss of the globalenergy content. The divertor operation led to the discovery of the HDH regimecharacterized by high density, and good energy and low impurity confinement. Based onEMC3/EIRENE simulations, experimental results and simple models, the paper presentsa detailed analysis of the neutral and impurity transport behavior in the island divertorunder different recycling conditions, aimed at identifying the role of the recyclingneutrals and the sputtering impurities in establishing improved confinement regimes.Special attention will be paid to the impurity screening effect of the edge islands. It isfound that the ratio of friction force to thermal force depends strongly on the recyclingconditions. For low-recycling, low-density plasmas, thermal forces (mainly from Ti)typically dominate, drawing the impurities towards the separatrix. In the high-densitycase, the friction prevails against the thermal forces and the strengthened plasma flowresulting from the enhanced recycling flux flushes impurities back to the targets. Thecarbon density around the separatrix, normalized to the total sputtering flux, is reducedby more than one order of magnitude with respect to low-density case, showing a strongscreening effect of the magnetic islands on impurities under high-density conditions.Although it is not clear how the impurity concentration in the core correlates to theimpurity density at separatrix, the impurity outflushing in the islands certainly favours areduction of the impurity density in the core to prevent a high-density plasma from fallinginto a radiation collapse.

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Critical Design Issues of Wendelstein 7-X

1M. Gasparotto, 1S. Bäumel, 1V. Bykov, 1C. Damiani, 1W. Dänner, 1A Dudek, 1K. Egorov,1D. Hartmann, 2B. Heinemann, 2N. Jaksic, 1J. Lingertat, 2B. Mendelevitch, 1L. Sonnerup,

1J. Tretter

1 Max-Planck-Institut für Plasmaphysik, Euratom Association , Teilinstitut Greifswald,Wendelsteinstraße 1, D- 17491 Greifswald, Germany2 Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany

The WENDELSTEIN 7-X stellarator (W7-X) is the next step device of IPP in thestellarator line and is presently under construction at the Greifswald branch institute. Theexperiment aims at demonstrating the steady state capability of a stellarator machine at reactorrelevant parameters.

The main parameters of W7-X are: average major radius 5.5 m, average plasma radius0.53 m, magnetic field on the plasma axis 3.0 T, total weight 725 t. The magnetic system ofthe machine consists of 50 non planar and 20 planar superconducting coils supported by acentral structure made of 10 sectors. The magnetic system is kept at 4K by liquid heliuminside a cryostat. An important feature of W7-X is the high geometrical accuracy of themagnetic field configuration: perturbations (_B/B) with a periodicity different from the five-fold periodicity of the device should be kept below 10-4.

The plasma vessel is composed of 10 half-modules welded together during the assemblyphase. A large number of ports (about 300) are connecting the plasma vessel to the cryostatwith bellows in between to compensate the relative movements of the two vessels duringoperation due to temperature differences.

An extensive structural analysis of the magnet system (coils and support structure) is inprogress with two independent finite element models (FE) global created with the ADINAand ANSYS commercial codes. Another FE global model based on the ANSYS code hasbeen developed to study the behaviour of plasma vessel, cryostat, ports and relative supports.

Critical components are the support elements connecting the coils each other and to thecentral structure. These supports must operate in high vacuum and at cryogenic temperature,withstand high loads and moments and allow the assembly of the machine with highaccuracy. The stresses are derived from the FE global model. The support elements are aproper combination of contact sliding elements and welded boxes between the coils in theinner and outer side, respectively; and bolted connections between coils and central supportring in the inner side. An experimental test program was launched to validate the proposedsolutions.

Challenges to the design and assembly of W7-X come from the complex 3D geometry;tight tolerances in-between the coils, between the coils and the support structure, the plasmavessel and the outer vessel; the high electromagnetic loads and the high geometric accuracy ofthe magnetic field configurations. Precautions have to be taken in limiting the deformations ofthe coils and the plasma vessel during the welding processes.

The paper will report about the most critical issues related to the W7-X magnet systemand vessel system and the main activities performed with respect to FE analyses andmechanical tests on mock-ups in order to validate and optimise the adopted design.

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Validation of Wendelstein 7-X assembly stagesby magnetic field calculations

T. Andreeva1, J. Kisslinger2

1 Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald, EURATOM AssociationWendelsteinstraße 1, D-17491 Greifswald2 Max-Planck-Institut für Plasmaphysik, EURATOM AssociationBoltzmannstraße 2, D-85748 Garching bei München

The Wendelstein 7-X stellarator, which is currently under construction in Greifswald, is a5-period machine, and many of the planned operational plasma scenarios are characterized by arotational transform ?/2p=1 at the plasma boundary. Such magnetic configurations are verysensitive to the symmetry breaking perturbations caused by fabrication and assembly errors,which can occur at different stages of the device construction. As a consequence, new islands atany periodicity can be produced, existing islands can be modified, stochastic regions can beenhanced and power load onto the divertor plates can be increased. Therefore magnetic fieldcalculations are used for continuous validation of coil manufacturing and of each assembly step.This is a necessary requirement to insure successful achievement of the designed parameters.For that purpose a numerical procedure has been developed, which allows one the calculation ofthe main resonant harmonics in the Fourier spectrum of the magnetic field taking themanufacturing deviations and the assembly displacements as input parameters.

Manufacturing deviations of non-planar and planar winding packs (WPs) from theirdesigned shapes can be split in systematical and statistical parts. This approach has beenconfirmed by comparison of the average absolute deviations of already fabricated WPs from thedesigned geometry and from the average shape found for each coil type. Only perturbing 5-foldsymmetry statistical deviations influence the error fields of W7-X. The level of the perturbedmagnetic fields as a function of the number of non-planar winding packs manufactured will bepresented for two cases. In one case we assume the not yet manufactured WPs to have exactlythe designed geometry. In the second case they have an average shape simulated for each coiltype. The investigation shows that the expected level of the perturbed magnetic field at the end ofthe manufacturing stage is around 1·10-4.

Different misalignments during the assembly procedure will be estimated from themeasurements of the reference points. Main assembly steps, where such measurements areplanned to be done, will be considered. Assessments of their impacts on the perturbed magneticfield will be shown for different kinds of misalignments. Main construction uncertainties arealso summarized and their possible input in the final estimations of W7-X magneticconfiguration is considered.

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Implications of the Quasi-Neutrality Conditionfor Neoclassical Transport in Stellarators

C.D. Beidler, H. MaaßbergMax-Planck-Institut fur Plasmaphysik, IPP–EURATOM Ass., Greifswald, GERMANY

In conventional stellarator neoclassical theory, the transport coefficients are determinedso as to satisfy the so-called ambipolarity constraint on the radial particle fluxes but withoutregard to the additional requirement that the underlying solutions of the kinetic equation alsofulfill local quasi-neutrality. This neglect is consistent with the assumption that density, � andelectrostatic potential,

�, are constant on a flux surface and is justified in the literature with

analytic scaling arguments which demonstrate that quasi-neutrality introduces variations of �and

�on a flux surface which have only a modest impact on bulk-plasma transport [1-3]. The

consequences for impurity transport have not been considered.In this contribution, the implications which the quasi-neutrality condition has for neo-

classical transport in stellarators are investigated using a version of the General Solution ofthe Ripple-Averaged Kinetic Equation (GSRAKE) which accounts for the variation of

�on

flux surfaces. Solutions of the kinetic equation which simultaneously fulfill the ambipolarityand the quasi-neutrality conditions are determined iteratively using standard methods forsolving systems of non-linear equations, given specified density and temperature profilesfor pure hydrogen plasmas. For a conventional heliotron device, it is shown that quasi-neutrality significantly reduces the radial extent of the region in which multiple solutions ofthe ambipolarity condition can exist. Especially in the plasma periphery, where strong densityand temperature gradients are found, the magnitude of the “ion” root is reduced significantlyleading to increased particle and energy fluxes. For strongly drift-optimized stellarators, onthe other hand, bulk plasma transport is much less affected. In a small number of cases, thenon-linear system of equations produces additional solutions which are not possible whenonly ambipolarity is enforced [4], but such cases are rare. Finally, it is demonstrated for fullyionized carbon in the tracer approximation that impurity transport coefficients are stronglyaffected by the quasi-neutrality-induced variation of

�on flux surfaces. This is true for all

stellarators, whether classical or drift-optimized, and the effects are further accentuated forhigh- � impurities.

[1] H.E. Mynick, Phys. Fluids 27 (1984) 2086.[2] D.E. Hastings and K.C. Shaing, Phys. Fluids 28 (1985) 1409.[3] D.D.-M. Ho and R.M. Kulsrud, Phys. Fluids 30 (1987) 442.[4] L.M. Kovrizhnykh and S.G. Shasharina, Sov. J. Plasma Phys. 13 (1987) 299.

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61

Experimental Design: Case studies of Diagnostics Optimization for W7-X

H. Dreier, A.Dinklage, R. Fischer, H.-J. Hartfuß, M. Hirsch, P. Kornejew, E. Pasch, Yu. Turkin

Max-Planck-Institut für Plasmaphysik, EURATOM-Association,

Greifswald and Garching, Germany

The preparation of diagnostics for Wendelstein 7-X is accompanied by diagnostics simulations and optimization. Starting from the physical objectives, the design of diagnostics should incorporate predictive modelling (e.g. transport modelling) and simulations of respective measurements. Although technical constraints are governing design considerations, it appears that several design parameters of different diagnostics can be optimized. However, a general formulation for fusion diagnostics design in terms of optimization is lacking.

In this paper, first case studies of Bayesian experimental design aiming at applications on W7-X diagnostics preparation are presented. The information gain of a measurement is formulated as a utility function which is expressed in terms of the Kullback-Leibler divergence. Then, the expected range of data is to be included and the resulting expected utility represents the objective for optimization. Bayesian probability theory gives a framework allowing us for an appropriate formulation of the design problem in terms of probability distribution functions.

Results are obtained for the information gain from interferometry and for the design of polychromators for Thomson scattering. For interferometry, studies of the choice of line-of-sights for optimum signal and for the reproduction of gradient positions are presented for circular, elliptical and W7-X geometries. For Thomson scattering, the design of filter transmissions for density and temperature measurements are discussed.

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62

H-mode edge rotation in W7-AS

M. Hirsch, J. Baldzuhn, H. Ehmler, P. Grigull, H. Maassberg, K. McCormick,

F. Wagner, H. Wobig and the W7 Team

Max-Planck-Institut für Plasmaphysik, EURATOM Association, Greifswald, Germany

In W7-AS three regimes of improved confinement exist which base on negative radialelectric fields at the plasma edge resulting there from ion-root conditions of the ambipolar radialfluxes. Experimental control besides the magnetic configuration is given via the edge densityprofile i.e. the recycling and fuelling conditions. However, the ordering element seems to be theradial electric field profile (respectively its shear) and its interplay with the gradients of iontemperature and density.

At low to medium densities the so called optimum confinement regime occurs withmaximum density gradients located well inside the plasma boundary and large negative valuesof rE extending deep in the bulk plasma. For a large inner fraction of the bulk the iontemperature can be sufficiently high that ion transport conditions already can be explained byneoclassics. This regime delivers maximum values of iT , eτ and ie Tn τ .

Density gradients located right inside the plasma boundary result in the classical H-modephenomena reminiscent to other toroidal devices with the capability of an edge layer withnearly complete suppression of turbulence either quasi stationary (in a quiescent H-mode) orintermittently (in between ELMs).

At even higher densities and highly collisional plasmas with the maximum of n∇ shiftedto or even out of the plasma boundary the High Density H-mode (HDH) opens access to steadystate conditions with no measurable impurity accumulation.

These improved confinement regimes are accessed and left via significant transitions of thetransport properties albeit these transitions occur on rather different timescales.

A comprehensive picture of improved edge confinement regimes in W7-AS is drawnbased on the assumption that a weak edge bounded transport barrier resulting from the ionroot conditions (thus rE <0) is the ground state of the (turbulent) edge plasma and alreadybehaves as a barrier for anomalous transport. On top of that the classical H-mode develops asan additional spin-up of BE× rotation with the capability for a sudden and nearly completesuppression of transport carrying turbulence.

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63

Transition to improved confinement mode of operation triggered by strong gas fueling

Yu. Igitkhanov 1), H. Ohyabu 2), B.Peterson2), E. Polunovski3),

K.Yamazaki4) and H. Wobig1)

1) Max-Planck Institut für Plasmaphysik, Greifswald, Germany, 2) National Institute for Fusion Science, Oroshi-cho 322-6, Toki 509-5292, Japan 3) ITER, JWS Garching, Germany, 4) Nagoya University,. Nagoya, Japan E-mail: contact of main author: yli@ipp.mpg.de

The analysis of the density equation in stellarator or tokamak plasmas shows that the

bifurcation can occurs between two stable solutions, which are characterized by different density

gradients at the plasma edge. A strong gas puffing at the edge or pellet injection can trigger this

bifurcation, which appears due to the non-linearity in the particle source term and a non-

monotonic behavior of the neutral source term for different values of the separatrix plasma

density. This mechanism is suggested here as a plausible physical explanation of an advanced

high density H-mode (HDH) regime on the W7-AS stellarator, which can be achieved only under

a high rate of particle fuelling during the starting phase of the discharge, when the average

density exceeds some critical level [1,2]. This mechanism can also be responsible for TB

formation in LHD during pellet injection. When the puffing rate exceeds the diffusive speed the

density profile grows at the source position, and this leads to the formation of the density gradient

sufficient for effective suppression of the plasma turbulence (the Edge Transport Barrier

formation). The appearance of the ETB depends on the initial condition, namely on the fuelling

rate, but a steady-state operation with improved confinement can be achieved at some critical

average density, which can be assessed from the energy and particle balance at the edge [2]. In

this paper we emphasize the primary role of neutrals in bifurcation between two stable solutions,

reminiscent of the different modes of operation in W7-AS and LHD plasmas. The possibility of

bifurcation during the density formation in the different divertor configuration in the LHD

stellarator (Helical and Island divertor) is also discussed.

[1] P. Grigull et al, Plasma Phys. Control. Fusion 43 (2001) A175

[2] Yu. Igitkhanov, G. McCormick and P.E. Grigull, FST 46, 101-105 (2004)

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64

p p

Poster preferred

Magnetic field accuracy and Correction Coils in Wendelstein 7-X

J. Kißlinger1, T. Andreeva2

1Max-Planck-Institut für Plasmaphysik, EURATOM Ass., Boltzmannstr. 2,D-85745 Garching, Germany

2Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald, EURATOM Ass.,Wendelsteinstraße 1, D-17491 Greifswald

The super-conducting magnet system of Wendelstein 7-X consists of five identical fieldperiods (modules). Magnetic field errors arise if the modules are not exactly identical. Evensmall deviations in the coil shapes of the same type or misalignments of coils or modulesbreak the periodicity of the system and cause error field components which can be resonantin lowest order to the rotational transform, which is 1 in the standard configuration. Suchfield perturbations lead to additional islands and cause asymmetric thermal loads on thedivertor targets.At the end of April this year, 40 oft he 50 non planar coils are 40 and all planar coil windingpackages were manufactured. Their shapes show systematic deviations to the nominalgeometry and statistical deviations from the mean filament geometry of all investigatedwinding packs of the same type. Only the statistical deviations generate error fieldcomponents with periodicity other than five, the systematic deviations only add negligiblefield components. Assuming that the remaining winding packs show statistical deviations inthe same range, the dominant Fourier components of the error fields ∆B11/B00 and ∆B22/B00

would contribute 0.59_10-4 and 0.62_10-4, respectively, to the field errors.Geometrical errors during assembly of the magnet system result from misalignments ofsingle coils, distortions during welding of the lateral support elements and frommisalignments of half-modules and modules. Numerical analyses have shown that statisticalextrapolations of inaccuracies occurring during all assembly steps result in an averagedeviation of each coil of 3.5mm and in Fourier components ∆B11/B00 and ∆B22/B00 of about3_10-4 and 1.5_10-4, respectively. Comparing the different figures it is evident that assemblyerrors contribute significantly more than manufacturing errors of individual coils.At the final assembly step of the magnet system an individual adjustment of all five moduleswithin a sphere of 5mm radius is possible by applying shims between the module sectors ofthe coil support structure. This correction measure is able to reduce error field componentsdue to geometrical deviations known at that time. Additional compensation of field errorscould be achieved by extra coils. In W7-X, there will be 10 control coils installed, foreseento optimise the boundary magnetic configuration, but which may also be used for error fieldcompensation. However, their capability in respect to the B11 Fourier component is too low,only 0.4mT can be generated. From this point of view an additional set of correction coils isrequired. To find an appropriate solution for correction coils some alternatives wereinvestigated: normal conducting coils inside the plasma vessel and outside the cryostat vesselas well as super-conducting helical windings inside the cryostat. The coils close to theplasma and the helical windings have the advantage that the required currents are smallercompared with those needed outside the cryostat vessel. However the technical realisationand the accessibility is easier in the case of outer coils. For the generation of B11 and smallB22 components it is sufficient to have five correction coils (one per field period) on the outervessel. Using five coils, each should have a current capability of 100kA-turns.

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Optimization of ECE diagnostic for W7-X stellarator

N.B. Marushchenko, A. Dinklage, H. Hartfuß, M. Hirsch, H. Maaßberg, Yu. Turkin

Max-Plank-Institut fur Plasmaphysik, EURATOM-Association,Greifswald, Germany

The interpretation of diagnostic data at W7-X stellarator (under construction in Greifswald)will be supported by the concept of integrated data analysis

��� �. This concept is demonstrated

to be feasible for the Thomson scattering diagnostic on W7-AS�. For the ECE diagnostic, the

basic idea is to fit the spectral intensity�������

simulated by modelling the data (the antenna,the reciever, etc) for a �� profile. Simulations are performed with a newly developed ray-tracing code, which includes an option to calculate the emission by electrons with an arbitrarydistribution function.

The antenna for (standard) ECE measurements will be installed on low-field-side (lfs) nearthe bean-shaped plane, where ��� is largest, without spectral overlapping of cyclotron harmon-ics. In order to estimate the limit of spatial resolution, which comes from relativistic broadeningof the emission line � , the calculated ECE spectrum, i.e. radiation for each frequency channel��������

, is “mapped” onto the radial coordinate. Vice versa, using the obtained radial uncertain-ties for disturbance of the �� parametrized profiles, the sensitivity of the ECE spectrum withrespect to the implemented radial �� -profiles is checked.

In the initial stage, W7-X will operate in the ��� ����� �!� range of densities, with strong ECRheating by X2-mode at 140 GHz. For a highly localized deposition profile, one has to expectthe appearance of a suprathermal population of electrons. The question how to distinguish thethermal and non-thermal contributions in the ECE spectrum is also discussed. The attractiveidea of using vertical chords with " �#"%$'&)(+*�,�- as sightlines for the reconstruction of the elec-tron distribution function will fail due to the diamagnetic effects (no way to find the chord with" �#".$/&0(1*2,�- for an appropriate range of 3 -values). However, a high-field-side (hfs) observation(especially along the same sightline as lfs 4 ) appears to be much more promissing: despite thenot so high spatial resolution of a hfs ECE diagnostic, the existence of suprathermal electronscan be identified by comparison of both lfs- and hfs-ECE spectra. Moreover, the energy rangeof the non-thermal fraction can be identified. The capability of (possible) hfs multichord imag-ing is also checked.

1. A. Dinklage, R. Fischer,, J. Svensson, Fusion Sci. Technol. 46 (2004) 3552. R. Fischer, A. Dinklage, Rev. Sci. Instrum. 75 (2004) 42373. R. Fischer, A. Dinklage, E. Pasch, Plasma Phys. Control. Fusion 45 (2003) 1095.4. V. Tribaldos, Spatial Resolution of ECE for JET Typical Parameters, Report EFDA-JET (2000)5. N.B. Marushchenko et al, 31st EPS Conference Plasma Phys., London, 28 June - 2 July 2004 ECA

Vol.28G, P-1.204 (2004)

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Statistical Analysis of the equilibrium configurations of the W7-Xstellarator using Function Parameterization

P. J. Mc Carthy1, A. Sengupta1, J. Geiger2, A. Werner2

1Department of Physics, University College Cork, Association Euratom-DCU, Cork, Ireland2Max-Planck-Institut für Plasmaphysik, Euratom Association, Greifswald, D-17491 Germany

The W7-X stellarator, under construction at IPP-Greifswald, is being designed todemonstrate the steady state capability of fusion devices. Due to the pulse lengthinvolved, real time monitoring and control of the discharges is a crucial issue in steadystate operations. For W7-X, we have planned a sequence of in-depth analyses of themagnetic configurations which, ultimately, will lead to a proper understanding of plasmaequilibrium, stability and transport. It should also provide insight into theparameterization of the various plasma-related quantities which is important from thepoint of view of real time study. The first step in our sequence of analyses involved astudy of the vacuum configuration, including the detectable magnetic islands, of W7-X[1]. We now proceed to the scenario at finite beta considering fullmagnetohydrodynamic (MHD) equilibria based on vmec2000 calculations. A databaseof order 10000 equilibria was calculated on the same parameter space for the coil currentratios as in [1]. The parameters which were varied randomly and independently consistof the external coil current ratios (6), the parameters of the profiles (as functions ofnormalised toroidal flux) of plasma pressure and toroidal current (4+4) and the plasmasize (aeff) which is required to vary the plasma volume. A statistical analysis, usingFunction Parametrization (FP), was performed on a sample of well-convergedequilibria. The plasma parameters were varied to allow a good FP for the expectedvalues in W7-X, i.e. volume-averaged <ß> up to 5% and toroidal net-current of up to±50 kA for a mean field strength of about 2 T throughout the database. The profileswere chosen as a sequence of polynomials with the property that the addition of ahigher order polynomial would not change the lower order volume-averaged moments ofthe resulting profile. The aim of this was to try to avoid cross correlations in theindependent input parameters for the database generation. However, some restrictionshad to be incorporated in order to maximize the number of converged vmec runs withrandomly generated inputs. Therefore, the peaking factor ßaxis/<ß> for the pressureprofile was restricted to avoid values of ßaxis > 12%. This is reasonable in view ofexperimental scenarios where large peaking factors are usually connected with lowvalues of <ß>. Additionally, the central current density was limited in order to avoidvery small values of central iota. This was to ensure a reasonable vmec-convergence. Wewill present in detail the regression models that were employed and a statisticaldescription of the recovery accuracy of plasma information from this database such asthe profiles of the rotational transform and the differential volume V' as well as those ofthe leading order Fourier coefficients for the geometry and the magnetic field strength.

1. A. Sengupta, P.J. McCarthy, J. Geiger, A. Werner, Nucl. Fusion 44 (2004) 1176.

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Feasibility study for Heavy Ion Beam Probing (HIBP) project on stellarator

W7-X

L.I. Krupnik, A. V. Melnikov1, S. V. Perfilov1, H.J. Hartfuss2

NNC ”KhIPT”, Kharkov, Ukraine1RRC ”Kurchatov Institute”, Moscow Russia,2 IPP Max-Plank Institute, Greifswald, Germany

The feasibility study for HIBP on the stellarator W7-X was done to provide the

measurements of the radial profiles of plasma potential, density and their fluctuations.

Calculations of probing Tl+ beam trajectories were done for previously chosen port

combination A11-N11 and the various W7-X magnetic configurations with B0 = 2.5 T. They

show that satisfactory access is possible for this port combinations. The trajectory optimisation

aiming for the maximal plasma observation was done for chosen port combination.

The initial calculation shows that HIBP allows us getting radial profiles of plasma

parameters. The detector line of equal energy ETl+

= 2.0 MeV allows us to obtain a series of

radial profiles for outer half of the plasma column (0.45 < ρ < 0.95) during single shot by

changing of the entrance angle with the scan of the control voltage. There was found a

possibility to get quite good spatial resolution 0.012<∆ρ<0.015 for 2 cm beam diameter.

The special beam-line for the primary particles is necessary to transfer them from the

accelerator to the plasma through the area of magnetic field. The special beam-line for the Tl++

secondary particles is also necessary to transfer them from the plasma through the area of

magnetic field to the ion energy analyser. The beam-lines are also plan to be used to control the

beam trajectories and to drive them to energy analyzer with optimized entrance angle. It was

found that toroidal focusing of the secondary trajectories will lead to construction of rather

complex secondary beam-line. The size of toroidal correction plates of the secondary beam-line

may be comparable to the size of the electrostatic analyzer. Such electrostatic beam control

looks to be the necessary elements of the HIBP hardware for large optimised stellarators like

W7-X.

The beam attenuation of the primary and secondary probing beams due to collisions of

the ions with plasma particles is acceptable for the measurements in all the typical magnetic

configurations.

The work of Kurchatov team was supported by RFBR, grant 05-02-17016.

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Development of Heavy Ion Beam Probing (HIBP) diagnostic forstellarator WEGA

L.Krupnik, A.Melnikov(1), S.Perfilov(1), A.Zhezhera, G.Dezhko, M.Otte(2

NNC ”KhIPT”, Kharkov, Ukraine, (1) RRC ”Kurchatov Institute”, Moscow Russia,

(2)Max-Plank Institute, IPP, Greifswald

The feasibility study of the HIBP diagnostic for stellarator WEGA was done to

provide the measurements of the radial profiles of the electric plasma potential, electron

density and their fluctuations. The HIBP diagnostic is a unique method of the direct

electric potential measurements in full volume of plasmas: in the core and in the edge

plasma. Installation of the HIBP on a given device start with the optimized calculations

of the probing beam parameters connected with its geometry and magnetic fields.

Calculations of probing Na+ beam trajectories were done for high field WEGA

magnetic configuration with B0 = 0.5 T. The trajectory optimization aiming for the

maximal plasma volume observation was done for chosen port combinations.

The initial calculation shows that HIBP allows getting radial profiles of plasma

parameters. The detector line of equal entrance angle connects the centre and the edge

of the plasma column with ENa+ = 30 - 60 keV. This produces the full radial profile on

shot-to shot basis. The detector line of equal energy ENa+ = 40 keV allows us to obtain a

series of radial profiles (0.1 < ρ < 1) during single shot by changing of the entrance

angle with the scan of control voltage.

The special beam-lines for the primaries and the secondaries are necessary to

transfer the particles from the accelerator to plasma through the area of magnetic field

and further to secondary Na++ion detection electrostatic energy analyzer. They are also

necessary to control the beam trajectory and drive them to energy analyzr with

optimized entrance angle. Such electrostatic control looks to be the necessary elements

of the HIBP hardware even for small stellarators like WEGA.

On the base of these calculations were developed of the HIBP diagnostic

technique. The hardware consists of two main parts. They are: injector of the

accelerated primary probing beam up to 100keV. and parallel plate electrostatic energy

analyzer Special calibration of the analyzer shows rather good energy resolution

satisfied the requirement of the plasma potential measurements.

This work has been partially supported by INTA project reference 01-0593

The work of Kurchatov team was supported by RFBR, grant 05-02-17016.

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Impurity Transport in Drift Optimized Stellarator Ergodic and Nonergodic Plasma Configurations

O. A. Shyshkin1, R. Schneider2, C. Beidler2

1Kharkov “V.N.Karazin” National University, Svobody sqr.4, Kharkov-77, 61077, UKRAINE

2Max-Planck-Institut fur Plasmaphysik, EURATOM Assosiation, Teilinstitut Greifswald, D-1791 Greifswald, GERMANY

Simulation of the tungsten ions transport is carried out for two magnetic field

configurations, ergodic and nonergodic, in the drift optimized stellarator plasma configurations with five periods of the magnetic field. Such kind of configuration will be realized in stellarator Wendelstein 7-X and stellarator reactor HELIAS. Both configurations correspond with the finite plasma pressure parameter %3=β . At the heart of numerical code, which is developed, the integration of the guiding center equations with the use of magnetic coordinates is put. The ergodic magnetic field configuration is presented with the use of additional magnetic filed perturbations 141711 =nm and 182222 =nm to create the island chains, which overlap and give raise to the stochastic layer at the radial position of plasma radius. Coulomb scattering of the tungsten ions on the background plasma particles (electrons, deuterons and tritons) is simulated by means of discretized collisional operator

3/2

1, which is presented in terms of pitch angle scattering and energy slowing down and scattering. The changes of tungsten ion charge state is taking into account by coronal model as for the pseudo particle model2. The background plasma temperature profile for the ergodic configuration considered to possess the flattening in the stochastic layer region. The diffusion coefficients for tungsten ions in two plasma configurations are evaluated in accordance with

commonly known expression3 ( ) [∑=

−=N

iiN

D1

20

1

2

1 ψψτ

τ ] . The reduction of radial diffusion

of impurities in magnetic configuration with stochastic layer is shown. The effect of transport barrier on heavy impurities motion with high charge state is observed. This work is partly carried out under the support of the Science and Technology Center in Ukraine, Project N 2313. 1. William D. D’haeseleer and Craig D. Beidler, (1993) Computer Physics Communications 76, 1 2. K. Asmussen, K.B. Fournier, J.M. Laming, et al, (1998) Nuclear Fusion, 38, 967 3. Allen H. Boozer and Gioietta Kuo-Petravic, (1981) Phys. Fluids 24, 851

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Kinetic modelling of the nonlinear ECRH in stellarators ∗

S.V. Kasilov1, W. Kernbichler2, R. Kamendje2, M.F. Heyn2

1 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and

Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine2 Institut für Theoretische Physik - Computational Physics,Technische Universität Graz,

Petersgasse 16, A–8010 Graz, Austria

At power levels typical for the present day ECRF heating experiments in tokamaks and stel-larators, the quasilinear and nonlinear effects of heatingon the electron distribution functioncan be important. This is especially true in scenarii with 2nd harmonic X-mode heating withnear-perpendicular injection of the microwave beam. In this case, both, the nonlinear effectsof the wave-particle interaction and the distortion of the electron distribution function are sig-nificant. A method for the kinetic description of these effects on ECRH and ECCD within aMonte Carlo modelling have been developed and applied to tokamak geometry in [1,2].

In stellarators, an additional complexity is introduced bythe absence of axial symmetry ofthe device which results also in new effects such as generation of convective supra-thermalelectron radial fluxes by ECRH. In order to meet the requirements of ECRH modelling inthese cases, a specific Monte Carlo method, a stochastic mapping technique (SMT), which hasmuch higher efficiency than the conventional Monte Carlo method, has been developed in [3].There, the convective electron fluxes have been modelled assuming that ECRH provides a pointsource of supra- thermal electrons in the phase space. In thepresent report methods of Refs.[1-3] are combined into a consistent model which is applied to a stellarator with parameterstypical to W-7AS.

References[1] R.Kamendje, S.V. Kasilov, W. Kernbichler, and M.F. Heyn, Phys. Plasmas10, 75 (2003)

[2] R.Kamendje, S.V. Kasilov, W. Kernbichler, I.V. Pavlenko, E. Poli, and M.F. Heyn, Phys.Plasmas12, 12502 (2005)

[3] S.V. Kasilov, W. Kernbichler, V.V. Nemov and M.F. Heyn, Phys. Plasmas9, 3508 (2002)

∗This work has been carried out within the Association EURATOM-ÖAW and with funding from the AustrianScience Fund (FWF) under contract P16797- N08. The content of the publication is the sole responsibility of itspublishers and it does not necessarily represent the views of the Commission or its services.

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Additional criteria for optimization of trapped particle confinement instellarators ∗

V.V. Nemov1, S.V. Kasilov1, W. Kernbichler2, G.O. Leitold2

1 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics andTechnology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine

2 Institut für Theoretische Physik - Computational Physics, Technische Universität Graz,Petersgasse 16, A–8010 Graz, Austria

Improving the collisionlessα-particle containment in stellarators is one of the key issuesin stellarator optimization problems. The most consequent approaches for the investigation ofthis problem are realized in codes which follow particle orbits and, therefore, allow for directcomputation of particle losses. To increase computing efficiency, of course, also simple criteriawhich address this problem properly are of big interest (e.g., minimization of the geodesiccurvature of the magnetic field line, residuals in the magnetic spectrum of quasi-symmetricsystems, effective ripple, WATER parameter) .

In the present work, new simplified criteria are proposed which are based on the computa-tion of the bounce averaged∇B-drift velocity of trapped particles across magnetic surfaces.For a given stellarator magnetic field, the pertinent optimization parameters are numericallycalculated using a field line following code. With such optimization parameters being zero,an absolute confinement of reflected particles is guaranteed. Comparisons between results fordifferent simplified criteria as well as for direct computations ofα-particle losses reveal theapplicability of the method.

The proposed criteria are applied to some magnetic configurations for which the neoclassi-cal confinement properties were studied formerly by different methods. In particular, a bench-mark with effective ripple results is performed. From those results follows that the consideredtechnique provides a convenient auxiliary approach for the investigation of collisionless con-tainment of trapped particles in stellarators.

∗This work has been carried out within the Association EURATOM-ÖAW and with funding from the AustrianScience Fund (FWF) under contract P16797-N08. The content of the publication is the sole responsibility of itspublishers and it does not necessarily represent the views of the Commission or its services.

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Computation of neoclassical transport in stellarators with finite

collisionality ∗

W. Kernbichler1, S.V. Kasilov2, G.O. Leitold1, V.V. Nemov2, K. Allmaier1

1 Institut für Theoretische Physik - Computational Physics, Technische Universität Graz,

Petersgasse 16, A–8010 Graz, Austria2 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and

Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine

A new numerical method is presented which allows for an efficient evaluation of neoclas-sical transport coefficients and of the bootstrap coefficient in stellarators for the case there isno radial electric field. In this method, the approach [1] used in code NEO to compute the 1/ν

transport coefficient during integration along the magnetic field line is generalized to arbitrarycollisionality regimes.

In more detail, the linearized steady-state drift kinetic equation (DKE) is solved by a finite-difference method. The solution of the DKE is described in terms of the phase space fluxdensity throughs= constcuts, wheres is the distance measured along the magnetic field line.The phase space is split into "ripples" which cover finite intervals overs and extend into thevelocity space. Within such a ripple, the problem is discretized by introducing levels over theperpendicular action. The distribution of these levels is specific for the ripple. The DKE isapproximated by a coupled set of ordinary differential equations overs for the integrals of thephase space flux density over bands between the levels. The general solution of the kineticequation for a single ripple is then expressed in terms of a set of matrix relations betweenthe discretized phase space flux densities of particles entering and leaving the ripple troughits boundaries. The whole set of these matrices is called a "propagator". The final solution isobtained after subsequent joining of these propagators using their group property.

The method has similar advantages as the NEO code, such as high speed, good conver-gence in low collisionality regimes as well as the possibility of computations for magneticfields given in magnetic and real space coordinates, in particular, for magnetic fields resultingdirectly from the Biot-Savart law and from new equilibrium codes such as PIES and HINT.

References[1] V.V. Nemov, S.V. Kasilov, W. Kernbichler and M.F. Heyn, Phys. Plasmas6, 4622 (1999)

∗This work has been carried out within the Association EURATOM-ÖAW and with funding from the AustrianScience Fund (FWF) under contract P16797-N08. The content of the publication is the sole responsibility of itspublishers and it does not necessarily represent the views of the Commission or its services.

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Study of neoclassical transport in the 1/ν regime for a research fusion reactor

V.N.Kalyuzhnyj, S.V.Kasilov, V.V.Nemov

Institute of Plasma Physics, National Science Centre “ Kharkov Institute of Physics andTechnology”, Akademicheskaya 1, 61108 Kharkov, Ukraine

In frame of the concept of a steady-state operated research fusion reactor (RFR)in papers [1-4] the RFR with an increased plasma-wall detachment was proposed withthe purpose to enable not only the production but also a long-term confinement of a self-sustained plasma at the existing technology level. In connection with complication ofthe corresponding magnetic configuration an investigation of the neoclassical transportis desirable for such systems.

In the present work neoclassical transport for a magnetic configuration of l=2torsatron type variant of RFR system with an additional opposite toroidal magnetic field(see [4]) is investigated numerically. A so-called 1/ν transport regime, in which thetransport coefficients are increased with reduction of particle collision frequency ν isconsidered. For calculating of transport coefficients a technique [5], based onintegration along magnetic field lines in a given stellarator magnetic field is used. Themagnetic field of helical windings is calculated by Biot-Savart law. The obtainedtransport coefficients are presented in a standard form containing a factor depending onthe magnetic field geometry. From analysis of the received results follows that in respectof the neoclassical transport the proposed magnetic configuration turns out to be closerto configuration of the classical stellarator (with helical winding), than to configurationof the classical torsatron/geliotron.

1. V.G.Kotenko, G.G.Lesnyakov, S.S.Romanov, VII Ukranian Conference on Controlled ThermonuclearFusion and Plasma Phisics, Kiev, 20-21 September 1999, Abstract Book, p.32 (in Ukranian).

2. V.G.Kotenko, V.I.Lapshin, G.G.Lesnyakov et al., Plasma Fusion Res. SERIES, v.3 (2000) p.541.

3. V.G.Kotenko, V.I.Lapshin, G.G.Lesnyakov et al., Problems of Atomic Science and Technology, N3,2000, Series: Plasma Phisics (5), p.70.

4. V.G.Kotenko, S.S.Romanov, N.T.Besedin, Ukr.Fiz.Zh. 46, N11 (2001), p.1127 (in Ukranian).

5. V.V.Nemov, S.V.Kasilov, W.Kernbichler, M.F.Heyn, Phys.Plasmas 6, 4622 (1999).

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Observation of Ion Bernstein Wavesduring Alfven Wave Plasma Heating in URAGAN-3M Torsatron

O.S.Pavlichenko, A.I.Skibenko, V.G.Konovalov, V.E.Kulaga, V.L.Ocheretenko, I.B.Pinos,A.M.Shapoval, A.S.Slavniy, S.V.Tsybenko, E.D.Volkov, O.Yu.Volkova

Institute of Plasma Physicsof the National Science Center “Kharkov Institute of Physics and Technology”

61108 Kharkov Ukraine

In URAGAN-3M (U-3M) torsatron plasma is produced and heated by absorption ofpower from Alfven ( ciωω ⋅÷≈ 8.07.0 ) waves excited in plasma by RF antennae. Two

different frame type antennas allowing gas breakdown, plasma build-up and heating hasbeen used in recent years. Both electron and ion heating for experiment condition wereobserved (PRF ≈200 kW, Te(0) ≈500 eV, Ti(0) ≈ 340 eV, ne(0) ≤2.1018 m-3) and explainedin [1] as a result of Cherenkov absorption of energy of the fast (EM) and slow (kineticAlfven) waves by electrons and turbulent ion heating due to excitation of short wave ionBernstein waves (IBW).

During plasma fluctuation studies (microwave reflectometry, edge H_ emission, ECE)narrow band density fluctuations have been observed (Fig.1)

Fig.1These spectra were obtained by using FFT of signals digitized by ADC with sampling rateFsamp up to 3.3 MHz (Nyquist frequency ≈ 1.65 MHz). Analysis of spectra showed that thefrequency of one of the bands (f=100-250 KHz) corresponds to the “beat” frequency ofsignals of 2 RF oscillators.

More information was obtained after numerical calculation of spectra of signals withfrequency Fx larger the Nyquist frequency. It was shown that FFT of such signals results inappearence of “phantom” bands Fphantom in the Nyquist band. All frequencies (Fphantom, Fx

and Fsamp ) are connected by a relation: Fx=n· Fsamp ± Fphantom (n=0,1,2….). The value of Fx

can be determined by using of 3 different sampling rate values.Analysis of observed frequency spectra showed that observed “phantom” bands are

the results of fluctuations with frequencies of RF oscillators (F1≈8.7 MHz, F2≈8.5 MHz), their“beat” frequency (F12=F1-F2) and ion cyclotron frequency (Fci=10.7 MHz). This conclusionwas confirmed by determination of spectra of microwaves reflected by plasma with a help ofmicrowave spectro-analysator.

1. N.T.Besedin, S.V.Kasilov et al., X Intern.Workshop on stellarators, Garhing (1993)

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Transport barriers in helical systems

E.D.Volkov, V.L.Berezhnij, V.V.Chechkin, L.I.Grigor'eva, A.E.Kulaga, A.P.Litvinov,Yu.K.Mironov, V.V.Nemov, V.L.Ocheretenko, O.S.Pavlichenko, I.B.Pinos, V.S.Romanov,T.E.Shcherbinina, A.I.Skibenko, A.S.Slavniy, E.L.Sorokovoy, I.K.Tarasov, S.A.Tsybenko.

Institute of Plasma Physics, National Science Center "Kharkov Institute of Physics andTechnology", Kharkov, Ukraine

There are some publications with indications that the formation of transportbarriers in toroidal devices could take place in the vicinity of low order rational surfaces(RS). It is necessary to note that the environs of RS have very important peculiarities. Inparticular, a stochastic layer of magnetic field lines forms instead of separaterix whichmust separate the island surfaces from the adjacent to them non-island surfaces instellarator magnetic configurations.

The attempt to realize the formation of transport barriers near RS and to study theirinfluence on the RF discharge plasma confinement was undertaken in presentedexperiments on the U-3M torsatron. The presupposition was made that the radial electricfield profile would have sharp change on the width of stochastic layer near RS in the caseof collisionless longitudinal motion of electrons in this layer. Experimental data obtainedon the U-3M torsatron during the formation of interior and edge transport barriers are in agood agreement with this presupposition.

The results of experiments on the U-3M torsatron are discussed in comparisonwith data of other helical systems. It is shown that the number of dependences (thethreshold power and density, the time of barrier formation, the localization of radialelectric field shear layer) are in a good agreement for all these systems.

In conclusion, the common features of formation of transport barriers in non-axisymmetric and non-axisymmetric systems are discussed.

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Magnetic Islands and Plasma Transport in Helical Devices

Alexander Shishkin

Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology”,Kharkov-108, UKRAINE

and Department of Physics and Technology

Kharkov “V.N.Karazin” National University, Kharkov-77, UKRAINE

The penetration into the plasma of the impurity ions from the chamber wall and radiation loss increase is the serious problem of the modern and future controlled fusion devices. This phenomenon is observed experimentally and there are some theoretical explanations of this physics from the MHD and kinetic approach. Some special ways exist to protect the plasma. The impurity ion flux into the core of plasma can be partly stopped with the magnetic island chains at the periphery of the magnetic confinement volume1. This physics idea to protect plasma from the impurity ions can be examined on the new devices of stellarator type National Compact Stellarator Experiment (NCSX), which is under construction at Princeton Plasma Physics Laboratory, USA and Wendelstein-7X, which is being constructed at Max-Planck-Institut fuer Plasmaphysik, Germany. On the base of the MHD approach the impurity ions flows are studied in the configuration with the parameters of NCSX and Wendelstein-7X with the magnetic islands. The magnetic islands =5/3 and

=6/3 can be excited with the trim coils in NCSX. The magnetic islands =5/5 should be the part of the magnetic divertor in Wendelstein-7X. It is shown that the solving of the flow trajectory equations can lead us to the conclusion that ion flow trajectories are

concentrated in the region of the magnetic islands.

nm /nm / nm /

0=× αurd

The mass flow trajectories as the solution of the equation 0=× αurd are obtained for the

configurations with and without islands. One can see the strong effect of the islands on the mass flows. On NCSX it is possible to examine this dependence of the impurity fluxes on the magnetic islands. We can conclude that magnetic islands can be the transport barriers on the way of the impurity ions into the plasma core. Right now we think that the similar behavior can be expected for the main plasma ions also. This problem is under study now. The change of the island geometry: the excitation of the islands with “wave” numbers =m 5,

=3 and 6, =3, which can be produced with the trim coils, separately and simultaneously (in different discharges), can help to control the impurity flows in the helical plasmas. Adjacent resonance can lead to the study of stochastic layer effect on main and impurity ions. NCSX and Wendelstein – 7X can be the most appropriate devices for such study.

n =m n

1. Alexander Shishkin. About the Possibility of Impurity Ion Accumulation in the Island Region in Helical Plasma. Journal of Plasma and Fusion Research SERIES v.6, 2004, pages 500-503.

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Surface flute modes in the bumpy magnetic fieldI.O. Girka, V.O. Girka, V.I. Lapshin

Kharkiv National University, Svobody Sq.4, Kharkiv, 61077, Ukraine.girkai@univer.kharkov.ua, lapshyn@kipt.kharkov.ua

Surface electromagnetic waves are often determined as the most possible cause of

undesirable heating of edge plasma that leads, in turn, to strengthening of plasma – wall

interaction in stellarators and increased plasma contamination. The propagation of surface

flute modes near the interface of plasma column separated by a vacuum layer from the ring

cylindrical ideally conductive metallic chamber is studied. The external steady bumpy

magnetic field r0rz0z0 eBeBBrrr

+= was considered, B0z=B00[1+εm(r)cos(kmz)], here εm’≡dεm/dr,

km=2π/L, L is the period of nonuniformity. «Mirror» non-uniformity of 0Br

is planned to be

dominant in the confining magnetic field of the modular stellarator Helias, εm ~ 0.13.

In the bumpy magnetic field the electromagnetic disturbance propagates in the form of

the wave envelope, in which one alongside with the fundamental harmonic, proportional to

exp[i(mϑ− ωt)], infinite set of satellite spatial harmonics, proportional to exp[i(mϑ ±

jkmz − ωt)], j=1,2,3…, is present. It is shown, that in the first approximation in the respect to

εm, amplitudes of the fundamental harmonics of the E-wave with the field components Er, Eϑ,

Bz do not vary, small satellite harmonics of these fields arise, proportional to exp[i(mϑ ±

kmz − ωt)]. At the same time due to weak coupling of _- and _- modes, caused by 0Br

nonuniformity and nonzero axial wave number of satellite harmonics, small satellite

harmonics of H-wave with the field components Ez, Br, Bϑ also arise. The amplitudes of

satellite harmonics of E-wave are shown to be symmetric: Er(+)=Er

(−), Eϑ(+)=Eϑ

(−), Bz(+)=Bz

(−),

and the amplitudes of H-wave are antisymmetric: Br(+)=−Br

(−), Bϑ(+)=−Bϑ

(−), Ez(+)=−Ez

(−).

In the second approximation in the respect to εm corrections to the amplitudes of the

fundamental harmonic of E-wave arise. The correction to the eigen frequency of the wave,

caused by the nonuniformity of 0Br

, appears to be the small value of the second order in the

respect to εm. The application of the obtained results for determining the simple analytical

expressions for the correction to the eigen frequency of surface flute modes in the limiting

case is demonstrated.

Acknowledgments. The research was supported by Science and Technology Center in

Ukraine, Project No 2313.

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Optimization of energy confinement in Uragan-2M1

B. Seiwald1, V. N. Kalyuzhnyj2, S. V. Kasilov2, W. Kernbichler1, V. V. Nemov2

1Institut fur Theoretische Physik - Computational Physics, Technische UniversitatGraz, Petersgasse 16, A–8010 Graz, Austria

2Institute of Plasma Physics, National Science Center “Kharkov Institute ofPhysics and Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine

In the frame of optimization of confinement properties of the torsatron Uragan-2M (U-2M) [1] the normalized stored energy is analyzed in the 1/ν transport regime.Using the NEO code [2], optimization runs [3] are performed for the heat conduc-tivity computation with an energy source localized at the magnetic axis. In theprevious work [4] a difference of currents in adjacent toroidal field coils has beenused as a varying parameter (as it was proposed in [5]).

Now an additional vertical magnetic field which leads to an inward shift ofthe magnetic configuration is used as such a parameter. An optimum value of thevertical field is found for the standard configuration. In this work the best inwardshifted magnetic configuration is searched for. The normalized stored energy is com-puted for two cases: (i) only the usable plasma volume within the vessel is takeninto account; (ii) plasma volume is computed without actual limitations for existingwalls. The restriction of the plasma volume because of the existing vessel leads toan optimum depending mainly on the decreased neoclassical transport coefficients.

References[1] O. S. Pavlichenko for the U-2M group, First results from the ”URAGAN-2M” tor-satron, Plasma Phys. Control. Fusion 35, B223-B230 (1993).[2] V. V. Nemov, S. V. Kasilov, W. Kernbichler and M. F. Heyn, Phys. Plasmas 6, 4622(1999).[3] B. Seiwald, V. V. Nemov, S. V. Kasilov, W. Kernbichler, Proc. of 29th EPS Con-ference on Plasma Phys. and Contr. Fusion, Montreux, 17-21 June 2002, ECA,26B,P-4.099 (2002).[4] B. Seiwald, V. V. Nemov, V. N. Kalyuzhnyj, S. V. Kasilov, W. Kernbichler, Proc.of 31th EPS Conference on Plasma Phys., London, 28 June - 2 July 2004, ECA,28G,P-5.118 (2004).[5] C. D. Beidler, N. T. Besedin, V. E. Bykov, et al., Proc. of 13th IAEA Conf. on NuclearFusion, Washington, Vol.2 (Vienna: IAEA) p.663 (1991).

1This work has been carried out within the Association EURATOM-OAW and with fundingfrom the Austrian Science Fund (FWF) under contract P16797-N08. The content of the publicationis the sole responsibility of its authors and it does not necessarily represent the views of theCommission or its services.

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Optimization Studies of TJ-II Stellarator1

B. Seiwald1, V. V. Nemov2, S. V. Kasilov2, W. Kernbichler1,J. A. Jimenez3,V. Tribaldos3

1Institut fur Theoretische Physik - Computational Physics, Technische UniversitatGraz, Petersgasse 16, A–8010 Graz, Austria

2Institute of Plasma Physics, National Science Center “Kharkov Institute ofPhysics and Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine

3Asociacion Euratom-CIEMAT, Madrid, Spain

A new numerical code SORSSA has been developed for computing the energycontent of different stellarator configurations based on a simple transport modeldepending on the neoclassical effective helical ripple. The procedure consists inestimating εeff by following magnetic field lines, for arbitrary coil systems, and thusfor β = 0 using the NEO code [1]. This method is particularly suited for existingstellarators since it allows to skip the calculation of Boozer coordinates and the usualneoclassical transport codes (drift equation solver like DKES or Monte Carlo).

The flexibility of TJ-II [2], a medium size (R = 1.5m, a < 0.2m) four fieldperiod stellarator, in obtaining different configurations arises from its four differentsets of independently fed coils: 32 helically displaced toroidal coils (responsible forthe main magnetic field), one central circular coil, one central helical coil (followingthe winding law of the toroidal coils), and two vertical field coils. SORSSA codehas been used for searching improved confinement configurations in TJ-II. To fur-ther extend the parameter space, and account for even better configurations, theeight toroidal coils of each period were separated in four different sets (to maintainthe stellarator symmetry). Results for the optimization in the eight-dimensionalparameter space will be presented and compared with the results of the standardconfiguration.

References[1] V. V. Nemov, S. V. Kasilov, W. Kernbichler and M. F. Heyn, Phys. Plasmas 6, 4622(1999).[2] C. Alejaldre et al. Fusion Technol. 17, 131 (1990).

1This work has been carried out within the Association EURATOM-OAW and with fundingfrom the Austrian Science Fund (FWF) under contract P16797-N08. The content of the publicationis the sole responsibility of its authors and it does not necessarily represent the views of theCommission or its services.

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Fast ion dynamics of NBI plasmas in Heliotron J

M. Kaneko1,S. Kobayashi2, Y. Suzuki3, T. Mizuuchi2, K. Nagasaki2, H. Okada2, Y. Nakamura1, K. Hanatani2, S.Murakami4, K. Kondo1, and F. Sano2

1Graduate School of Energy Science, Kyoto University, Gokasho, Uji 611-0011, Japan

2Institute of Advanced Energy, Kyoto University, Gokasho, Uji 611-0011, Japan 3National Institute Fusion Science, Toki, Gifu 509-5292, Japan

4Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan

In the Heliotron J device, the confinement characteristics and behavior of fast ions by tangentially injected neutral beam (NB) are investigated with a charge exchange (CX) neutral particle analyzer (NPA) system. In particular, configuration effects on the particle confinement are studied experimentally through measurements of the temporal change of CX-flux and its energy spectra. The CX-NPA system has been upgraded so as to change the horizontal (φNPA) and vertical (θNPA) angles simultaneously with the range of φNPA from –10 ο to +18 ο and θNPA from –3 ο to +10 ο.

The hydrogen NB is injected into Heliotron J deuterium plasmas heated by electron cyclotron heating (ECH). The injected ions have pitch angle from 150 ο to 175 ο. The injected energy and power of NBI are 28kV and 0.5 MW respectively. When the horizontal angel φNPA is changed from –3 ο to 12 ο, the pitch angle of detected particles varies from 107 ο to 130 ο. In the standard configuration of Heliotron J, the detected CX-flux increases, as CX-NPA is oriented to the beam facing direction. The peaks in the energy spectra corresponding to beam energy components (Eb, Eb/2 and Eb/3) are observed at φNPA > 6 ο.

A theoretical calculation has pointed out that controlling Fourier components in the magnetic field plays a key role in the fast particle confinement1. In order to investigate the configuration effect, the behavior of the CX-flux is studied by changing one of the Fourier components in the magnetic field, bumpiness component, B04/B00 from 0.04 to 0.15. Here Bmn is the Fourier component of magnetic field strength in the Boozer coordinates where m and n denote poloidal and toroidal mode numbers. In these configurations, the magnetic axis position (<R> =1.2 m), plasma volume (Vp = 0.7 m3) and rotational transform at LCFS (ι/2π(a) = 0.56) are almost fixed. In this scan, since the electron density is almost kept constant, 0.8 × 1019m-3, the ion collisionality is considered to be almost the same. The electron-ion collisionality normalized by bounce frequency of banana orbit particles at energy of 25 keV, ν*, is about 0.5. In the range of φNPA from 0 ο to 9 ο, CX-flux in high bumpiness configuration is lower than the other configurations. In the φNPA = 12 ο, no clear dependence of energy spectra on the bumpiness component is observed. A non-collisional orbit calculation predicts that the dependence of CX-flux on the bumpiness component is due to the change in the loss cone shape. The decay time of the CX-flux just after NB turned-off provides information regarding the slowing down and the confinement of fast ions. In the energy range from Eb/2 to Eb, the 1/e decay time of CX-flux increases with decreasing the energy for all configurations. It is also found that the decay of CX flux becomes slower with bumpiness, for example at B04/B00 = 0.04 0.08 and 0.15, the decay times of CX-flux at energy of 17 keV are 2.3, 3.1, 4.5 ms, respectively. The Fokker-Planck calculation taking into account of anomalous loss will be performed to understand the dependence of the fast particle confinement on bumpiness. 1. M. Yokoyama, et al. Nucl. Fusion 40 (2000) 261

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Dependence of Toroidal Current on Magnetic FieldConfiguration in Heliotron J

G.Motojima, H.Okada1), Y.Nakamura, K.Y.Watanabe2), F.Sano1), K.Nagasaki1),S.Yamamoto3), T.Mizuuchi1), S.Kobayashi1), K.Kondo, Y.Suzuki2),

K.Hanatani1), Y.Torii1), M.Kaneko, H.Arimoto, H.Yamazaki4), T.Tsuji,H.Nakamura, S.Watanabe, H.Kitagawa, H.Yabutani, S.Fujikawa, M.Uno

Graduate School of Energy Science, Kyoto Univ., Uji 611-0011, Japan1)Inst. of Advanced Energy, Kyoto Univ., Uji 611-0011, Japan

2)National Institute for Fusion Science, Toki, Gifu 509-5292, Japan3)Graduate School of Engineering, Osaka Univ., Suita 565-0871, Japan

4)Dept. of Fusion Science,The Graduate Univ. for Advanced Studies,Toki,Gifu 509-5292,Japan

It is important to understand the mechanism of a non-inductive current even inhelical devices since the toroidal current has a possibility of affecting MHD equilibrium andstability. In Heliotron J, the magnetic configurations can be controlled by changing currentratios of five sets of coils. The objective of this research is to study the dependence of thetoroidal current on the magnetic configuration and plasma parameters, for understandingthe behavior of the toroidal current in Heliotron J.

The changes of the toroidal current by changing the bumpy field component (B04)for two different kinds of discharges have been observed, where Bmn is the Fourier com-ponent of the magnetic field strength; m(n) is the poloidal(toroidal) mode number. Oneis the ECH discharge and the other is the ECH+co-NBI combination discharge under thecondition of ne = 0.8× 1019 m−3. The toroidal current is measured using Rogowski coils,and the positive direction corresponds to the co-direction, which is defined as the direc-tion of the toroidal current to increase the rotational transform. In the ECH discharge,the toroidal current changes from 0.75 kA to 0.50 kA as B04/B00 decreases from 0.17 to0.028. In the ECH+NBI discharge, it changes from 1.77 kA to 0.81 kA. The differenceof the current is considered to be due to the changes of bumpiness component, internalenergy(ECH only or ECH+NBI), and the NB current drive(Ohkawa current).

In order to investigate the dependence of the net toroidal current on B04, the neo-classical bootstrap current has been calculated using the SPBSC code[1].The calculationresults show that the bootstrap current is positive everywhere along the minor radius inthe case of B04=0.18. As B04/B00 decreases from 0.18 to -0.05, the bootstrap currentdensity is reversed at the small minor radius of the plasma and the net bootstrap currentchanges from positive to negative direction, indicating that the bootstrap current dependsstrongly on B04.

In the ECH discharge, the behavior of the toroidal current is found to be mainlyexplained by the theoretical prediction of the bootstrap current. In the ECH+NBI dis-charge, the Ohkawa current may flows at higher bumpy configurations than at lowerbumpy configurations, comparing the ECH+NBI discharge to the ECH discharge. Thissuggests that the Ohkawa current also depends on the magnetic configuration.

At the low electron density case(ne = 0.1× 1019 m−3), the net toroidal current of 0.7kA in the counter-direction has been observed. This direction is different from that of thebootstrap current calculated without Er. When the large positive Er terms are included,the current direction is found to be consistent with the experimental results. A possiblemechanism causing the reversal of the direction may be the Ohkawa effect of ECCD.　

[1]K.Y.Watanabe et al, Nucl. Fusion 35 (1995) 335.

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Effect of the Bumpy Field Component on the Bootstrap Current

Yuji Nakamura, N. Nakajima 1), K. Y. Watanabe 1), M. Yokoyama 1)

Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan 1) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

It is well known that the existence of particles trapped in the magnetic field well and

radial gradient of the plasma pressure causes spontaneous plasma current called “bootstrap current” in a magnetically confined toroidal plasma. In a recent high beta tokamak plasma, the bootstrap current comprises a large fraction of plasma current which is necessary for MHD equilibrium and plasma confinement. From this point of view, control of the bootstrap current is believed to be the most important issue for a long-pulse or steady state tokamak operation. In most of previous estimation of the bootstrap current based on the neoclassical transport theory, a tokamak plasma is considered to be axisymmetric one. Since there is non-axisymmetry in a realistic tokamak due to the toroidal field ripple produced by discreteness of toroidal field coils, it is important to estimate the effect of the toroidal field ripple on the bootstrap current in a tokamak plasma.

In a helical plasma, on the other hand, magnetic field configuration which is necessary for plasma confinement is mainly produced only by the external coil current. The estimation of the bootstrap current, therefore, is important in different sense from tokamaks. Both the magnitude and the direction of the bootstrap current depend not only on the pressure gradient but also on the configuration itself in a helical plasma. For example, it has been observed in Heliotron J that the direction of the bootstrap current can be changed according to the magnitude of the bumpy field component. However, since it is not easy to include the bootstrap current in the optimization study for an advanced helical system, the configuration is often optimized without considering net plasma current. In the present study, we estimate the bootstrap current in a non-axisymmetric (three dimensional) toroidal plasma and discuss the effect of the bumpy field component on the bootstrap current both in a rippled tokamak plasma and in a helical plasma.

* This work is partly supported by 21st Century COE program “Establishment of COE on Sustainable Energy System” from the MEXT, Japan.

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Formation and Confinement of High Energy Ions in Heliotron J

H. Okada, Y. Torii, S. Kobayashi, M. Kaneko1), J. Arakawa1), H. Kitagawa1), T. Mizuuchi,

K. Nagasaki, Y. Suzuki1), Y. Nakamura1), T. Takemoto1), S. Yamamoto2), H. Arimoto1),

K. Hanatani, K. Kondo1) and F. Sano

Institute of Advanced Energy, Kyoto University, Uji 611-0011, Japan 1) Graduate School of Energy Science, Kyoto University, Uji 611-0011, Japan 2) Graduate School of Engineering, Osaka University, Suita 565-0871, Japan

The high energy particle confinement and MHD stability are key issues of a

helical-axis heliotron device, Heliotron J as an advanced helical device. High energy ions

generated by ion cyclotron range of frequencies (ICRF) heating, or injected by neutral beam

injection (NBI) heating are utilized for the investigation of energetic ion confinement in

Heliotron J. A charge exchange neutral particle energy analyzer (CX-NPA) is scanned in the

toroidal direction in order to observe ions in the wide range of the velocity distribution.

The ICRF heating is performed in the minority heating mode for the investigation of

energetic ions using a loop antenna. The high energy flux up to 10 keV is observed during

ICRF pulse imposed on ECH target plasmas. The measured hydrogen-minority flux decreases

as increasing the toroidal angle (decreasing the pitch angle) because of the perpendicular

acceleration of protons by ICRF heating. It is noted that the loss region along the NPA’s line

of sight increases when the toroidal angle decreases from the result of the orbit calculation.

Therefore, there is a flux peak near the pitch angle = 117º. The loss region is studied in

relation to the direction of the field. The difference of the observed fluxes is also found. The

flux with the anti-parallel velocity is larger than that with parallel velocity.

High energy ion confinement is studied in relation to the magnetic configurations. It

is predicted that one of the magnetic Fourier components, toroidal mirror ripple component

(B04) plays a key role on the collisionless particle confinement in the Heliotron J

configuration. Three configurations are selected; the mirror ripples (B40/B00, where B00 is the

averaged magnetic field strength) are 0.02, 0.07 and 0.16 at the normalized minor radius ρ =

0.5. The case of 0.07 corresponds to the standard configuration of Heliotron J. This

experiment has been performed in the low density deuterium plasmas (<1x1019 m-3) since the

plasma should be collisonless. The ICRF frequency is adjusted so that the cyclotron resonance

layer may be positioned within ρ = 0.2. The observed high energy flux is largest in the case of

the highest mirror ripple and smallest for the lowest mirror. The loss region along the NPA’s

chord is larger in the case of 0.16 among the three configurations. This result suggests that the

configuration with larger mirror ripple have an effect to improve the confinement of high

energy ions.

P2-26

85

Studies of MHD Stability in Heliotron J Plasmas

S.Yamamoto1), K. Nagasaki2), Y. Suzuki3), T. Mizuuchi2), H. Okada2), S. Kobayashi2), B. Blackwell4), T. Fukuda1), K. Kondo5), G. Motojima5), N. Nakajima3), Y. Nakamura5),

C. Nührenberg6), Y. Torii2) and F. Sano2)

1) Graduate School of Enginnering, Osaka University, 2-1 Yamadaoka Suita, Japan 2) Institute of Advanced Energy, Kyoto University, Gokasho Uji, Japan 3) National Institute for Fusion Science, 322-6 Oroshi-cho Toki, Japan

4) Research School of Physical Science & Engineering, The Australian National University, Canberra, Australia

5) Graduate School of Energy Science, Kyoto University, Gokasho Uji, Japan 6) Max-Planck-Institut für Plasmaphysik, IPP-Euratom Association, Greifswald,

Germany

The main purpose of Heliotron J is to optimize the magnetic configuration aiming at the improvement in the neoclassical transport and the MHD stability. The magnetic configuration of Heliotron J has low magnetic shear in combination with a magnetic well, by which MHD instabilities particularly at low order rational surfaces can be avoided or stabilized. These properties provide extended stability against pressure driven MHD instabilities such as interchange and ballooning modes. It is important to clarify the modification of the magnetic configuration caused by the finite beta effect and plasma current and its effect on the MHD stability. Alfvén eigenmodes (AEs), which are destabilized by the energetic ions having the velocity comparable with the Alfvén velocity, is also important because the AEs would affect the energetic ion transport. In order to study these MHD instabilities, we have installed a magnetic probe arrays and Soft-X ray diode arrays in Heliotron J.

The two kinds of pressure driven MHD instabilities have been observed in ECH and/or NBI heated plasmas of Heliotron J. One is the low-n (n: toroidal mode number) interchange mode. The even m/n=1 (m: poloidal mode number) and odd m/n=3 MHD instabilities having intense magnetic fluctuations have been observed in the plasmas with low order rational surface such as ι/2π~0.5(e.g. m/n=2/1) and 0.6(e.g. m/n=5/3) (ι/2π: rotational transform). When these MHD instabilities are observed, the bulk plasma parameters such as plasma stored energy and electron density are saturated and/or decreased indicating that they affect global energy confinement. The other is the MHD instability which are observed although the low order resonance surfaces do not exist and the Mercier criterion is stable. However, these modes are considered to be a pressure driven MHD instability because their amplitude is scaled with the plasma beta and they are observed in the ECH heated plasmas.

In NBI heated plasmas, MHD instabilities in the frequency range of the Alfvén eigenmode are typically observed. In order to identify the observed modes, we have compared between the frequencies of the observed modes and the global mode analysis using CAS3D3 code [1]. The observed modes are identified with the global AEs (GAEs) destabilized by the energetic ions. The bursting GAEs with intense magnetic fluctuations have been observed in a certain magnetic configuration. They might affect the energetic ion transport from the result that some plasma parameters such as Hα and Te are simultaneously modulated with the bursting GAEs. [1] C. Nührenberg, Phys. Plasmas 6 (1999) 137.

P2-27

86

On the in-out asymmetry of divertor plasma flows in heliotron/torsatron devices

V.S.Voitsenya, S.Masuzaki1, T.Mizuuchi2, T.Morisaki1, V.D.Pustovitov3

Institute of Plasma Physics, NSC KIPT, 61108 Kharkov, Ukraine, 1National Institute for Fusion Science, Toki, Japan,

2Institute of Advance Energy, Kyoto University, Gokasho, Uji, 611 Japan, 3RRC Kurchatov Institute, 123182, Moscow, RF

Abstract

To understand the mechanism which causes the divertor flow asymmetry in heliotron/ torsatron type fusion devices is important from the viewpoint of the safety of the in-vessel components, such as divertor collector plates subject to direct impact of divertor plasma, when optimizing the regime of plasma confinement, e.g., by suppression of Pfirsch-Schluter current [1, 2], or the components of the scheme of measurements of the particle and energy fluxes to the divertor plates, i.e., electrical probes and thermocouples. In the previous works [3, 4], the divertor flow distributions in a heliotron/torsatron type fusion device, Heliotron E, was studied mainly with emphasis on asymmetry in vertical direction. The in-out asymmetry was only briefly mentioned in the review [5], nevertheless the divertor flows registered in Heliotron E by horizontally disposed collector arrays displayed some in-out asymmetry. In this paper we focus on the in-out asymmetry of divertor flows and discuss the dependence on the magnetic axis position (the horizontal shift due to variation of the vertical magnetic field or plasma pressure), power of neutral beams (NBI), and the plasma parameters.

As a measure of the in-out asymmetry in Heliotron E we use the ratio of divertor flows along the corresponding divertor legs measured in the cross section where the longer axis of an elliptical plasma cross section was directed horizontally. One flow was registered by the collector in the collector array located near the outer X-point, above the central plane, another – by the collector of the array located near the inner X-point, below the central plane.

The central plasma parameters (Te(0), ne(0)) do not strongly affect the in-out asymmetry. But a noticeable effect was observed when the port-through NBI power varied in the range 0.4-3.3 MW. However, as results indicate, the strongest change of the in-out asymmetry is observed when the magnetic axis is horizontally shifted in the range 0-4 cm from the position of the geometrical toroidal axis. The corresponding re-distribution of divertor flows between collectors was found as a result of movement of the divertor legs when magnetic axis was shifted, in a qualitative agreement with data obtained in LHD experiments.

The obtained results will be systematically discussed and analyzed. References 1. S. Besshou, V.D. Pustovitov, N. Fujita et al. Complete integral suppression of Pfirsch-Schlutter current in a

stellarator plasma in Heliotron E. – Physics of Plasmas, 5 (1998) 481. 2. M. Yokoyama, K. Itoh, K. Nagasaki, et al. Confirmation of theoretical evaluation of equilibrium current in

helical systems through the Heliotron E result for dipole current suppression and reversal. – Nuclear Fusion, 40, (2000) 1909.

3. T. Mizuuchi, V.S. Voitsenya, V.V. Chechkin et al. Influence of magnetic configuration and heating methods on distribution of divertor plasmas in Heliotron E. – J. Nucl. Mater., 266-269 (1999) 1139.

4. V.V. Chechkin, V.S. Voitsenya, T. Mizuuchi et al. Main divertor flows in Heliotron E: their distribution and dependence on NBI and ECH. – Nucl. Fusion, 40 (2000) 785.

5. V.S. Voitsenya, V.V. Chechkin, T. Mizuuchi et al. Influence of experimental conditions on distribution of divertor plasma flow in the Heliotron E fusion device. – Plasma Devices and Operations, 10 (2002) 227.

The corresponding author: Vladimir Voitsenya, voitseny@ipp.kharkov.ua

P2-28

87

35 years since the start up and the first plasma of the stellarator-torsatron “Saturn”. Main results for one decade of operation

V.S.Voitsenya, A.V.Georgiyevsky1, S.I.Solodovchenko

1Princeton Plasma Physics Laboratory, USA (consultant); Institute of Plasma Physics, NSC KIPT, 61108 Kharkov, Ukraine

Abstract

The l=3 stellarator-torsatron “Saturn” installation was the first of a series of torsatron-like devices designed, fabricated and built in Kharkov Institute of Physics and Technology (KIPT) in seventies: later were “Vint-20”, “U-3”, “U-3M”. Saturn was assigned for providing comparative investigations on the same device of properties of magnetic configurations in stellarator and torsatron regimes and for experimental examination of their effect on plasma confinement. The thorough measurements of magnetic structure in both regimes demonstrated their high equivalence. Investigations of torsatron without toroidal coils supported the principal possibility to have the spatial divertor configuration which was realized in U-3 – the first torsatron with a spatial divertor. The results on Saturn, obtained for the first time with pure torsatron configuration, have opened the prospect for torsatrons to be an alternative to tokamaks in development of a future fusion reactor. After various regimes of magnetic configurations were studied, the investigations were provided of the confinement and RF heating of injected hydrogen plasma; the characteristics of ECR plasma (frequency 10GHz) were studied depending on parameters of magnetic configuration, i.e., magnetic field strength, radius of the last magnetic surface, shear of magnetic filed lines, mean magnetic well, etc. For the first time it was shown in experiments on this device:

1. Due to special precautions and high assembling accuracy, the characteristics of magnetic configurations (radii of the last magnetic surfaces, rotational angle, shear values) in both regimes (stellarator and torsatron) were found to correspond well to calculations.

2. The dependence of particle confinement time on collision frequency for the injected plasma in both regimes was followed qualitatively to the neoclassical theory however was somehow below the absolute value predicted by theory;

3. Under RF heating of the injected plasma the rise of perpendicular ion energy (up to 1 keV) most effectively was observed at harmonics (from 2 – 5) of the ion cyclotron frequency.

4. In conditions of low hybrid resonance the electron current driven by RF was observed; 5. Plasma confinement time of injected plasma was shown to increase by excitation the

fluctuating longitudinal electric fields with frequency range overlapping the electron bounce frequency range, - due to untrapping some particles trapped in local magnetic traps, what was supported by data obtained in experiments with an ECR plasma at the first ultimate l=1 torsatron “Vint-20” with higher helical inhomogeneity of magnetic field;

6. Stabilizing effects of magnetic shear, magnetic well and ion mass on drift fluctuations of an ECH plasmas were investigated in toroidal geometry;

7. The loss of ions with energy much exceeding that corresponding to thermal ion velocity was observed due to drift across magnetic field when moving in phase with a drift wave;

8. The poloidal distributions of divertor plasma flows were measured both in stellarator and torsatron regimes with different characteristics of the Saturn magnetic configuration.

In the presentation we are going to find the bridge between those results and the nowaday experiments on existing stellarator-type fusion devices and to analyze what particular Saturn results were supported by those obtained later. The corresponding author Vladimir Voitsenya: voitseny@ipp.kharkov.ua

P2-29

88

WEDNESDAY

5th October

89

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RT-02

91

Properties of ballooning modes in the HeliotronconfigurationsN.Nakajima 1), S.R.Hudson 2), C.C.Hegna 3)

1) National Institute for Fusion Science, Oroshi-cho 322-6, Toki 509-5292, Japan2) Princeton Plasma Physics Laboratory, P.O.Box 451, Princeton NJ 08543, USA.3) Department of Engineering Physics, University of Wisconsin-Madison, WI 53706, USA.

e-mail contact of main author: nakajima@nifs.ac.jp

The stability of ballooning modes is influenced by the local and global magnetic shearand local and global magnetic curvature so significantly that it is fairly difficult to get thosegeneral properties in the three dimensional configurations with strong flexibility due to theexternal coil system. In the case of the planar axis heliotron configurations allowing a largeShafranov shift, like LHD [1], properties of the high-mode-number ballooning modes have beenintensively investigated.

It has been analytically shown that the local magnetic shear comes to disappear in thestellarator-like global magnetic shear region, as the Shafranov shift becomes large [2]. Basedon this mechanism and the characteristics of the local and global magnetic curvature, itis numerically shown that the destabilized ballooning modes have strong three-dimensionalproperties (both poloidal and toroidal mode couplings) in the Mercier stable region, and thatthose are fairly similar to ballooning modes in the axisymmetric system in the Mercier unstableregion [3]. As is well known, however, no quantization condition is applicable to the ballooningmodes in the three-dimensional system without symmetry, and so the results of the high-mode-number ballooning modes in the covering space had to be confirmed in the real space. Such aconfirmation has been done in the Mercier stable region [4] and also in the Mercier unstableregion [5] by using three dimensional linearized ideal MHD stability code cas3d [6].

Confirming the relation between high-mode-number ballooning analyses by the global modeanalyses, the method of the equilibrium profile variations has been developed in the treedimensional system, giving dι/dψ − dP/dψ stability diagram corresponding to the s − αdiagram in tokamaks [7]. This method of profile variation are very powerful to investigatethe second stability of high-mode-number ballooning modes and has been more developed[8]. Recently it has been applied to the plasma in the inward-shifted LHD configuration [9],where it has been shown that the plasma core region stays in the second stability region ofthe high-mode-number ballooning modes, and that the peripheral region is near the marginalstable.

In this work, the ballooning researches in the planar axis heliotron configurations will besummarized systematically, and recent research related to the ballooning modes like the secondstability and so on in the inward-shifted LHD configurations will be extended.

[1] A.Iiyoshi, et.al, Nucl.Fusion 39 (1999) 1245.[2] N.Nakajima, Physc.Plasmas 3 (1996) 4545.[3] N.Nakajima, Physc.Plasmas 3 (1996) 4556.[4] J.Chen, N.Nakajima, and M.Okamoto, Physc.Plasmas 6 (1999) 1562.[5] N.Nakajima, C.Nuhrenberg, and J.Nuhrenberg, J.Plasma Fusion and Res. SER. 6 (2005)45.[6] C.Nuhrenberg, Physc.Plasmas bf 6 (1999) 137.[7] C.C.Hegna, N.Nakajima, Physc.Plasmas, 5 (1998) 1336.[8] S.R.Hudson and C.C.Hegna, Physc.Plasmas 10 (2003) 4716 .[9] N.Nakajima, S.R.Hudson, C.C.Hegna, and Y.Nakamura, IAEA20, TH5/6

IT-14

92

Brillouin limit for electron plasmas confined on magnetic surfaces

Allen H. Boozer

Department of Applied Physics and Applied MathematicsColumbia University, New York, NY 10027

As is well known, the density of pure electron plasmas that are confined by amagnetic field is limited by the Brillouin density,

†

nB ≡ e0B2 /2me . However, the electron

density can be limited to a much lower value when the electrons are confined on magneticsurfaces, such as the surfaces produced by a stellarator. If the electron temperature is aspatial constant, the electron force-balance equation,

†

me

er v ⋅

r — v +

r — pen

=r — F -

r v ¥r B ,

can be rewritten as

†

r — F* =

r v ¥r B * .

The effective electric potential and the effective magnetic field are

†

F* ≡ F -me

2ev 2 - T ln(n) and

†

r B * ≡

r B - me

e— ¥

r v .

The electron density for magnetic confinement in a cylinder with

†

r B = Bˆ z is

bounded by the Brillouin limit. If one assumes the electrons are pressureless and have aspatially constant density n0, then

†

F = (en0 /4e0)r2 . Both

†

r B * and

†

F* vanish when n0 = nB,and the equation

†

r — F* =

r v ¥r B * has no solutions for n0 > nB.

The confinement of electrons on magnetic surfaces is lost when the field lines ofthe effective magnetic field

†

r B * leave the confinement region and strike the chamber walls.

If the magnetic surfaces of the true field

†

r B are described by the toroidal flux, yt that they

enclose, so

†

r B ⋅

r — y t = 0, then confinement is easily lost when

†

r — y t ⋅

r — ¥

r v has Fourierterms that resonate with the rotational transform of

†

r B , for then the

†

r B * surfaces are split by

islands. The resonant Fourier terms are given by

†

(r B ¥

r — y t ) ⋅

r — (v|| /B) . In other words,

resonant Fourier terms in the parallel flow of the electrons can cause a break up of thesurfaces of the

†

r B * field. The parallel flow is determined by the condition that

†

r — ⋅ (nr v ) = 0,

which implies

†

r B ⋅

r — (v|| /B) = -

r — ⋅ (nr v ) . When n 0<<nB, the divergence of the

perpendicular flow is given by

†

r — ⋅ (nr v ) = (

r B ¥

r — F) ⋅

r — (n /B2) . Variations in the

geometry, which cause the electron density n to vary on the magnetic surfaces, andvariations in the magnetic field strength on the magnetic surfaces can both drive resonantFourier terms in

†

r — y t ⋅

r — ¥

r v that are proportional to n/nB. These terms cause a loss ofconfinement when they are sufficiently large to destroy the surfaces of the effectivemagnetic field

†

r B *. This work was supported by the grant DE-FG02-95ER54333 from the U.S.

Department of Energy and PHY-0317359 from the National Science Foundation.

IT-15

93

Sheared plasma flow generation - a new measure for stellaratoroptimization

D. A. Spong,

Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169

Recent stellarator optimization efforts have primarily targeted transport measures such asquasi-symmetry, effective ripple and alignment of particle guiding center orbits with fluxsurfaces. For the three forms of quasi-symmetry (helical/toroidal/poloidal), as well as for avariety of nearly-omnigenous systems, this has led to significant reductions in neoclassicallosses so that, at least for near-term experiments, the neoclassical transport of particles andenergy can be made insignificant compared to anomalous transport. However, momentumtransport properties provide an additional dimension for characterizing optimized stellarators.The momentum and flow damping features of optimized stellarators can vary widely,depending on their magnetic structure, ranging from systems with near tokamak-likeproperties where toroidal flows dominate to those in which poloidal flows dominate andtoroidal flows are suppressed. We have developed a set of tools1 for self-consistentlyevaluating the flow characteristics of different types of stellarators based on using a momentsmethod2 coupled with the DKES3 model; applications to a variety of stellarators will bediscussed. The understanding of momentum transport in three-dimensional systems is ofimportance due to its relevance to transport barrier generation, enhanced confinement regimeaccess, impurity transport, bootstrap current prediction, and magnetic island suppression.Although it is too early to define what constitutes the optimal form of momentum transportcharacteristics, the wide variation of possibilities1 in present and planned stellaratorexperiments provides an attractively diverse environment both for answering this questionand developing improved scientific understanding. Comparisons across devices can aid inunfolding the interplay between anomalous and neoclassical damping effects as well as theimpact of momentum transport properties on related plasma phenomena.

Acknowledgements – Research sponsored by the U.S. Department of Energy under ContractDE-AC05-00OR22725 with UT-Battelle, LLC.

1D. A. Spong, Phys. of Plasmas 12, 056114-1 (2005).2H. Sugama, S. Nishimura, Phys. of Plasmas 9, 4637 (2002).3W. I.Van Rij and S. P. Hirshman, Phys. Fluids B, 1, 563 (1989).

IT-16

94

Heavy Ion Beam Probe investigations of plasma potential in ECRHand NBI in the TJ-II stellarator

A.V.Melnikov, A.A. Chmyga(*), N. Dreval(*), L. Eliseev, S.M. Khrebtov (*), A.D.Komarov (*), A.S. Kozachok (*), L. Krupnik(*), S. V. Perfilov

Institute of Nuclear Fusion, RRC Kurchatov Institute, Moscow, Russia*Institute of Plasma Physics, NSC KIPT, Kharkov, Ukraine

A. Alonso, J. L. de Pablos, A. Cappa, A. Fernández, C. Fuentes, C. Hidalgo, M.Liniers, M.A. Pedrosa,

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, Madrid, Spain

Direct measurements of electric potential and its fluctuations are of a primaryimportance in magnetic confinement systems. The Heavy Ion Beam Probe (HIBP)diagnostic is used in TJ-2 stellarator to study directly plasma electric potential profileswith spatial (up to 1cm) and temporal (up to 10 µs ) resolution. The singly chargedheavy ions Cs + with energies up to 125 keV are used to probe the plasma columnfrom the edge to the core. Both ECRH and NBI heated plasmas (PECRH= 200 -400kW, PNBI = 400kW, ENBI = 28 kV) were studied.

The significant improvement in the HIBP beam control system and the acquisitionelectronics leads us to increase the possibilities of the diagnostic. The most crucialone is the extension of the signal dynamic range, which allows us to have the reliableprofiles from the plasma center to the plasma edge both in the high and low field sideregions.

Low density ECRH (n = 0.5-1.1×1013 cm–3) plasmas in TJ-2 are characterised by corepositive plasma potential of order of 500 – 1000 V and positive electric fields up to 50V/cm. Edge radial electric fields remain positive at low densities and became negativeat the threshold density that depends of plasma configuration [1].

NBI plasmas are characterized by negative electric potential in the full plasma columnand negative radial electric fields (in the range of 10 – 40 V/cm). The density riseduring the NBI phase is accompanied by the decay of core plasma potential. Whendensity is getting the level of n ≈ 2.0 ×1013 cm–3, the potential stops its evolution andremains constant. The evolution of plasma potential near density limit is underinvestigation. These observations, reported in different magnetic configurations, showthe clear link between plasma potential and plasma density.

[1] M.A. Pedrosa et al., This conference

Or-09

95

Current control by ECCD for W7-X

Yu. Turkin, H. Maaßberg, C.D. Beidler, J. Geiger, N.B. Marushchenko

Max-Planck-Institut für Plasmaphysik, EURATOM-Association,D 17491 Greifswald, Germany

One of the optimization criteria for the stellarator W7-X is the minimization of thebootstrap current1. The plasma current changes the magnetic configuration, especially near theplasma edge, where X-points and islands are located. It was shown2 that the plasma parameterdistributions in the divertor region and the particle and energy depositions on the divertorplates depend strongly on the island geometry. An estimation of the tolerable plasma currentobtained from the shift of the island structure close to the target plates shows that the plasmacurrent should be controlled within a range of about 10 kA. The bootstrap current even for thestandard configuration can easily exceed this value. The W7-X is not equipped with anOhmic transformer, so the only means for compensating this current is electron cyclotroncurrent drive (ECCD) and/or neutral beam current drive (NBCD).

In this report we study the compensation of residual bootstrap current by using ECCD.To model the control of the toroidal current we use a predictive 1D transport code, which isunder development3. For evaluation of the bootstrap current and neoclassical transportcoefficients we use results from an international collaboration on neoclassical transport instellarators4. Power deposition and current drive profiles due to electron cyclotron resonanceheating are calculated by a new ray tracing code5. The modeling showed that the loop voltageinduced by ECCD leads to a redistribution of the current density with the diffusion time ofabout two seconds. The relaxation time of the total current is much longer than this time – fora typical ECRH-plasma the total toroidal current reaches steady state after several L/R-timethat is about hundreds of seconds. In order to keep current in an acceptable range and to avoidlong relaxation times we propose Feed-forward or Predictive control using ECCD as actuator,the steps are as follows:– calculate the bootstrap current distribution using measured plasma parameters in the

online transport analysis,– determine and apply ECCD needed.

The results of modeling of the Feed-forward control showed that it is possible to keepthe residual toroidal current in a tolerable range.

1. C. Beidler et al. Fusion Technology 17, 148(1990)2. Y. Feng et al. . 30th EPS Conf. on Plasma Phys., St. Petersburg, 7-11 July 2003 ECA Vol. 27A, O-4.4C3. Yu. Turkin et al. 31st EPS Conf. on Plasma Phys. London, 28 June - 2 July 2004 ECA Vol.28G, P-1.1984. C.D. Beidler et al. 30th EPS Conf. on Plasma Phys., St. Petersburg, 7-11 July 2003 ECA Vol. 27A, P-3.25. N.B. Marushchenko et al. Optimization of ECE diagnostic for W7-X stellarator, 15th International

Stellarator Workshop 2005, 3 - 7 October 2005

Or-10

96

Quasi-isodynamic Configuration with Large Number of Periods

V.D. Shafranov1, W.A. Cooper2, M.Yu. Isaev1, V.N. Kalyuzhnyj3, S.V. Kasilov3,W. Kernbichler5, M.I. Mikhailov1, V.V. Nemov3, C. Nuhrenberg4,

J. Nuhrenberg4, A.A. Subbotin1, R. Zille4

1 Russian Research Centre ”Kurchatov Institute”, Moscow, Russia2 CRPP, Association Euratom-Confederation Suisse, EPFL, Lausanne, Switzerland

3 Institute of Plasma Physics, National Science Center ”Kharkov Institute of Physicsand Technology”, Kharkov, Ukraine

4 Max-Planck-Institut fur Plasmaphysik, IPP-EURATOM Association, Germany5 Institut fur Theoretische Physik, Technische Universitat Graz, Austria

It has been previously reported that quasi-isodynamic (qi) stellarators [1,2] withpoloidal direction of the contours of B on magnetic surface can exhibit very good fast-particle collisionless confinement. In addition, approaching the quasi-isodynamicity con-dition leads to diminished neoclassical transport and small bootstrap current. The cal-culations of local-mode stability show that there is a tendency toward an increasing betalimit with increasing number of periods (see, e.g. reports [3-5]). The consideration of thequasi-helically symmetric systems [6] has demonstrated that with increasing aspect ratio(and number of periods) the optimized configuration approaches the straight symmetriccounterpart, for which the optimal parameters and highest beta values were found byoptimization of the boundary magnetic surface cross-section [7]. The qi system consid-ered here with zero net toroidal current do not have a symmetric analogue in the limitof large aspect ratio and finite rotational transform. Thus, it is not clear whether someinvariant structure of the configuration period exists in the limit of negligible toroidaleffect and what are the best possible parameters for it. In the present paper the results ofan optimization of the configuration with N = 12 number of periods are presented. Suchproperties as fast-particle confinement, effective ripple, structural factor of bootstrap cur-rent and MHD stability are considered. It is shown that MHD stability limit here is largerthan in configurations with smaller number of periods considered earlier. Nevertheless,the toroidal effect in this configuration is still significant so that a simple increase of thenumber of periods and proportional growth of aspect ratio do not conserve favourableneoclassical transport and ideal local-mode stability properties.

1. S. Gori, W. Lotz and J. Nuhrenberg, 1996 Theory of Fusion Plasmas (International Schoolof Plasma Physics) (Bologna: SIF) p. 335.2. M.I. Mikhailov et al, Nuclear Fusion 42 2002 L23.3. J. Nuhrenberg et al, ”Report on INTAS Projecr No. 592: Novel Approaches to Improve Con-finement in 3D Plasma Magnetic Systems”, 14th International Stellarator Workshop, September2003, Greifswald.4. M.A. Samitov et al, ”Numerical Optimisation of a Three-Period Stellarator Configurationwith Respect to Quasi-isodynamicity”, report on IAEA Technical Meeting on Innovative Con-cepts and Theory of Stellarators, Greifswald, Germany, 29.09-01.10 2003.5. V.D. Shafranov et al, ”Optimized N=9 Stellarator Configuration with Poloidally ClosedContours of B on the Magnetic Surfaces”,report on IAEA Technical Meeting on InnovativeConcepts and Theory of Stellarators, Greifswald, Germany, 29.09-01.10 2003.6. J. Nuhrenberg and R.Zille, 1988 Theory of Fusion Plasmas (International School of PlasmaPhysics) (Bologna: SIF) p. 3.7. R. Gruber, P. Merkel, J. Nuhrenberg, F. Troyon, Nuclear Fusion 23 (1983) 1061.

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Development of Integrated Simulation System for Helical Plasmas

Yuji Nakamura, M. Yokoyama 1), N. Nakajima 1), A. Fukuyama 2), K. Y. Watanabe 1), H. Funaba 1), Y. Suzuki 1), S. Murakami 2), K. Ida 1), S. Sakakibara 1), H. Yamada 1)

Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan 1) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

2) Graduate School of Engineering, Kyoto University, Kyoto, Kyoto 606-8501, Japan Recent progress of computers (parallel/vector-parallel computers, PC clusters, for

example) and numerical codes for helical plasmas like three-dimensional MHD equilibrium codes, combined with the development of the plasma diagnostics technique, enable us to do the detailed theoretical analyses of the individual experimental observations. Now, it is pointed out that the experimental data analysis from the viewpoints of integrated physics is an important issue to understand the confinement physics globally. To do that, the development of the integrated simulation system which has a modular structure and user-friendly interfaces is necessary. The integrated numerical simulation will also be a good help to draw up new experimental plans. In this study, we have started the development of such a system.

The integrated simulation system to be developed has a modular structure which consists of modules for calculating MHD equilibrium/stability, transport and heating. Each module can be selected in accordance with a user’s request and can be combined with other modules. In order to maintain the independence of each module, which is an independent and complete program, sequences of the integrated simulation are controlled by a shell or script (perl or ruby, for example). Since some modules are suitable for running on the vector machine and others are on the PC cluster, we are going to develop a module-by-module distributed computing system through the network.

When we want to perform the integrated simulation during the entire plasma duration, a transport module is to be a core module. An integrated tokamak transport code, TASK[1], which is a core code for BPSI (Burning Plasma Simulation Initiative; research collaboration among universities, NIFS and JAERI in Japan) activity, will be extended for the helical configuration and used as a transport module. As the first step of the extension of the TASK, time evolution of the plasma net current, which is consistent with the three-dimensional MHD equilibrium (by VMEC), is solved for LHD plasmas by taking into account of the bootstrap current and the beam-driven current (obtained by the BSC code). We will compare the result to the experimental data, and the knowledge obtained by the comparison will be used for code development as a feedback.

* This work is supported by the LHD Coordinated Research program of NIFS and 21st Century COE program “Establishment of COE on Sustainable Energy System” from the MEXT, Japan.

1. A. Fukuyama, S. Murakami, M. Honda, Y. Izumi, M. Yagi, N. Nakajima, Y. Nakamura, T. Ozeki, Advanced Transport Modeling of Toroidal Plasmas with Transport Barriers, Proc. of 20th IAEA Fusion Energy Conf., IAEA-CSP-25/TH/P2-3 (Vilamoura, Portugal, Nov. 1-6, 2004)

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High-speed turbulence imaging and wavelet-based analysis

during edge shear flow development in TJ-II plasmas.

J.A. Alonso, S.J. Zweben1, H. Thomsen2, C. Hidalgo, T. Klinger2,

B.Ph. van Milligen, J.L. de Pablos, M.A. Pedrosa

Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, 28040 Madrid, Spain1 Princeton Plasma Physics Laboratory, Princeton, NJ, USA

2 Max-Planck-Institut für Plasma Physik, EURATOM Ass., 17491 Greifswald, Germany

Transport in fusion devices is a phenomenon with high degree of complexity. Two-dimensional

images of edge plasma turbulence have been obtained by high-speed imaging in the visible

range in the edge of tokamak devices [1], [2].

Recently, a 2-D visualization of transport has been investigated in the plasma edge of the TJ-II

stellarator. A Princeton Scientific Instruments intensified camera with CCD sensor (PSI-5) was

used with Hα filter, achieving recording ratios up to 250.000 frames per second. The storage

capacity is 300 frames with 64 by 64 pixels resolution, thus giving 1.2ms total recording time

at maximum speed with an image every 4µs.

The view plane is in a near-poloidal cross-section with optimized B-field perpendicularity.

Neutral recycling at the poloidal limiter is used to light up the outer plasma region(ρ ∼ 0.8-

1). Bright, long-living structures are frequently seen with a spatial extent of few centimeters.

Those structures show predominant poloidal movements with typical speeds of 103 - 104 ms−1

in agreement with the expectedE×B drift rotation direction.

Image analysis techniques were implemented for characterising blob geometry (aspect ratio,

orientation...) in TJ-II different velocity shear regimes. The method has a detection-recognition

scheme based on isotropic (detection) and anisotropic (recognition) 2D wavelets. Three differ-

ent scales were considered in the analysis (3cm, 1.5cm and 0.75cm).

Preliminary results show a reduction in the angular dispersion of blobs as the shear layer is

stablished in the boundary, as well as a slight though visible shift of the aspect ratio histogram

towards higher values. These results are consistent with the picture of the shear layer stressing

blobs as well as ordering them.

The evolution of 2D turbulent structures during biasing induced improved confinement regimes

is under investigation.

References

[1] S.J. Zwebenet al, Nucl. Fusion44, (2004) 134.

[2] J.L. Terryet al, Phys. Plasmas10, (2003) 1739.

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Ion Temperature Profiles on TJ-II Stellarator During NBI PlasmaHeating

R. Balbín, S. Petrov1, J.M. Fontdecaba, K. J. McCarthy, J. M. Carmona, J. Guasp, M.Liniers, C. Fuentes, F. Castejón

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain1A.F. Ioffe Physical Technical Institute, St. Petersburg, Russia

The ion temperature of plasmas in the TJ-II flexible heliac [1] has been measuredusing two Acord-12 neutral particle analysers [2]. These analysers can scan the plasmapoloidally to obtain ion temperature profiles. The measurements presented were performedduring NBI plasma heating three similar magnetic configurations whose volume insidetheir last closed flux surface is about 1 m3 and whose effective minor radius is 0.20 m. Inaddition, their rotational transform at the centre varies from 1.49 to 1.7. Also, for theconfigurations studied the rotational transform increases slightly from the centre to theedge, since TJ-II is an almost shearless device, without giving rise to magnetic islandsinside the plasma volume.

The plasmas studied were created in hydrogen using two gyrotrons having a totalpower of about 400 kW. The pulse duration was 250 ms and the power deposition profilewas off-axis in two of the configurations. In the other configuration the power depositionprofile was on-axis. In these discharges ~350 kW of neutral beam injection (30 keV, 150ms) was used for additional plasma heating [3]. These plasmas were characterized by astrong increase in plasma density during the NBI pulse and by the high fraction of powerabsorbed by the electrons.

As shown previously, the ion temperature profile is flat in ECRH plasmas createdin the TJ-II [4]. In these new studies, this profile remains flat during part of theECRH+NBI stage. Both of theses stages are distinguished by low density (ne ≤ 8 x 101 8

m-3) and highly peaked electron temperature profiles. During the high-densityECRH+NBI stage the plasmas have low electron temperatures while the ion temperatureprofile changes from flat to peaked. This result suggests that NBI heating occurs withinthe ρ = 0.5 effective radius.

[1] E. Ascasibar et al., Fusion Eng. Des. 56-57 (2001) 145[2] A.B. Izvozchikov, M. P. Petrov, S. Ya. Petrov et al., Tech. Phys., 37 (1992) 201.[3] M. Liniers et al., "First Experiments in NBI Heated Plasmas in the TJ-II Stellarator"

Proc. 31st EPS Conf. On Controlled Fusion and Plasma Physics (London) Vol 28G(ECA) (Mulhoulse: EPS) P4_183 (2004).

[4] J. M. Fontdecaba et al., Fusion Science and Technology, 46(2), pp. 271-278, (2004).

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Microwave Reflectometry in TJ-II

E. Blanco, T. Estrada, L. Cupido*, M.E. Manso*, V. Zhuravlev** and J. Sánchez

Laboratorio Nacional de Fusión, Asociación Euratom-CIEMAT, Madrid, Spain*Associação Euratom-IST, CFN, Instituto Superior Técnico, Lisboa, Portugal

** Institute of Nuclear Fusion, RNC Kurchatov Institute, Moscow, Russia

Microwave reflectometry is commonly used to measure electron density profiles andfluctuations. In TJ-II a broadband fast frequency hopping system [1] has been recentlyinstalled for measuring plasma turbulence while an Amplitude Modulationreflectometry system [2] provides information on the density profile. The first systemallows probing several plasma layers within a short time interval during the discharge,permitting the characterization of the radial distribution of plasma fluctuations. Thesecond system provides the time evolution of the density profile what allows the radiallocalization of the fluctuation measurements. In addition, we have developed a two-dimensional full-wave numerical code [3] to help in the interpretation of theexperimental data and to study the viability and performance of different reflectometrytechniques.Experimental measurements have permitted the characterization of the shear layer in theperpendicular rotation velocity of the fluctuations. These observations have beencrosschecked with results obtained using the two-dimensional full-wave code. Bothexperimental and numerical results demonstrate the capability of the reflectometer tomeasure the velocity shear layer with a high spatial resolution [4].The experiments also show a modifications in the reflectometry signals spectraassociated with the presence of a low order rational surface in the rotational transformprofile within the radial range covered by the reflectometer. These experimental resultscan be interpreted in terms of a localized increase in the perpendicular rotation velocityof the fluctuations.Finally we present some numerical studies that have been performed to study theviability of the Doppler reflectometry technique [5] to determine the perpendicularrotation velocity in TJ-II.

[1] L. Cupido, J. Sánchez and T. Estrada. Rev. Sci. Intrum. 75 (2004) 3865[2] T. Estrada, J. Sánchez, B. van Milligen, L. Cupido, A. Silva, M.E. Manso and V. Zhuravlev.Plasma Phys. Control. Fusion 43 (2001) 1535[3] E. Blanco, S. Heuraux, T. Estrada, J. Sánchez and L. Cupido. Rev. Sci. Intrum. 75 (2004)3822[4] T. Estrada, E. Blanco, L. Cupido, M.E. Manso and J. Sánchez. Submitted to Plasma Phys.Control. Fusion.[5] M. Hirsch, E. Holzhauer, J. Baldzuhn, B. Kurzan and B. Scott. Plasma Phys. Control. Fusion43 (2001) 1641

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Experimental evidence of coupling between density tails and turbulent

transport in the scrape-off layer region in the TJ-II stellarator

E. Calderón, M.A. Pedrosa, C. Hidalgo, C. Silva *, O. Orozco

EURATOM-CIEMAT, 28040-Madrid, Spain

*EURATOM-IST, Lisbon

The importance of intermittent plasma turbulence to explain non-exponential decays ofthe plasma parameters profiles in the scrape-off layer (SOL) has been investigated intokamak plasmas. Furthermore, the statistical properties of turbulent particle flux havebeen investigated in the plasma boundary region of tokamak and stellarator devicesshowing a striking similarity 1, 2

This paper shows a direct link between non-exponential SOL decays and the statisticalproperties of turbulent particle flux in the plasma boundary region of the TJ-IIstellarator. Comparative studies of the structure of turbulence in ECRH and NBIplasmas in the TJ-II stellarator has shown a drastic decrease in the level of turbulence inthe transition from ECRH (200 - 400 kW) to NBI (400 kW) plasmas. As a consequence,the radial effective velocity of transport decreases by about a factor of ten and non-exponential tails usually observed in ECRH plasmas disappear in the NBI regime.

The influence of electrode biasing in the structure of plasma boundary profiles andfluctuations is under investigation3. Experimental results show that it is possible tomodify global particle confinement and edge plasma parameters and fluctuation levelswith both positive and negative biasing. As a consequence the radial effective velocityand non-exponential tails are reduced.

These findings provide evidence of coupling between radial velocity of turbulenttransport events and the structure of SOL profiles in the TJ-II stellarator

1. C. Hidalgo et al., New Journal of Physics 4 (2002) 51.1

2. J.A. Boedo et al., Phys. of Plasmas 10 (2003) 1670.

3. C. Silva et al., This conference

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Ion temperaturre and flows measurements by means of a combined force-Mach-Langmuir probe

E. Calderón-Obaldía, T. Lunt*, C. Hidalgo, M. A. Pedrosa

Laboratorio Nacional de Fusión-CIEMAT, Madrid 28040*Humboldt-Universität zu Berlin, Institut für Physik.

D. Chavers et. al1 have recently proposed the use of a force sensor to measure momentumfluxes and it has been shown experimentally that forces in the range of mN are measurable ina non-fusion plasma discharge. Recently a new diagnostic, the combined Force-Mach-Langmuir probe, has been developed and manufactured to provide ion temperature and flowmeasurements.

First experimental results were carried out at the plasma generator PSI-2 showing iontemperatures in the order of 1 eV for Argon and Helium (Fig. 1). The combined Force-Mach-Langmuir probe, measuring the force and ion saturation current differences between its twosurfaces and the electron temperature by means of the tips on the bottom of the probe, issuitable for determining the ion temperature and flows. The calibration procedure of thediagnostic is discussed. Experiments are in progress to investigate ion temperature and flowsin the boundary of toroidal plasmas using the combined Force-Mach-Langmuir probe.

1. D. G. Chavers, Franklin R. Chang-Díaz, Review of Scientific Instruments, 73 (2002).2. E. Calderón- Obaldía et al., 6th international workshop on electrical probes in magnetized plasmas,

Seoul (Korea), May 2005.

1

1.5

2

2.5

100 Amp

200 Amp150 Amp

time (s)0 100 200 300

ARGON

Ion

tem

per

atu

re (

eV)

time (s) 100 200 300

100 Amp

200 Amp

150 Amp

HELIUM

Fig. 1. Comparison of the ion temperature for Argon and Helium plasmas at different dischargecurrents.

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103

Experimental dependence of ECR plasma breakdown on wave

polarization in the TJ-II stellarator

A. Cappa1, F. Castejón1, K. Nagasaki2, F. Tabarés1, A. Fernández1,

D. Tafalla1, E. de la Cal1, T. Estrada1

1 Laboratorio Nacional de Fusión, Madrid, Spain2 Institute of Advanced Energy, Kyoto University, Japan

Recently, second harmonic ECRH plasma breakdown and its dependence on the initial con-

ditions such as neutral gas pressure, injected power or beam polarization has been the subject of

theoretical as well as experimental work [1, 2, 3]. Although those studies have been carried out

in the context of stellarators, they are particularly relevant in the case of large tokamaks, such as

ITER, where conventional inductive breakdown is expected to be strongly improved if ECRH

is used. A matter of interest is the dependence of breakdown time on wave polarization. In the

existing theoretical models, wave polarization is not taken into account because it is assumed

that the injected ECRH power is initially scrambled by the vessel walls and that the energy

source for breakdown is only due to the non-linear wave-particle interaction between deeply

trapped electrons and the averaged electric field. However, while this seems reasonable for the

very beginning of the discharge, it may not be so as we progress towards breakdown. Actually,

as experiments in Heliotron J have demonstrated, wave polarization must be taken into account

in the description of the energy source.

Breakdown experiments in TJ-II were performed in order to get a deep insight into this matter

and part of the results of breakdown dependence on wave polarization were already discussed

in [4]. In particular, it was demonstrated that the hypothesis about the energy source used in

the models is failing long before full ionization is completed. But more information in relation

with our understanding of the second harmonic ECRH breakdown, such as the toroidal and

radial breakdown propagation, which is seen to be non-diffusive, can be extracted. Thus, the

experiment results provide valuable data that can be used not only to improve the energy source

but also to include spatial dimensions in the breakdown models.

References

[1] A. Cappa, F. Castejón, F.L. Tabarés, D. Tafalla, Nucl. Fusion41, 363 (2001).

[2] K. Nagasaki et al., Nucl. Fusion45, 13 (2005).

[3] J.W. Radder et al., 13th International Stellarator Workshop, Canberra (2002).

[4] A. Cappa et al., 32th EPS Conference, Tarragona (2005).

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A study of central impurity ion temperatures during ECR and NBI

heating phases in TJ-II stellarator plasmas

J.M Carmona, K. J. McCarthy, J.M Fontdecaba, S. Petrov1, R. Balbín, V. I. Vargas, B. Zurro

Laboratorio Nacional de Fusión, Asociación Euratom-CIEMAT, E-28040 Madrid, Spain1A.F. Ioffe Physical Technical Institute, St. Petersburg, Russia

Doppler spectroscopy of lines emitted by impurity ions is one of the most powerful

tools for estimating ion temperatures in fusion plasmas. For this spectral lines emitted by

impurity ions are fitted by a Gaussian function in order to determine their impurity temperature

from their line-widths. In the TJ-II spectral line information is repeatedly collected during

discharges with a f/10.4 1 m normal-incidence vacuum spectrometer equipped with 1200 and

3600 lines/mm gratings and a CCD camera with 400 × 1340 pixels (20 × 20 µm2). Also, in this

heliac device strong collisional coupling between majority (H+) and impurity ions should ensure

that these ions should be well thermalised. However, in a previous study carried out in TJ-II the

measured impurity temperatures deduced from line-width measurements were found to be

significantly higher than the proton temperatures [1]. These differences were attributed to non-

thermal velocities that were shown to produce a Gaussian contribution to line-width.

In this paper, spectral line widths of several highly-ionised impurity ions are measured

along discharges and the ion temperatures deduced are compared for both ECRH and NBI

phases in order to determine how the effect observed previously evolves with plasma electron

density and heating method. Simultaneously, majority ion temperatures are measured using two

Acord-12 neutral particle analysers [2]. These analysers can poloidally scan the plasma in order

to obtain ion temperature profiles during ECRH and NBI phases.

[1] K.J. McCarthy et al, Europhys. Lett. 63, 49-55 (2003).

[2] R. Balbín et al., to be presented at this conference.

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Ion orbits and ion confinement studies on ECRH plasmas in TJ-IIstellarator

F. Castejón1,4, J. M. Fontdecaba1, D. López-Bruna1, R. Balbín1, J. Guasp1, D. Fernández-Fraile2, L. A. Fernández2,4, V. Martín-Mayor2,4, J. M. Reynolds3,4, A. Tarancón3,4

1Laboratorio Nacional de Fusión –Asociación Euratom/Ciemat, 28040-Madrid, Spain2Universidad Complutense de Madrid, 28040-Madrid, Spain.

3Universidad de Zaragoza, 50009-Zaragoza, Spain4Bifi: Instituto de Biocomputación y Sistemas Físicos Complejos, 50009-Zaragoza, Spain

It has been observed that the ion temperature profile of several ECR heated stellaratorplasmas is almost flat and it is even possible to find energetic ions well outside last closemagnetic surface. For instance, this feature has been observed in TJ-II Flexible Heliac [1]and LHD Heliotron [2]. Of course, the heat diffusivity obtained for such ion temperatureprofiles is very high and one should consider the possibility that transport cannot bedescribed by Fick’s law. In a previous work, the neutral fluxes and corresponding energieswere measured for ECR heated plasmas in TJ-II. The measurements were carried out bymeans of two charge–exchange neutral particle analysers for radial positions r/a > 0,6 andshowed that the absolute fluxes of hot neutrals go down as the minor radius increases, buttheir mean energies remain roughly constant even outside the last closed magnetic surface[3].

The explanation that was given in [3] for such flat mean energy profile was that theion orbits are wide enough to communicate distant parts of the plasma radius, thereforegiving an effective flat ion temperature profile, for the low density plasmas considered inthat experiment. Some recent calculations show that ion orbits are pretty wide in tokamaks[4], which makes feasible the former explanation. The size of the orbits is determined by theenergy of the ions and they are heated mainly in the plasma core by collisions with hotelectrons.

Ion trajectories with different energies, pitches and starting points have beenestimated and compared with the experimental data presented in [3], paying attention to theion velocity distribution. The dependence of ion orbits and, hence, of ion confinement on theenergy is studied with the results of the calculations. In particular, it is possible to check thevalidity of the previous explanation for the detected energy spectra of the CX-neutralsescaping from the plasma and, especially, for those hot CX-neutrals detected well outsidelast plasma surface.

References [1] F Castejón et al. Review of Scientific Instruments 74 (2003) 1795[2] K Ida et al. Plasma Physics and Controlled Fusion 46 (2004) A45[3] J M Fontdecaba et al. Fusion Science and Technology 46 (2004) 271[4] JP Christiansen and JW Connor. Plasma Physics and Controlled Fusion 46 (2004) 1537

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The quest for the divertor effect in the TJ-II stellarator

I. García-Cortés, F. L. Tabarés, D. Tafalla, A. Hidalgo, J. A. Ferreira, K. J.

McCarthy and the TJ-II team

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain

Density control during NBI heating is particularly challenging in small or medium-

sized fusion devices. The reason for this is the strong wall-plasma coupling that leads to

strong recycling of plasma and NBI particles coupled with poor control over fuelling by

external gas sources (puffing). This problem has been solved in other machines by the use

of divertors that are capable of removing the excess neutral gas. This solution has been

particularly successful in W7-AS, where the development of a new high-confinement

mode (the HDH) has been achieved under such a scenario [1].

The use of NBI heating in the TJ-II stellarator also faces the problem of unwanted

particle sources, that for relatively low injected powers, drives the plasma to collapse at

relatively low line densities. The problem is aggravated by an enhancement in particle

confinement that occurs as density increases. This has led to the investigation of TJ-II

magnetic configurations with potential divertor effects. In particular, configurations having

rational numbers that result in island chains at the edge have been explored for possible

application in “divertor-type” plasmas. Experiments aimed at characterizing the fuelling

efficiency of plasma particles and injected impurities have been carried out systematically

[2]. In this paper, an overview of the results obtained for these configurations will be

presented together with a discussion of their possible use for density control under strong

NBI heating under the light of recent observations.

[1] K. McCormick et al., Phys. Rev. Lett. 89, 015001 (2002)

[2] I. García-Cortés, F.L. Tabarés et al. J, Nucl. Matter. Vol. 337-339, (2005) 441-445.

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Impact of gas puffing location on density control and plasma

parameters in TJ-II.

F.L.Tabarés, I. Garcia-Cortés, T. Estrada D. Tafalla, A.Hidalgo, J.A. Ferreira, I.Pastor, J. Herranz and E. Ascasibar

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain

Under pure Electron Cyclotron Resonance Heating (ECRH) conditions in TJ-IIplasmas (P<300 kW, 53.2 GHz, 2nd harmonic X-mode, power density < 25 W/m3),plasma start-up and good density control are obtained only by the propercombination of wall conditions and gas puffing characteristics. Such a control isparticularly critical for the optimisation of the NBI power transfer to the targetplasmas. The relatively low cut-off limit is easily reached due not only to theunfavourable wall/puffing-fuelling ratio but also due to the steep density profilesdeveloped during the Enhanced Particle Confinement (EPC) modes1. These modes aretriggered by the gas puffing waveform, and they cannot be achieved for high iotamagnetic configurations in TJ-II. Comparative experiments under metallic andboronised wall conditions have shown that the sensitivity of the EPC modes to thepuffing rate is at least partially related to the energy balance at the plasma peripheryunder central heating scenarios 2.In this work, the impact of gas-fuelling location on the plasma parameters and densitycontrol is described. For that purpose, three different fuelling locations have beeninvestigated; broad distribution from a side ports, localized injection from long tubesat different poloidal positions and highly localized injection through a movablelimiter. Edge density and temperature profiles from a broad set of diagnostics (atomicbeams, reflectometry, Thompson Scattering ECE, etc…) are analysed and compared.It has been found that preventing from transition to the EPC mode is achieved byusing slow puffing rates, while neutral penetration into the plasma core can beenhanced for highly localized gas sources. Wall inventory, however, has been found toplay a dominant role in the fuelling of the plasma under most conditions.

1 F.L. Tabarés, B. Brañas, I.García-Cortés, D. Tafalla, T. Estrada and V. Tribaldos. Plasma Physics and

Controlled Fusion 43 (2001) 10232F.L. Tabarés, D, Tafalla R. Balbín et al. J. Nucl. Mater. 313-316 (2003) 839

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Influence of the stray light on the recorded Thomson electronic distribution function J. Herranz, and I. Pastor

Laboratorio Nacional de Fusión, CIEMAT, Madrid, Spain

In Thomson scattering diagnostics, one must have a very intense laser radiation

source in order to provide an acceptable signal level. Along its trajectory across the plasma, the input laser beam passes through vacuum windows at its entrance and exit of the vacuum vessel. At these surfaces, scattering of the laser beam occurs and despite all kinds of precautions, like light baffles, viewing dumps, high rejection spectral notch filters or removing the windows far away from the collection area, the intensity of the stray light can be comparable, or even surpass the whole plasma scattering signal1.

In the TJ-II stellarator2 the intense

ruby laser beam intersects the plasma next to the hard-core surface, where it is not possible to install a proper viewing dump as a black background. Therefore, multiple scattering of the strong parasitic light from vacuum surfaces, entrance and exit windows, finally enters into the collection angle of the spectrometer altering randomly some of the central spectral channels of the spectra.

The influence of this particular

noise in the recorded electronic distribution function is being analysed. This will let us determine and correct the level of distortion introduced in the electron temperature and density profiles measured by the TS system3. Different deformations brought on the reconstructed electron temperature and density profiles by this unwanted signal will be evaluated. In very low density plasmas, ne ∼0.4x1019 m-3, the stray light signal can double the density values, whereas the plasma temperatures are overestimated or undervalued ∼50% for Te ∼200 eV and ∼1400 eV, respectively.

Finally, we will point out the solutions that could be applied both, in the specific

geometry of TJ-II as well as in other conditions where the plasma device is physically so restrictive.

1 J. Sheffield, Plasma Scattering of Electromagnetic Radiation, Academic Press. 2 C. Alejaldre, et al., Nucl. Fusion 41, No. 10 (2001) 1449. 3 J. Herranz, F. Castejón, I. Pastor y K.J. McCarthy, Fusion Eng. Des. 65, 4 (2003) 525-536.

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Electromagnetic Instabilities in Strongly MHD Stable TJ-IIHelicac

J.A. Jimenez1, S.V. Shchepetov2, E. de la Luna1, I. Garcıa-Cortes1,

A.B. Kuznetsov2andR. Jimenez1

1 Asociacion Euratom-CIEMAT, Madrid, Spain2A.M.Prokhorov General Physics Institute, Moscow, Russia

ELM (edge-localized-mode) events, as in broad variety of tokamaks [1] and stellara-tors [2], were observed during TJ-II heliac experiments [3]. In order to stress that theyappear in a low confinement regime such events are named ELM-like events followingref. [2]. It was found [3] that ELM-like events have a threshold in heating power andappear only if the rational magnetic surface with rotational transform µ = 3/2 is locatedinside the plasma region. However, the nature of the plasma instability that triggers theELM-like transport event remained unclear as TJ-II presents a vacuum magnetic well allover the plasma volume that stabilize magnetohydrodynamic interchange and ballooningmodes (both ideal and resistive) even at values of the pressure one order of magnitudelarger than those observed in the experiment [4]. The primary goal of this work is toanalyze the prerequisites for the ELMs formation and clarify the physical nature of theinstability that triggers these ELMs.

It is shown that ELM-like events appear only if the rational magnetic surface µ(a) =n/m is located in the vicinity of the maximum density gradient region (0.5 ≤ a/ap ≤ 0.7)and, up to now, they have been observed for three low order resonances, namely 3/2,5/3 and 8/5. Higher order resonances that appear in plasma in the variety of magneticconfigurations of flexible TJ-II Heliac do not give rise either to electromagnetic activity(measured by Mirnov probes), ELM-like events or flattening of plasma electron tem-perature and plasma density. At lower heating power the ELM-like events can only beobserved at sufficiently high densities and are not present in the discharges where Te ishigh but Ti is very low. Therefore, we have performed an analysis based on the cou-pling of ion-temperature-gradient modes to Alfven and acoustic modes using a simplifiedmodel that take into account only the averaged curvature of the magnetic field lines andemploys a high mode number approximation [5]. Several types of stable and unstableelectromagnetic modes were found. It is shown that the unstable modes have a thresholdin the ion pressure, however, only the modes with moderate mode numbers can be unsta-ble. Higher mode numbers are stable which can, in principle, explain why they are notfound experimentally. In Electron Cyclotron Heated discharges the total plasma pressureis sufficiently low and therefore such modes can not be stabilized by the deep magneticwell of TJ-II, which has a universal stabilizing effect on any electromagnetic activity.

1. M. Hirsch et al. In Controlled Fusion and Plasma Phys.(Proc. of the 25th EPS Conference,Prague, 1998), vol. 22C, p. 2322, European Physical Society, Geneva, 1998.2. ITER Physics Expert Group on disruptions, plasma control, and MHD. Nucl. Fusion, 39(1999) 2251.3. Garcıa-Cortes I., et al. Nuclear Fusion, 40, 1867 (2000).4. R. Sanchez, J. A. Jimenez, L. Garcıa and A. Varias. Nucl. Fusion, 37 (1997) 1363.5. S. V. Shchepetov, A. B. Kuznetsov and J. A. Jimenez. In Controlled Fusion and PlasmaPhys. (Proc. of the 30th EPS Conference, St. Petersburg, 2003), vol. 27A , p. P–4.6, EuropeanPhysical Society, Geneva, 2003.

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Analysis of MHD instabilities in TJ-II plasmas

R. Jiménez-Gómez1, T. Estrada1, I. García-Cortés1, D. Spong2, J. A. Jiménez1, B. van

Milligen1, A. López-Fraguas1, I. Pastor1 and E. Ascasíbar1

1 Laboratorio Nacional de Fusión, Asociación Euratom-CIEMAT, Madrid Spain2 Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

MHD instabilities in TJ-II Stellarator are being experimentally characterized in

various plasma parameter regimes and heating scenarios. Magnetic field fluctuations data are

collected using various Mirnov coil sets distributed at different toroidal sector of the vacuum

vessel. Special analysis is carried out by a new poloidal array of 15 probes measuring poloidal

magnetic field fluctuations with frequency resolution up to 1MHz. This array only spans a

poloidal angle of ±p//2 mainly due to the complicated TJ-II vacuum vessel geometry.

Most of the observed MHD activity depends on heating method (ECH or NBI). In

ECH plasmas, the effect of low order rationals inside the rotational transform profile on MHD

and transport properties has been previously described [1,2]. The analysis of Mirnov coils

data by Singular Value Decomposition (SVD) method and correlation analysis techniques [3]

is being used in order to understand the MHD involved in these phenomena. As preliminary

results, in discharges having vacuum rotational transform 1.65 at the edge, a rotating coherent

mode has been found and it appears to be a resonant m = 3, n = 5 mode, moving in the ion

diamagnetic drift direction with frequency in the range 20-25 kHz. Signals from reflectometer

are compatible with mode observation although no rotation can be deduced. On the other

hand, high frequency (200-300 kHz) modes have been found in plasmas with line density

range 0.6 – 2.5 x 1019 m-3 and heated with ON/OFF-axis ECH (two gyrotrons, 200 kW each)

and NBI (240 kW). The frequency of these modes decrease with density and species mass and

their appearance seems to depend on density profile shape. Considering the low shear of TJ-

II, they are good candidates for Global Alfvén Eigenmodes related to some of the main low

order resonances n/m, 3/2 and 5/3. Reflectometer results show that the mode is located at r ≤

0.5-0.6. Toroidal Alfvén Eigenmodes modes have been also studied in high magnetic shear

configurations that can be obtained by inducing toroidal plasma current (Ip≤ 10kA) with the

OH coils. The resulting rotational transform profile intersects several rational values, 5/3, 5/4

and possibly 5/5. Fluctuations spectra are substantially modified.

1. I. García-Cortes et al., Nuclear Fusion 40 (2000) 1867-1874

2. T. Estrada et al., Plasma Physics and Controlled Fusion, 44 (2002) 1615-1624

3. M. Anton et al., 24th EPS, Berchtesgaden 1997,1ECA 21A part IV, 1645-1648

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Recent results with NBI plasmas in the TJ-II stellarator

M. Liniers, E. Ascasíbar, T. Estrada, F. L. Tabarés, M. Acedo, J. Alonso, R. Balbín, E, Blanco, B.Brañas, E. Calderón, A. Cappa, R. Carrasco, F. Castejón, A. Fernández, J. A. Ferreira, J. M.

Fontdecaba, C. Fuentes, A. García, I. García-Cortés, J. Guasp, J. Herranz, A. Hidalgo, C.Hidalgo, R. Jiménez-Gómez, D. López-Bruna, A. López-Fraguas, G. Marcon, K. J. McCarthy,F. Medina, M. Medrano, M. Ochando, I. Pastor, M. A. Pedrosa. S. Petrov1, D. Rapisarda, E.

Sánchez, M. Sánchez, J. Sánchez, D. Tafalla, G. Wolfers, B. Zurro.

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain1 A.F. Ioffe Physical Technical Institute, St. Petersburg, Russia

In the last year, the NB injector currently in operation in the TJ-II heliac has beenoperated with steadily increasing parameters. ECH plasma targets with line-average electrondensities ranging from 0.5 to 1.1 x 10 1 9 m-3 are produced with two gyrotrons (2x200 kW). Themaximum values of beam (H0) energy and current achieved so far (30 kV, 55 A) correspond toan estimated port-through power of 400 kW. Maximum beam duration is 150 ms.

So far, density control with NBI plasmas has not been achieved. In most dischargesplasma density increases continuously as the beam is injected until a thermal collapse thatterminates the discharge is reached. The fuelling efficiency of the neutral beam, as measured bythe slope of the electron density temporal trace, seems to be essentially independent on the targetelectron density when the neutral injection starts. On the other hand, the fuelling efficiency hasbeen found to decrease for off-axis ECH heating and, exceptionally, density plateaus longer than100 ms have been achieved.

Values of central electron density up to 6.5 x 10 1 9 m-3 have been achieved with typicalcentral electron and ion temperatures of 200 and 130 eV, respectively. The energy content of thebest NBI plasmas attains values of 2.2 kJ, about a factor 2 larger than the typical ECH ones.

New experimental features are found in the high-density plasmas achieved with NBIheating. Negative radial electric fields are measured by the HIBP (gradient region) [1,2] andprobe (edge) [3] diagnostics, in agreement with the poloidal plasma rotation measured byspectroscopy. Ion temperature profile changes from flat (ECRH) to peaked (NBI) [4]. Highfrequency modes (200-300 kHz) with frequency decreasing with density and species mass areobserved. They disappear as density profile becomes increasingly peaked. In view of the lowshear of TJ-II, they are good candidates for Global Alfven Eigenmodes related to the mainresonance (n/m = 3/2 or 5/3 depending on the magnetic configuration). Reflectometer resultsshow that the mode is located at ρ = 0.5-0.6.

Evaluations of the neutral beam power losses (shine through) and power absorptionare being done in order to estimate the energy confinement time in NBI plasma discharges andcompare it with previous results found in ECH plasmas [5].

[1] A. Melnikov et al. “Heavy Ion Beam Probe investigations of plasma potential in ECRH andNBI in the TJ-II stellarator”. This conference[2] L. Krupnik et al. “Characterization of quasi-coherent oscillations by HIBP diagnostic in theTJ-II stellarator”. This conference[3] E. Calderón et al., “Experimental evidence of coupling between density tails and turbulenttransport in the scrape-off layer region in the TJ-II stellarator”. This conference[4] R. Balbín et al., “Ion temperature profiles on TJ-II stellarator during NBI plasma Heating”.This conference[5] E. Ascasíbar et al. Nuclear Fusion 45 (2005) 276

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Up-down and in-out asymmetries monitoring based on broadbandradiation detectors

M. A. Ochando, F. Medina, B. Zurro, K. J. McCarthy, A. Baciero, M. A. Pedrosa, C. Hidalgo,E. Sánchez, J. Vega, A. B. Portas, HIBP Group, ECRH Group, NBI Group and TJ-II Team.

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain

Vertical (up-down) and in-out asymmetries in the particle and heat divertor flowdistributions, or in plasma emissivity from the confined volume, are recognized as universalphenomena, but each type of magnetic confinement device presents its own particular balancebetween different sources of asymmetries. The direction of the toroidal magnetic field, thenature, intensity and toroidal position of the heating source, the convection-like losses of fastions and electrons have been found to modify significantly the flux asymmetries. The search forphysical mechanisms responsible for the asymmetry and possible methods of asymmetrycorrection has become an imperative goal of divertor research for large stellarator type devicesand next generation devices.

In the TJ-II stellarator, changes in wall recycling due to changes in the ECRH drivenconvective flux of trapped particles were detected by means of toroidal asymmetries in radiationnear the plasma periphery. In this high-ripple low-shear stellarator, changes in the transport ofripple-trapped particles before they reach the limiter or the divertor region can also induceasymmetries in some bulk plasma parameters, such as global radiation. Although the spatialdistribution as well as the degree of asymmetry would depend on birth position, the productionrate and energy spectrum of the trapped particle populations and total radiation depends onelectron density and temperature as well as on plasma composition, the systematic study of theasymmetry in signals from twin detectors located at selected toroidal and poloidal positions canserve to assess the relative importance of the different drift mechanisms. This is a non-perturbing method that is especially appropriate when the shape of the vacuum chamber does notallow for installing probes around the complete poloidal section at any toroidal position, as is thecase of TJ-II.

Recently, a set of bolometer systems distributed has been installed about the vacuumchamber to monitor up-down and in-out radiation asymmetries that are observed in transitions todifferent confinement regimes. Preliminary data obtained under several plasma operationscenarios (ECRH-NBI transition, ECR power modulation, laser blow-off impurity injection andedge biasing experiments) reveal different degrees of up-down and in-out radiation asymmetries.

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On the influence of ExB sheared flows in the statistical properties of turbulence in

the plasma boundary of the TJ-II stellarator

O. Orozco, E. Faleiro*, C. Hidalgo, M.A. Pedrosa, C. Silva**, E. Sánchez,

J. M. Gómez*, E. Calderón,

EURATOM-CIEMAT, 28040-Madrid, Spain

*Universidad Complutense de Madrid, Spain

**IST, Lisbon, Portugal

In the paper we report the investigation of the influence of ExB sheared flows and

magnetic topology in the statistical properties of turbulence in the plasma boundary

region of the TJ-II stellarator.

Experiments were carry out in Electron Cyclotron Heated plasmas (PECRH= 200 – 400

kW, BT = 1 T, R = 1.5 m, <a> ≤ 0.22 m) in the TJ-II stellarator.. The statistical

properties of fluctuations were also investigated during electrode biasing experiments.

In agreement with previous findings [1], fluctuations show clearly a non Gaussian

features with pulses that are asymmetric in time. The degree of asymmetry is minimum

near the Last Closed Flux Surface (LCFS) and increases in the SOL region. The degree

of asymmetry is higher in plasmas regimes without edge-sheared flows.

The statistical properties of fluctuations have been also investigated during density scan

and ECRH power modulation experiments in which the initial plasma density was set

near the critical value to trigger the onset of sheared flows. Experimental findings show

that, in the proximity of the LCFS, the deviation from a gaussian distribution is

dynamically coupled with the appearance / disappearance of sheared flows.

The influence of electrode biasing electric fields on fluctuations depends on plasma

radius and plasma parameters (e.g. density) [2]. In particular, at high ECRH plasmas (n

≈ 0.8 x 1019 m-3) and in the plasma edge regions, fluctuations become more gaussian

once the electrode biasing is turned on.

Present findings show the importance of both magnetic configuration and sheared flows

to determine the statistical properties of fluctuations in the plasma boundary region.

[1] E. Sánchez et al., Phys. of Plasmas 7 (2000) 1408.

[2] C. Silva et al., this conference.

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Experimental investigation of edge sheared flow development andconfiguration effects in the TJ-II stellarator

M.A. Pedrosa, C. Hidalgo, A. Alonso, E. Calderón, O. Orozco, J.L. de Pablosand the TJ-II team

Laboratorio Nacional de Fusion, Euratom-Ciemat, 28040 Madrid, Spain

Experimental results have shown that the generation of spontaneous perpendicular shearedflow (i.e. the naturally occurring shear layer) requires a minimum plasma density or gradientin the TJ-II stellarator1. This finding has been observed by means of multiple plasmadiagnostics, including probes, fast cameras, reflectometry and HIBP2. The obtained shearingrate of the naturally occurring shear layer results in general comparable to the one observedduring biasing-improved confinement regimes3. It has been found that there is a couplingbetween the onset of sheared flow development and an increase in the level of plasma edgefluctuations pointing to turbulence as the main ingredient of the radial electric field drive;once the shear flow develops the level of turbulence tends to decrease4.

The link between the development of sheared flows and plasma density in TJ-II has beenobserved in different magnetic configurations and plasma regimes. Preliminary results showthat the threshold density value depends on the iota value and on the magnetic ripple(plasma volume)5. Recent experiments carried out in the LHD stellarator have shown thatedge sheared flows are also affected by the magnitude of edge magnetic ripple: the thresholddensity to trigger edge sheared flows increases with magnetic ripple6. Those results havebeen interpreted as an evidence of the importance of neoclassical effect in the physics ofExB sheared flows.

For some TJ-II magnetic configurations with higher edge iota (ι/2π≥1.8) there is a sharpincrease in the edge density gradient simultaneous to a strong reduction of fluctuations andtransport and a slight increase of the shearing rate and perpendicular rotation (≥2 km/s) asdensity increases above the threshold. The role of the edge ripple, the presence of edgerational surfaces and properties of turbulent transport are considered as possible ingredientsto explain the spontaneous development of edge sheared flows in TJ-II.

1 M.A. Pedrosa et al., Plasma Phys. Control. Fusion, 47 (2005) 777.

2 M.A. Pedrosa et al. EPS-2005.

3 C. Hidalgo, M.A. Pedrosa et al., Plasma Phys. Control. Fusion 46 (2004) 287.

4 C. Hidalgo, M.A. Pedrosa et al., Phys. Rev. E 70 (2004) 067402.

5 M.A. Pedrosa, C. Hidalgo et al., 8th Workshop on the Electric Fields, Structures, and Relaxation in Edge

Plasmas 20056 K. Ida, M. Yoshinuma et al., Nucl. Fusion 45 (2005) 391.

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Transport and fluctuations during electrode biasing on TJ-II

C. Silva1, M.A. Pedrosa2, C. Hidalgo2, K. McCarthy2, E. Calderón2, B. Gonçalves1, J. Herranz2, F. Medina2, M. A. Ochando2, I. Pastor2, O. Orozco2

1Associação Euratom/IST, Centro de Fusão Nuclear, Instituto Superior Técnico 1049-001 Lisboa, Portugal

2Asociación Euratom/Ciemat, 28040 Madrid, Spain

The influence of limiter biasing on plasma confinement, turbulence and plasma flows have been previously investigated in detail on the TJ-II stellarator [1]. Experimental results showed that it is possible to modify global confinement and edge plasma parameters with both positive and negative biasing and showed evidence of electric field induced improved confinement via multiple mechanisms. Electrode biasing is expected to introduce more substantial changes in energy and particle confinement than limiter biasing as it has the advantage of forcing an electric field in the edge plasma.

This contribution describes the behaviour of the plasma during electrode biasing experiments on TJ-II. As the bias is applied, the bias current amplitude increases rapidly for both polarities and the floating potential at the plasma edge is also modified in a rather short time scale (<50 µs) leading to a strong modification in the edge radial electric field in the region just inside the limiter. The plasma response is different at densities below and above the threshold value to trigger the spontaneous development of ExB sheared flows [2]. At low densities, the edge plasma potential is fully controlled by external biasing. In this case, strong increase in plasma density and reduction in edge fluctuation level and Hα signals is observed during biasing, leading to an increase in the ratio n /Hα up to 100% (Fig. 1). At higher densities edge plasma potential profiles are determined not only by external biasing but also by the electric fields spontaneous developed.

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[1] C. Hidalgo, M. A. Pedrosa et al., Plasma

Phys. Control. Fusion 46 (2004) 287 [2] C. Hidalgo et al., Phys. Rev. E 70, 067402

(2004); M.A. Pedrosa et al., Plasma Phys. Controlled Fusion, 47 (2005) 777.

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Figure 1: Time evolution of the main plasma parameters for a discharge with positive electrode bias.

A simulation code to estimate / deduce local toroidal rotation profiles inTJ-II plasmas from chord-integrated measurements

D. Rapisarda, B. Zurro, V. Tribaldos, A. Baciero, D. Jiménez and the TJ-II team

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain

An absolute calibrated spectroscopic system has been developed to measure chord-averaged toroidal rotation of protons and impurity ions from a single view1; at present thatsystem has been upgraded to measure profiles on a shot to shot basis. The interpretation ofthe chord-averaged measurements is difficult because of the strong three-dimensional structureof TJ-II stellarator. A local model capable of reconstructing the averaged emission of spectrallines has been developed to infer the local information. The procedure, similar to the one usedin a previous work in the TJ-I tokamak2, was implemented on a numerical code, that startingfrom given analytical profiles of local emissivity, ion temperature (estimated with charge-exchange neutral analyzer) and toroidal rotation simulates the chord-averaged emission spectraalong a selected line of sight. In addition, the code is able to separate the toroidal and poloidalvelocity contribution taking into account the TJ-II magnetic topology. Simulations of actualcases and its comparison with experimental results obtained in toroidal scans performed in TJ-II plasmas will be presented.

1. D. Rapisarda et al, Proc. 31st EPS Conf. on Controlled Fusion and Plasma Physics Vol.28G, P-4.173 (2004).

2. B. Zurro et al, Rev. Sci. Instrum. 63, 5196 (1992).

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Local transport in density and rotational transform scans in TJ-II ECRHdischarges

V. I. Vargas, D. López-Bruna, T. Estrada, E. Ascasíbar, E. de la Luna, M. Ochando, F.Medina, J. Herranz, A. Fernández, E. Sánchez

Laboratorio Nacional de Fusión –Asociación Euratom/Ciemat, 28040-Madrid, Spain

Aside from a number of analysis devoted to the study of particular discharges, systematiclocal (flux surface averaged) transport in the TJ-II heliac remains to be done in connectionwith confinement time scalings. In this work we present the results of performinginterpretative transport on two series of electron cyclotron resonance heating discharges, onebelonging to a rotational transform scan, the other to a density scan. After boronisation, TJ-IImatches reasonably well [1] ISS95 scaling [2] with rotational but the density dependencefound in TJ-II (exponential factor 1.06) is much stronger than the one in ISS95 (exponentialfactor 0.51).

The density profiles in the TJ-II are hollow in studied plasmas and the gradient zone isnormally in the normalized plasma radius equal to 0,6. Energy confinement time calculationsin the TJ-II were carried out considering the total radiation losses and a greater increase wasobserved when considering these losses.

In the density scan, a decrease of the electron heat diffusivities with the increase of the densitywas observed, moreover, TJ-II presents a peak in the electron heat diffusivities aroundnormalize plasma radius equal to 0,46 for standard configuration (ι/2π(ρ=2/3)=1.6), this peakdecrease with the increase of the density. For the rotational transform scan, peaks were alsoobserved in the electron heat diffusivities, that are located at the same normalized plasmaradius for each magnetic configuration (the same value of the rotational transform ) and someof these peaks correspond with rational surfaces of low order.

Finally, we present some results using a simplified transport model [3] that seems to capturethe radial dependences of the experimental heat transport coefficient profiles.

[1] E. Ascasíbar et al,Nuclear Fusion 45 276 (2005).[2] U. Stroth et al., Nucl. Fusion 36, 1063 (1996).[3] B. B. Kadomtsev, O. P. Pogutse, Nucl. Fusion 11, 67 (1971).

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TJ-II operation tracking from Cadarache

J. Vega, E. Sánchez, A. Portas, A. Pereira, A. López, E. Ascasíbar

Asociación EURATOM/CIEMAT para Fusión, Madrid, Spain

S. Balme, Y. Buravand, P. Lebourg, J. M. Theis, N. Utzel

Association EURATOM/CEA sur la Fusion, Cadarache, France

M. Ruiz, E. Barrera, S. López, D. Machón

Dpto. Sistemas Electrónicos y de Control, UPM, Madrid, Spain

R. Castro, D. López

Red.es - RedIRIS. Madrid. Spain

A. Mollinedo, J. A. Muñoz

CIEMAT. Computing Center. Madrid. Spain

The TJ-II remote participation system was designed to follow the TJ-II dischargeproduction, even allowing the physicist in charge of operation to be in a remote location. Thesystem has been based on both web servers and Java technology. These elements were chosendue to its open character, security properties, platform independency and technologicalmaturity. Web pages and Java applications permit users to access experimental systems, dataservers and the operation logbook. Security resources are provided by the PAPI system, adistributed authentication and authorization system.

The TJ-II remote participation tools have allowed us to command and follow thestellarator operation from Cadarache. Over 1,000 digitizer channels and more than 20diagnostic control systems were remotely available from web pages formonitoring/programming purposes. One Java application provided on-line information aboutthe acquisition status of channels and acquisition cards. A second Java application showedtemporal evolution signals that were refreshed in an automated way on the screen after eachshot. A third Java application provided access to the operation logbook. In addition to thesetools, we used the VRVS videoconferencing system (FUSION community, X-Point room) andthe EFDA Messenger Service for instant messaging (Jabber client).

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COMPARISON OF IMPURITY POLOIDAL ROTATION IN ECRH AND NBIDISCHARGES OF THE TJ-II HELIAC

B. Zurro, A. Baciero, D. Rapisarda, V. Tribaldos, D. Jiménez and TJ-II TeamLaboratorio Nacional de Fusión por Confinamiento Magnético.

Asociación EURATOM / CIEMAT para Fusión

Abstract

The poloidal rotation of C V ions has been deduced, in the TJ-II stellarator, from the lineshift measured using a high spectral resolution spectrometer and a nine fiber channelssystem1. The system has been recently upgraded to have better sensitivity and is capable ofmeasuring under wall-boronised discharges, where the impurity contamination issignificantly reduced.

It has been observed that the poloidal rotation direction changes sign depending on theauxiliary heating method used. Whereas in low-density ECRH plasmas the poloidal rotationdirection corresponds to a positive radial electric field, in higher density NBI plasmasnegative radial electric fields are deduced from the poloidal rotation. These measurementsare in agreement with neoclassical theory calculations2, that predicts a change in the sign ofthe radial electric field mainly because of a change in the ratio of the electron to iontemperatures.

When operated under wall-boronised ECRH, f = 53.2 GHz, TJ-II stellarator plasmas arecharacterized by peaked electron temperature profiles and rather flat, or even hollow,density profiles. The density is relatively low, because of the 2nd harmonic X-mode cut-offdensity (ne ≈ 1.7 x 1019 m-3), and due to the inefficient collisional coupling disparateelectron and ion temperatures are observed. For the central plasma column Γe

neo >> Γineo

and thus the radial electric field is positive, Er > 0. On the other hand, in the NBI heating(H+, E ≈ 30 keV) phase the density is much higher; the electron temperature is lower, it’sprofile flatter and the gap between electron and ion temperature shortens, so Γe

neo << Γineo

and Er < 0. In the outer part of the plasma the temperatures are always similar and theelectric field is always negative.

In this picture, the change in the radial electric field seems to be mainly linked to thedensity and only indirectly to the heating mechanism. The density range for the change ofsign and its radial dependence are studied through the use of different spatial cords of thesystem. It is observed that the C V rotates almost like a rigid body for most of the centralchords in boronised low density ECRH discharges, whereas a clear shear poloidal rotationis observed for the inner chords of high density discharges in particular those sustained byNBI.

1. A. Baciero, B. Zurro, K.J. McCarthy, C. Burgos and V. Tribaldos et al., Rev. Sci.Instrum. 72, 971-974 (2001).2. V. Tribaldos, Phys. Plasmas 8 1229 (2001).

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Characterization of the quasi-coherent oscillations by HIBP

diagnostic in the TJ-II stellarator

L. Krupnik, A.A. Chmyga, N. Dreval, L. Eliseev*, S.M. Khrebtov, A.D. Komarov,A.S. Kozachok, A.Melnikov*, S. V. Perfilov*

Institute of Plasma Physics, NSC KIPT, Kharkov, Ukraine*Institute of Nuclear Fusion, RRC Kurchatov Institute, Moscow, Russia

A. Alonso, J. L. de Pablos, C. Hidalgo, M.A. Pedrosa,

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, Madrid, Spain

Quasicoherent oscillations have been observed in TJ-II plasma with differentdiagnostic. A recent improvement in the signal to noise ratio of the Heavy Ion BeamProbe (HIBP) diagnostic has allowed to observe the radial structure of theseoscillations from the edge to the plasma core region.

Edge quasi-coherent fluctuations (with frequencies near 20 kHz) have been observedin some configuration windows when plasma density / heating power are above athreshold. The amplitude of those modes tends to be larger in the low field side region(Fig. 1). This result suggests the role of configuration (related to the presence of loworder rationals in the plasma edge) and threshold gradients to trigger quasi-coherencemodes. HIBP signals are strongly correlated with probe signals.

When rationals move towards the plasma core (ρ ≈ 0.3), the modes are clearly seen inECE emission and in HIBP secondary current and potential signals. These quasi-coherent oscillations (in range 20 kHz) have been connected with the development ofelectron internal transport barriers (e-ITB). Recent results show a decreasing in themode amplitude as e-ITBs are fully developed [1].

Fig.1 Plasma profiles ofsecondary ions in two slightlydifferent magnetic configuration(iota ≈ 1.6) with similar plasmadensity.

[1] T. Estrada et al., Thisconference

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Design and Testing of an Electron Bernstein Wave Emission Radiometer forthe TJ-II Stellarator*

J.B.O. Caughman,1 D.A. Rasmussen,1 A. Cappa,2 M.C. Carter,1 F. Castejón,2 A. Fernández,2

and J.B. Wilgen1

1Oak Ridge National Laboratory, Oak Ridge, TN USA2Laboratory Nacional de Fusión, EUROTOM-CIEMAT, Madrid, Spain

Efficient Electron Bernstein wave (EBW) mode conversion is important for heating denseplasmas in TJ-II. The O-X-B mode conversion scenario is being considered for heating plasmaswith densities over 1,3 x 1019 m-3 [1], which will be very interesting to study high-densityphysics and for heating NBI plasmas. Measurement of the thermal EBW emission from theplasma allows the EBW mode conversion efficiency to be determined, and also has the potentialto offer a diagnostic for measuring electron temperature profile evolution in overdense plasmas.A dual-polarized quad-ridged broadband horn with a focusing lens will be used to measure theEBW emission at 28 GHz on TJ-II. A focused beam is needed to achieve efficient coupling atthe mode conversion layer. Emission from the plasma is reflected from a steerable internalmirror [2], propagates through a glass lens, and is focused on the horn. The field pattern fromthe horn-lens combination has been measured as a function of horn-lens spacing and lens focallength with a 3-D scanning system in an effort to minimize the beam waist at the plasma edge.Beam waist sizes have been measured at distances of up to 80 cm from the lens. Details of theexperimental results and future plans will be presented.

*Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Dept. of Energy under contractDE-AC05-00OR22725. A part of this work is performed under support of Spanish “Subdirección General deProyectos de Investigación, Ministerio de Educación y Ciencia” with reference ENE2004-06957

[1] F. Castejón et al. Fusion Science and Technology 46 (2004) 327[2] A. Fernández et al. Fusion Science and Technology 46 (2004) 335

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Influence of plasma biasing on turbulence in the torsatron TJ-K

M. Ramisch, F. Greiner1), U. Stroth

Institut für Plasmaforschung, UniversityStuttgart,Germany1) Institut für ExperimentelleundAngewandtePhysik,UniversityKiel, Germany

Plasma confinement can be strongly improved by transport barriers. First in the ASDEX toka-

mak, spontaneous transitions from a low-confinement (L-mode) into a high-confinement regime

(H-mode) have been observed. L-H transitions are accompanied by the formation of a transport

barrier at the plasma edge. E×B shear flows have been considered as a candidate for trigger-

ing the transport barrier. They are assumed to limit the radial correlation length of turbulent

structures [2] and, thus, reduce radial turbulent transport. Besides spontaneous L-H transitions,

improved confinement regimes can also be achieved by externally induced electric fields [3]. In

the concept of plasma biasing, the plasma potential is locally modified by an inserted electrode.

In this contribution, biasing is applied to the low-temperature plasma in the torsatron TJ-K

in order to investigate the mechanism of transport reduction due to shear flows. The plasma

is throughout accessible for probe diagnostics and the dimensionless parameters are similar to

those at the edge of fusion plasmas. Turbulent structures are detected by means of an 8× 8

Langmuir probe array in order to study the shear decorrelation mechanism.

Different biasing schemes were tested to create sufficiently strong shear flows to have an

impact on turbulent structures and radial transport. A clear effect was achieved with ring-like

electrodes aligned on a flux surface. The plasma conditions and the fluctuations could strongly

be influenced. Steepened density gradients and reduced fluctuation and transport levels were ob-

tained when the shear was increased inside the confinement region. The direction of the poloidal

propagation of turbulent structures changed from the electron-diamagnetic to the E×B-drift

direction when strong radial electric fields were induced. The structures were found to be dis-

torted, but a decrease of the radial correlation length was not observed. Transport reduction can

be traced to enhanced stability reflected in the cross-phase between poloidal electric field and

density fluctuations and also to shortened lifetimes.

References

[1] F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982).

[2] H. Biglari, P. H. Diamond, and P. W. Terry, Phys. Fluids, B 2, 1 (1990).

[3] R. J. Taylor et al., Phys. Rev. Lett. 63, 2365 (1989).

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High Density Plasma Productions by Hydrogen Storage Electrode in the Tohoku University Heliac

H. Utoh, K. Nishimura1, S. Inagaki1, H. Takahashi, Y. Tanaka, M. Takenaga, M. Ogawa, J. Shinde, K. Iwazaki, K. Shinto, S. Kitajima and M. Sasao

Department of Quantum Science and Energy Engineering, Tohoku University, Sendai, Japan 1 National Institute for Fusion Science, Toki, Japan

In the Tohoku University Heliac (TU- Heliac), the influence of a radial electric field on

improved modes has been investigated by an electrode biasing. In both positive and negative biasing experiments by the stainless steel (SUS) electrode (cold-electron or ion collection), the improvement of plasma confinement was clearly observed. 1 Furthermore, by negative biasing with a hot cathode (electron injection), the radial electric fields can be actively controlled as a consequence of the control of the electrode current IE. 2-4 By using the electrode made of a hydrogen storage metal, for example Titanium (Ti) or Vanadium (V), the following possibility can be expected: (1) ions accelerated from the positive biased electrode allow the simulation for the orbit loss of high-energy particles, (2) the electrons/neutral-particles injected from the negative biased electrode provide the production of the high-density plasma, if hydrogen are successfully stored in the electrode. In this present work, several methods were tried as the treatment for hydrogen storage.

In the case of the Ti electrode biased positively after the treatment, the improvement of

plasma confinement was observed in He plasma, which were same as the experimental results of the SUS electrode. However, in the electron density profiles inside the electrode position there was difference between the biased plasma by the Ti electrode and that by the SUS electrode. In some of Ar discharges biased negatively with the Ti electrode after the treatment, the electron density and the line intensity of Hα increased about 10 times of those before biasing. This phenomenon has not been observed in the Ar plasma biased by the SUS electrode. This result suggested that the Ti electrode injected electrons/neutral-hydrogen into the plasma. This high-density plasma productions were observed only 1 ~ 3 times in the one treatment for hydrogen storage.

By using a Vanadium (V) electrode, productions of the high-density plasma, which was same as that in the Ti electrode experiments, were observed sequentially. In biasing experiments by the V electrode, the high-density plasma was observed in not only Ar plasmas but also He plasmas. The treatment condition for the V electrode was same as that for the Ti electrode. These results show that the V electrode was more useful than the Ti electrode for productions of the high-density plasma. The number of the high-density plasma productions increases so much that the detail study of this new type of discharge becomes possible. The measurement of the density and potential profiles will be carried out, and the formation of the density transport barrier will be investigated.

1. S. Inagaki et al.: Jpn. J. Appl. Phys. 36, 3697 (1997). 2. S. Kitajima et al.: J. Plasma Fusion Res. Series 4, 391 (2001) 3. S. Kitajima et al.: Int. J. Appl. Electromagnetics and Mechanics, 13 381 (2002). 4. S. Kitajima et al.: IEEE Conference Record of 2003 IEEE International Conference on Plasma Science, 465 (2003).

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Plasma Energy Balance at ECRH in the L-2M Stellarator.

O. I. Fedyanin, D.K. Akulina, G.M. Batanov, M.S. Berezhetskii, D.G.Vasilkov, G.A.Gladkov, S.E. Grebenshchikov, N.K. Kharchev, Yu.V. Khol’nov, L.M. Kovrizhnykh, N.F. Larionova,

A.A. Letunov, V.P. Logvinenko, N.I. Malykh, A.I. Meshcheryakov, A.A.Pshenichnikov, K.A.Sarksyan, N.N. Skvortsova, S.V. Shchepetov, G.S. Voronov

A.M.Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

Experiments on ECR heating of plasma with reduced radiative energy losses were carried out in the L-2M stellarator(which a classical l= 2, m= 7 stellarator with large shear ι(0) = 0.185, ι(a) =0.7; ι(2a/3) =0.35 major radius R = 100 cm, plasma minor radius a= 11.5 cm, B0 = 1.34 T). A low level of radiative energy losses was attained due to improvement of boundary conditions after boronization of the vacuum chamber.

In this work we study the influence of plasma density, heating power and parameters of magnetic configuration (mainly role rotation transform) on the energy confinement. To get database for plasma energy balance analysis ECRH experiments were carried out over a wide range of heating powers P= 100—300kW, plasma densities ne= (0.5—3.0) ⋅1013 cm-3 and angle of rotation transform ι(0) = 0.042-0.185. At ne = 2.65⋅1013 cm-3 and P = 250 kW, the plasma energy reached W = 650 J at Prad = 40 kW, and the energy confinement time was τE = 2.5 ms. Because of reduced radiation power, the duration of the free plasma energy decay phase (after the heating power was switched off) increased substantially up to 10 ms.

From data base obtained, it follows that the steady state of plasma in the L-2M is adequately described by Scaling-L2-05. It is significant that the free-decay phase also obey this law. Scaling L2-05 has some difference from the International Stellarator Scaling ISS95:

W L205 = 146 ι2/30.774 ne

0.778 P 0.27 ( [W]=J, [ne]= 1013cm-3, [P]=KW) and

W ISS95 =49.8 ι2/30.4 ne

0.51 P 0.41 ( for L-2M parameters).

Analysis of plasma energy balance had shown on existence some particularity for low and high density region: In the region ne ≥ 2.5⋅1013 cm-3 and W≥450 J the energy confinement time τE do not depends on the time ( It means existence real energy confinement time τE =const)

In the region ne ≤ 0.6⋅1013 cm-3 and W≤175J ITB ( Inner transport barrier ) has been detected.

The magnetic and Te-profile measurements indicate the existence “invariable” pressure profile in very wide region of the plasma energy (200 J ≤W ≤ 650 J). It testifies to a weak dependence of heat transport on local pressure values or plasma energy .

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Modification of the Electron Temperature Profile Depending on theHeating Power and Plasma Parameters

G. S. Voronov, E. V. Voronova, D. K. Akulina, G. A. Gladkov, and L-2M TeamA.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

Boronization of the vacuum chamber of the L-2M stellarator has resulted inmodification of the electron temperature profile1. In particular, a well-defined jump in theelectron temperature to __ ~ 100eV in a narrow region _r/ r ~ 0.05 is observed in thetemperature profile at the plasma edge. In the present paper, the value and shape of the jumpin Te are studied at different values of plasma parameters and ECR heating power.

8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,50

100

200

300

400

500 P=100 kW P=200 kW

ne=1.7 101 9 m-3

Te, e

V

r, cm

Fig. 1. Profiles __(r) . Fig. 2. Profiles __(r) near plasma edgeFigure 1 shows how the electron temperature profile changes with increasing ECRH

power from 100 to 200 kW. It is seen that a jump in Te is absent at a power of P~100 kW,whereas at P~200 kW the electron temperature drops within _r~0.5 cm. This radial interval isabout the limit of spatial resolution of the spectral method used for temperaturemeasurements, so it may be assumed that the actual gradient of Te at the edge is even steeper(Fig. 2). Measurements of Te at an intermediate heating power P~160 kW (Fig. 3) show thatthe threshold power for the formation of a jump in Te at ne~1.7 1019m-3 falls within the rangeP~100-160 kW.

8,0 8,5 9,0 9,5 10,0 10,5 11,0 11,50

100

200

300

400

500 P=100 kW P=160 kW P=200 kW

ne=1.7 101 9 m-3

Te, e

V

r, cm

Fig. 3. Refinement of the value of threshold power. Fig. 4. Profile of Te in theconfiguration with reduced helical field.

When the helical-field intensity was equal to half its standard value, a jump in Te at theplasma edge was absent (Fig. 4).

1. A.I. Meshcheryakov, D.K. Akulina, G.M. Batanov, et al., Plasma Physics Reports,Vol. 31, No. 6, 2005, pp. 452-461.

0 2 4 6 8 1 0 1 20

200

400

600

800

1000

1200

Te, e

V

r, cm

100 kW 200 kW

ne=1.7 101 9 m-3

4 5 6 7 8 9 1 0 1 1 1 2

0

5 0

100

150

200

250

300

350

ε = ε0 / 2

Te, e

V

r, cm

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Results of Measurements of the Ion Temperature Profile of ECR HeatedPlasmas in the L-2M Stellarator

G. S. Voronov, E. V. Voronova, S. E. Grebenshchikov, and L-2M Team

A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

After boronization of the vacuum chamber of the L-2M stellarator, the confinementcharacteristics and the electron temperature profile changed markedly1. In this connection, ourimmediate task was to carry out studies of the behavior of the ion temperature under theseconditions.

Previous measurements of Ti were performed by analyzing the energy distribution offast hydrogen ions produced by charge exchange2. In recent studies, the ion temperature wasdetermined from Doppler broadening of spectral lines of impurity ions. With the help of a setof mirrors, the plasma radiation was focused on the entrance slit of a VMS-1 monochromator(D/F=1:6.5, F=600 mm, 1200 lines/mm,1.3 nm/mm, 200 – 800 nm). The detector was a CCDplate (1040_1140 pixels of size 16_16 µm) covered in part with an opaque screen. The plasmaspectrum produced in the uncovered area was rapidly scanned and copied into the coveredregion. With this partial exposition method, the rate of recording was successfully increasedup to 1000 frames per second3. The instrument function of the whole system was 0.04 nm,which corresponds to Ti ~1 eV for hydrogen and ~17 eV for boron ions. The plasma iontemperature is considerably higher, so the accuracy of measurements of Ti is limited primarilyby a low intensity of signals from the plasma with a low impurity concentration.

The results of measurementsof the evolution of HeII, BII, andBIV ions temperature during theECR heating of a helium plasma areshown in he figure. The plasmadensity in these experiments was~2×1019 m-3, and the gyrotron pulsepower was ~200 kW.

The results of measurementsof Ti were compared with the timeevolution of the ion temperaturecalculated by using the TRANSZcode4. The latter includes a completeset of neoclassical equations and

involves additional anomalous fluxes corresponding to accepted empirical scalings. Thecalculated values of Ti are in fair agreement with the measured ones

1. A.I. Meshcheryakov, D.K. Akulina, G.M. Batanov, et al., Plasma Physics Reports,Vol. 31, No. 6, 2005, p. 452.

2. S.E. Grebenshchikov, L.M. Kovrizhnykh, I.S. Sbitnikova, et al., Soviet Journal ofPlasma Physics , Vol. 9, p.696. (1983).

3. www.silar.spb.ru4. S.E. Grebenshchikov, I.S. Danilkin, A.B. Mineev, Plasma Physics Reports, Vol. 22,

No.7, 1996, p. 551.

4 6 4 8 5 0 5 2 5 4 5 6 5 8 6 0 6 2 6 4 6 6 6 8 7 0 7 20

2 0

4 0

6 0

8 0

100

120

140

He plasma ECRH P=200 kW# 58151-203

Ti, e

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t, ms

BII HeII BIV

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Recent Results of Studies of Plasma Fluctuations in Stellarators byMicrowave Scattering Technique

N. N. Skvortsova*, G. M. Batanov*, L. V. Kolik*, A. E. Petrov*, A. A. Pshenichnikov*,K. A. Sarksyan*, N. K. Kharchev*, Yu. V. Khol'nov*, S. Kubo** and J. Sanchez***

*Institute of General Physics, Russian Academy of Sciences,119991, Moscow, Russia.**National Institute for Fusion Science, Toki, Japan.

***EURATOM-CIEMAT, 28040, Madrid, Spain.

Microwave scattering diagnostics are described that allow direct measurements of theturbulent processes in a high-temperature plasma of magnetic confinement systems. Plasmadensity fluctuations in the heating region of the L-2M stellarator were measured frommicrowave scattering at the fundamental and the second harmonics of the heating gyrotronradiation [1,2]. In the TJ-II stellarator, a separate 2-mm microwave source was used toproduce a probing beam; the measurements were performed at the middle of the plasmaradius [3]. Plasma density fluctuations in the axial (heating) region of the LHD stellaratorwere measured from microwave scattering at the fundamental harmonic of the heatinggyrotron radiation [3]. Characteristic features of fluctuations, common for all three devices,are revealed with the methods of statistical and spectral analysis. These features are the widefrequency Fourier and wavelet spectra, autocorrelation functions with slowly decreasing tails,and non-Gaussian probability distributions of the magnitudes and the increments of themagnitude of fluctuations. The drift-dissipative instability and the instability driven bytrapped electrons are examined as possible sources of turbulence in a high-temperatureplasma.

Observations showed the high level of coherence between turbulent fluctuations in thecentral region and at the edge of the plasma in L-2M. It is shown in L-2M that the relativeintensity of the second harmonic of gyrotron radiation on the axis of a microwave beam afterquasi-optical filtering in a four-mirror quasi-optical transmission line is about -50 dB of thetotal radiation intensity. Spatiotemporal structures in plasma density fluctuations wereobserved in the central region of the plasma column. The correlation time between thestructures was found to be on the order of 1 ms. It is shown that, the spectrum of the signalfrom the second-harmonic scattering extends to higher frequencies in comparison with thatfrom the fundamental-harmonic scattering.

New results were obtained with the use of a small-angle scattering of the heatinggyrotron radiation in LHD.

In TJ-II, plasma density fluctuations were studied in experiments with the neutralbeam injection. The experiments showed the presence of distinct quasi-harmonics in the firststage of the heating pulse. Simultaneously with these fluctuations, quasi-harmonics with thesame frequencies were detected in the fluctuation signals of magnetic probes. Long timesamples of density fluctuations (more than a million points at a sampling rate of 5 MHz) havefor the first time measured.

1. G. M. Batanov, K. A. Sarksyan, L.V. Kolik, et al., Pis’ma Zh. Éksp. Teor. Fiz. 72 (2000) 250.2. G. M. Batanov, L.V. Kolik, M. I. Petelin et al. Plasma Physics Reports. 29 (2003)1019.3. N.N. Skvortsova, G.M. Batanov et al. J. Plasma Fusion Res. SERIES, 5 (2002) 328.4. G. M. Batanov, L. V. Kolik, A. E. Petrov et al. Plasma Physics Reports. 29, (2003) 363.

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Keeping the options open for a reactor: issues in the stellarator roadmap

J. Sánchez and V. Tribaldos

Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain

The recent agreement on ITER construction consolidates the tokamak line as a an

option for an economically viable reactor as well as fusion in general as a potential energy source. In addition, as a side effect of the ITER site negotiations and within a positive climate towards research in new energy sources, projects like the materials irradiation facility (IFMIF) and strategies like the “fast track to fusion” get significantly reinforced. This positive scenario for fusion, and therefore for stellarators, brings as well pressure in our community in what concerns the role of stellarators and the “roadmap” towards a stellarator “DEMO” reactor.

The present keynote paper will therefore address the present scenario, and introduce the discussion on the following issues: how to present the role of stellarators to the public and to the policymakers, the comparative advantages beyond the steady state and the disruption-free operation, the problems to be solved in the progress of the stellarator line, the way findings from ITER could be taken onboard and, finally, the extrapolation from the LHD-W7X-NCSX generation devices to a reactor experiment.

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THURSDAY

6th October

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132

Internal Transport Barrier Physics in Helical Systems

M.Yokoyama, H.Maa_berg*, T.Estrada**, T.Minami, C.D.Beidler*, F. Castejon**, A.Dinklage*,A.Fujisawa, J. Herranz, K.Ida, S.Murakami***, O.Yamagishi and H.Yamada

National Institute for Fusion Science, Toki 509-5292, JapanMax-Planck Institut fur Plasmaphysik, Greifswald 17491, Germany*

Laboratorio Nacional de Fusion, CIEMAT-FUSION, Madrid 28040, Spain**Department of Nuclear Engineering, Kyoto Univ., Kyoto 606-8501, Japan***

The electron internal transport barrier (eITB) has been observed in wide range of helicalsystems, such as CHS[eg.,1], LHD[eg., 2], TJ-II[eg., 3] and W7-AS[eg., 4]. The eITB isÅ@defined ashighly peaked electron temperature (Te) profile with strongly positive radial electric field (Er) in thecentral region. These observations are reviewed in this paper to understand the device-independentcommon findings and also to draw the main differences. This is the first report from the InternationalStellarator Profile Database Activity.

The formation of the strong central positive Er has been understood mainly as a result of theambipolarity of neoclassical electron and ion fluxes [1-5], although some additional convective electronflux such as driven by ECRH is required in some situations [3,4]. This “neoclassical” physicspeculiar to low collisional regime of helical plasmas provides the commonly observed existence of theECRH power threshold (which is also depending on the density). This is contrastive characteristics tothe ITB observed in tokamaks [6]. The dependence of the ECRH power threshold on the magneticconfiguration and on the heating scenario among these devices are currently being examined by takingthe effective ripple [7,8] and the trapped particle fraction as parameters to achieve the comprehensiveunderstanding.

The roles of low order rational surfaces on the onset of eITB formation and also on its radialsize (location of the footpoint of the eITB) have been indicated in inward shifted configurations inLHD (depending on the relative locations of heating position and 2/1 island) [9] and TJ-II (eITBbecomes possible at higher density when 3/2 rational is introduced in the plasma core region) [10]. Itis speculated that, for the latter case, the resonance causes an extra electron flux to trigger the positiveEr. The interplay between low order rational surfaces and the formation of eITB still waits for thesystematic experiment and theoretical analysis. The external controllability of rational surface positionand also the magnetic island width, which is peculiar in helical systems, would provide additionalexternal knob for the eITB formation in a relevant high density regime (finding in TJ-II [10] ispromising).

1. T.Minami et al., Plasma Phys. Control. Fusion 46 (2004) A285.2. K.Ida et al., Phys. Rev. Lett. 91 (2003) 085003.3. F.Castejon et al., Nucl. Fusion 42 (2002) 271.4. H.Maa_berg et al., Phys, Plasmas 7 (2000) 295.5. M.Yokoyama et al., J.Plasma and Fusion Res. 79 (2003) 816.6. K.Ida et al., Plasma Phys. Control. Fusion 46 (2004) A45.7. H.Yamada et al., 20th IAEA Fusion Energy Conference (2004) EX/1-5.8. M.Yokoyama et al., 14th International Stellarator Workshop (2003) O.Tu2.9. K.Ida et al., Phys. Plasmas 11 (2004) 2551.10. T.Estrada et al., Plasma Phys. Control. Fusion 46 (2004) 277.

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Effect of Ripple-Induced Transport on H-mode Performance in Tokamaks

V. Parail1, J. Lonnroth2, T. Johnson3, T. Kiviniemi2, A. Loarte4, G. Saibene4, P. de Vries1, T.Hatae5, Y. Kamada5, S. Konovalov 5, N. Oyama5, K. Shinohara5, K. Tobita5, H. Urano5 and

JET EFDA contributorsa.1 EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, OXON OX14 3DB, UnitedKingdom; 2 Association EURATOM-Tekes, Helsinki University of Technology, P.O. Box 2200, 02015 HUT,Finland; 3 Association EURATOM-VR, Alfven Laboratory, Royal Institute of Technology, 10044 Stockholm,Sweden; 4EFDA Close Support Unit, c/o Max Planck Institut fur Plasmaphysik, Boltzmannstrasse 2, 85748Garching, Germany; 5 Naka Fusion Research Establishment, JAERI, 801-1, Mukoyama, Naka-city, Ibaraki,301-0193, Japan.

A number of experiments have shown [1,2] that ripple-induced transport influencesperformance of ELMy H-modes in the tokamak. A noticeable difference in confinement,ELM frequency and amplitude was found between JET (with ripple amplitude δ∼0.1%) andJT-60U (with δ∼1%) in otherwise identical discharges [1]. It was previously shown in JETexperiments with enhanced ripple [2] that a gradual increase in the ripple amplitude first leadsto a modest improvement in plasma confinement, which is followed by the degradation ofedge pedestal and further transition to the L-mode regime if δ increases further. The DIII-D[3] team recently reported a marginal increase in confinement in experiments with an edgetransport enhanced by the externally driven resonant magnetic perturbation. Numericalpredictive modelling of the dynamics of ELMy H-mode JET plasma relevant to a JET/JT-60Usimilarity experiment [1] has been conducted taking into account ripple-induced ion transport,which was computed using the orbit following code ASCOT [4]. This predictive modellingreveals that, depending on plasma parameters, ripple amplitude and localisation (the latterdepending on the toroidal coil design), this additional transport can either improve globalplasma confinement or reduce it. These controlled ripple losses might be used as an effectivetool for ELM mitigation and may provide an explanation for the difference between JET andJT-60U observed in the similarity experiments. A detailed comparison between ripple-induced transport and the alternative method of ELM mitigation by an externally driven edgemagnetic perturbation is discussed. The fact that ripple losses mainly increase ion transport,while a stochastic magnetic layer increases electron transport indicates that it might bebeneficial to use a combination of both methods in future experiments.This work was funded partly by the United Kingdom Engineering and Physical SciencesResearch Council and by the European Communities under the contract of Associationbetween EURATOM and UKAEA. The views and opinions expressed herein do notnecessarily reflect those of the European Commission. The work was also partly done underthe IEA agreement on Large Tokamak Facilities.

[1] G. Saibene et al., Plasma Phys. Control. Fusion 46 A195 (2004);[2] B. Tubbing, Proc. 22 EPS Conf. on Contr. Fus. Plasma Phys. Vol. 19C, p. IV-001 (1995);[3] T.E. Evans et al., Proc. 20th IAEA Fusion Energy Conference (2004);[4] T. Kiviniemi et al., 32 EPS Conference on Plasma Physics, Tarragona, Spain, 2005

a appendix of J.Pamela et al., Fusion Energy 2004 (Proc. 20th Int. Conf.,Vilamoura, 2004), IAEA, Vienna (2004).

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Study of Magnetic Fourier Components Effect on Ion Viscosity in Tohoku University Heliac

S. Kitajima, H. Takahashi, Y. Tanaka, H. Utoh, M. Takenaga, M. Yokoyama 1, S. Inagaki1, Y. Suzuki1, K. Nishimura1, H. Ogawa2, J. Shinde, M. Ogawa, H. Aoyama, K. Iwazaki,

K. Shinto and M. Sasao

Department of Quantum Science and Energy Engineering, Tohoku University, Sendai, Japan 1 National Institute for Fusion Science, Toki, Japan

2 Japan Atomic Energy Research Institute, Naka, Japan

Neo-classical theories explain that the non-linearity of the viscosity plays the important

role in the bifurcation phenomena of the L-H transition observed in large tokamaks and stellarators. In the Tohoku University Heliac (TU-Heliac), a helical axis stellarator, the effects of the viscosity maxima on the improved mode transition has been investigated by electrode biasing experiments using a hot cathode made of LaB6. The driving force J x B for a plasma poloidal rotation was externally controlled and the poloidal viscosity was successfully estimated from the driving force. It was experimentally confirmed that the local maxima in the viscosity play the key role in the L-H transition 1. One of further extended works is to clarify the effect of magnetic Fourier components on the neo-classical viscosity. The minimization of helical ripples allows the reduction of viscosity, which is expected to bring good accessibilities to the improved confinement modes. It is also important to find out the effect of low mode rational surfaces or magnetic islands on the viscosity, because magnetic islands, which have low poloidal mode numbers and locate along a plasma periphery, have the possibility to become a control knob on a radial electric field and a radial particle flux. In a heliac device toroidal ripples, helical ripples and bumpiness can be changeable by selecting ratios of coil currents, even though these flexibilities are not independent each other. The hot cathode biasing above-mentioned can be one of the useful methods for the evaluation of viscosities in the particular magnetic configurations.

In TU-Heliac the viscosities in various magnetic configurations were evaluated

experimentally by the hot cathode biasing method. The toroidal ripples, the helical ripples and the bumpiness were changed in the range of about 30, 20 and 80% respectively by shifting the magnetic axis under the fixed rotational transform profile. The preliminary experimental results showed that the viscosity maxima qualitatively agreed with neo-classical predictions 2, demonstrating the usefulness of the hot cathode biasing method in the viscosity evaluation. TU-Heliac has local vertical field coils which produce external perturbation fields to resonate the magnetic Fourier components of (n, m) = (3, 2), (5, 3) and to grow m = 2 and 3 magnetic islands. Increasing the width of magnetic islands located along the plasma periphery, the electrode current J required for the improved mode transition was increasing. It suggested that the ion viscosity increased according to the increase of the magnetic island width. In order to estimate precisely poloidal Mach numbers in the biased plasmas ion temperature measurements were carried out by a high-resolution spectrometer and the measurement of poloidal flow velocities was tried out by a multi-Langmuir probe to compare with the E x B drift velocities. 1. S. Kitajima et al., FEC (2004) IAEA-CN-116/EX/9-3. 2. H. Takahashi et al., J. of Plasma and Fusion Research SERIES 6 (2003) 366-370

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Overview and Future Plan of Helical Diverter Study in the Large Helical Device

S. Masuzaki, T. Morisaki, M. Shoji, Y. Kubota, M. Goto, S. Morita, H. Ogawa1, M. Kobayashi, N. Ohyabu, A. Komori, O. Motojima and LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292, JAPAN 1Graduate University for Advanced Studies, Hayama 240-0163, JAPAN

One of the characteristics of the heliotron-type magnetic configuration is that it has

intrinsic divertor structure (helical divertor, HD). Particle control using HD configuration to achieve improved confinement and sustatinment of steady state high performance plasma is a major experimental goal in the Large Helical Device (LHD). The LHD scrape-off layer (SOL) in HD configuration has unique magnetic field line structure which contains stochastic region, residual islands and whiskers structure contrasting to “onion-skin” like magnetic field line structure in poloidal divertor tokamaks SOL. Since 1998, the first experimental campaign, study for understanding of edge plasma properties in “open” HD configuration has been conducted experimentally and theoretically.

In this presentation, helical divertor study in LHD will be overviewed. It will contain: (1) Power and particle transport in LHD SOL; (2) Neutral pressure behavior in HD configuration. In the former topic, the relation between magnetic field line structure and heat and particle deposition profiles on divertor is a major issue. In the second topic, relatively low neutral pressure in divertor, up to 10-2 Pa, suggests the necessary of proper baffle structure for effective particle control using HD. Neutral transport simulation using DEGAS code will also be mentioned in this topic. These topics are essential for effective particle control using HD.

Development of new divertor plate to sustain steady state high performance plasma has been achieved. Comparing with the current divertor plate, heat properties are improved largely, and the tolerable heat flux becomes 3 times larger.

As the future plan of HD experiment, closure of HD by installation of baffle structure based on above results of HD studies and development of divertor plate will be presented.

IT-19

136

The Steady-State ECRH-System at Wendelstein7-XH. P. Laqua1, V. Erckmann1, R. Brakel1, H. Braune1, H. Maaßberg, N. Marushchenko1,G.

Michel1, Y. Turkin1, S. Ullrich1,G. Dammertz2, M. Thumm2, P. Brand3, G. Gantenbein3, W. Kasparek3,

the W7-X ECRH teams at IPP1, FZK2 and IPF3

1Max-Planck-Institut für Plasmaphysik, EURATOM Ass.D-17491 Greifswald, Germany,

2Forschungszentrum Karlsruhe, Association EURATOM-FZK,Institut für Hochleistungsimpuls- und Mikrowellentechnik,

Postfach 3640, D-76021 Karlsruhe, Germany,3Institut für Plasmaforschung, Univ. Stuttgart, D-70569 Stuttgart, Germany

Electron Cyclotron Resonance Heating (ECRH) is the main heating system for theWendelstein7-X (W7-X) stellarator and the only one for CW-operation in the first stage.The mission of W7-X, which is presently under construction at IPP-Greifswald, is todemonstrate the inherent steady state capability of stellarators at reactor relevant plasmaparameters. A modular 10 MW ECRH plant at 140 GHz with 1 MW CW-capabilitypower for each module is under construction to meet the scientific objectives. Simulationsof different ECRH scenarios, which are foreseen for W7-X operation and base on ray-tracing calculations and confinement studies, will be presented. A steady state ECRH hasspecific requirements on the stellarator machine itself, on the ECRH-sources,transmissions elements and on the experimental environment. In particular all elementshave to be sufficiently cooled, screened and armoured against microwaves. Thecommissioning of the ECRH plant is well under way, the strategy and status of the projectwill be reported. First full power, CW integral tests of one ECRH module have beenperformed. A large microwave stray radiation chamber for integrated in-vessel componenttests had been brought into operation. A bi-axially movable, motor driven ECRH antennamock-up was build and is tested for reliability now.

A strategy for the commissioning and the first experimental campaign at W7-X has beendeveloped.

IT-20

137

Long pulse plasma discharge experiment by ICRF heating in LHD

T. Seki, T. Mutoh, R, Kumazawa, K. Saito, Y. Nakamura, F. Shimpo, G. Nomura,S. Kubo, Y. Takeiri, S. Masuzaki, M. Sakamoto1, Y. Takase2, H. Kasahara2,M. Ichimura3, H. Higaki3, Y.P. Zhao4, J.G. Kwak5, T. Watari, A. Komori,

and LHD Experimental Group

National Institute for Fusion Science, Toki 509-5292, Japan1Kyushu University, Kasuga 816-8580, Japan

2University of Tokyo, Tokyo, Japan3University of Tsukuba, Tsukuba, Japan

4Institute of Plasma Physics, Academia Sinica, Hefei 230031, P.R. China5Korea Atomic Energy Research Institute, Daejeon 305-600, Korea Rep.

Long pulse plasma discharge experiment has been carried out using an ion cyclotronrange of frequencies (ICRF) heating in LHD. The pulse length was extended up to about 30minutes. The plasma was sustained mainly by an ICRF heating of 520 kW with assist of anECH of 100 kW and an NBI heating of 60 kW (average). A total injected heating energy was1.3 GJ. A helium plasma with a hydrogen ion as a minority species was used for the ICRFheating. The magnetic field was 2.75 T and the wave frequency was 38.47 MHz. The ioncyclotron resonance layer was located at the saddle point of the magnetic field and a minorityheating was expected. The line-averaged electron density was 0.8x1019m-3 and the ion andelectron temperatures were 1.5 to 2 keV.

One of the key factors to the success of the long pulse discharge was a scatter of of theheat load on the divertor plate. Temperature increase of the divertor plate was reduced by theswing of the magnetic axis inward and outward. The position of the magnetic axis was swung18.5 times between 3.67 m and 3.7 m during the longest plasma discharge. An operation of theICRF heating system was improved for the long pulse experiment. The temperaturemeasurement of the ICRF antenna was conducted by the IR camera. The distance between theantenna and the plasma was set to 12 cm for the steady state operation. The impedance matchingsystem was improved for the long pulse operation, during which the reflected RF powerincreased gradually. Methods of the fine frequency change and the shift of the liquid level of theliquid stub tuner were actually used.

The length of the plasma discharge is limited by the plasma collapse. Just before thecollapse of the plasma, the intensity of FeX signal increased abruptly and the electrontemperature decreased rapidly. This abnormal plasma termination is often in connection with thespark in the vacuum vessel, which is observed by the visible CCD camera. It is necessary toovercome the problem of the metallic impurity penetration into the plasma for the achievement ofthe higher power and longer pulse experiment in future.

IT-21

138

FRIDAY

7th October

139

140

Significance of MHD Effects in Stellarator Confinement

A. Weller1, K.Y. Watanabe2, S. Sakakibara2, K. Toi2, J. Geiger1, M.C. Zarnstorff3,S.R. Hudson3, A. Reiman3, A. Werner1, C. Nührenberg1, S. Ohdachi2, Y. Suzuki2,

W7-AS Team1, LHD Team2

1Max-Planck-Institut für Plasmaphysik, EURATOM-IPP Association,D-17491 Greifswald, Germany

2National Institute for Fusion Science, Toki 509-5292, Japan3Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA

AbstractSubstantial progress has been achieved to raise the plasma beta in stellarators and helical

systems by high power neutral beam heating, approaching reactor relevant values. In theWendelstein W7-AS stellarator, quasi-stationary plasmas with volume averaged beta inexcess of 3 % could be established at B = 0.8...1.0 T [1,2]. The maximum beta could befurther pushed up to values of <β> > 4 % in the Large Helical Device (LHD) atB = 0.4...0.5 T [3]. The achievement of high-β operation is closely linked with configurationeffects on the confinement and with magnetohydrodynamic (MHD) stability issues.

The magnetic configurations and their optimization for high-β operation within theflexibility of the devices are characterized. A comparative description of the accessibleoperational regimes in W7-AS and LHD is given. The finite-β effects on the flux surfacesdepend on the degree of configuration optimization. In particular, a large Shafranov shift isaccompanied by formation of islands and stochastic field regions as found by numericalequilibrium studies [2,4]. However, the observed pressure gradients indicate some mitigationof the effects on the plasma confinement, presumably because of the high collisionality ofhigh-β plasmas and island healing effects (LHD [5,6]). As far as operational limits bypressure driven MHD instabilities are concerned, only weak confinement degradation effectsare usually observed, even in linearly unstable regimes.

The impact of the results concerning high-β operation in W7-AS and LHD on the futurestellarator programme will be discussed, including relations to tokamak research. Some of thefuture key issues appear to be: - the control of the magnetic configuration (including toroidalcurrent control), - the modification of confinement and MHD properties towards the lowcollisional regime, - and the compatibility of high-β regimes with power and particle exhaustrequirements to achieve steady state operation.

[1] Weller et al, Plasma Phys. Control. Fusion 45 (2003) A285-A308.[2] Zarnstorff et al, 21th IAEA Fusion Energy Conference, Vilamoura, 2004, Paper EX/3-4.[3] Motojima et al, 21th IAEA Fusion Energy Conference, Vilamoura, 2004, Paper OV1-4.[4] K.Y. Watanabe, S. Sakakibara, US-Japan JIFT Workshop, Kyoto, 2005.[5] Y. Nagayama et al, Nucl. Fusion 45 (2005) 888-893.[6] R. Kanno et al, Nucl. Fusion 45 (2005) 888-893.

RT-04

141

Suppression of large edge localized modes with edge resonant magnetic fieldsin high confinement DIII-D plasmas

P.R. Thomasc), T.E. Evans , R.A. Moyera), J.G. Watkinsb), T.H. Osborne, M.Becouletc), J.A. Boedob), E.J. Doyled), M.E. Fenstermachere), K.H. Finkenf), R.J.Groebner, M. Grothe), J.H. Harrisg), G.L. Jackson, R.J. La Haye, C.J. Lasniere), S.Masuzakih), N. Ohyabuh), D.G. Prettyg), H. Reimerdesi), T.L. Rhodesd), D.L.Rudakova), M.J.Schaffer, M.R. Wadej), G. Wangd), W.P. West, and L. Zengd)

General Atomics, P.O. Box 85608, San Diego, California, 92186-5608 U.S.A.a)University of California San Diego, La Jolla, California, U.S.A.b)Sandia National Laboratory, Albuquerque, New Mexico, U.S.A.c)CEA-Euratom Association, CEA-Cadarache, 13109 St Paul-lez-Durance, Franced)University of California, Los Angeles, California, U.S.A.e)Lawrence Livermore National Laboratory, Livermore, California, U.S.A.f)FZ-Jülich Euratom Association, Jülich, Germanyg)Australian National University, Canberra, Australiah)National Institute for Fusion Science, Gifu-ken, Japani)Columbia University, New York, New York, U.S.A.j)Oak Ridge National Laboratory, Oak Ridge, Tennessee, U.S.A.email: paul.richard.thomas@cea.frAbstract.Large divertor heat pulses due to Type-I edge localized modes (ELMs) have beeneliminated reproducibly in DIII-D with small dc currents driven in a simplemagnetic perturbation coil. The current required to eliminate all but a few isolatedType-I ELMs, during a coil pulse, is less than 0.4% of plasma current. Modellingshows that the perturbation fields resonate with plasma flux surfaces across most ofthe pedestal region (0.9 ≤ _N ≤ 1.0), when q95 = 3.7±0.2 creating small remnantmagnetic islands surrounded by weakly stochastic field lines.

The stored energy, _N, H–mode quality factor and global energy confinement timeare unaltered by the magnetic perturbation. At high collisionality (ν*~0.5-1), thereis no obvious effect of the perturbation on the edge profiles and yet ELMs aresuppressed, nearly completely, for up to 9τE. At low collisionality (ν*<0.1), there isa density pump-out and complete ELM suppression, reminiscent of the DIIID QH-mode. Other differences, specifically in the resonance condition and the magneticfluctuations, suggest that different mechanisms are at play in the differentcollisionality regimes.

In addition to a description and interpretation of the DIIID data, the application ofthis method to ELM control on other machines, such as JET and ITER will bediscussed.

IT-22

142

Assessment of Global Stellarator Confinement: Status of the International Stellarator Confinement Scaling Data Base

A.Dinklage(1,*), E.Ascasibar(2), C.D.Beidler(1), V. Dose(1), J. Geiger(1), J.H. Harris(3), A. Kus(1), S. Murakami(4), S. Okamura(5), R. Preuss(1),

F. Sano(4), U. Stroth(6), Y. Suzuki(5), J. Talmadge(7), V.Tribaldos(2), K.Y.Watanabe(5), H.Yamada(5),M.Yokoyama(5)

(1) Max-Planck-Institut für Plasmaphysik, EURATOM-Association, Greifswald, Germany (2) Laboratorio Nacional de Fusión, EURATOM-CIEMAT, 28040 Madrid, Spain (3) Australian National University, Canberra, Australia (4) Kyoto University, Kyoto, Japan (5) National Institute for Fusion Science,Toki,Gifu 509-5292, Japan (6) University of Stuttgart, Stuttgart, Germany (7) University of Wisconsin, Madison, USA (*) dinklage@ipp.mpg.de

Different stellarator/heliotron devices along with their respective flexibility cover a large magnetic configuration space. Since the ultimate goal of stellarator research aims at an alternative fusion reactor concept, the exploration of the most promising configurations requires a comparative assessment of the plasma performance and how different aspects of a 3D configuration influence it.

Therefore, the International Stellarator Confinement Database (ISCDB) has been re-initiated in 2004 and the ISS95 database has been extended to roughly 3000 discharges from eight different devices. Further data-sets are continuously added1.

A revision of a data set restricted to comparable scenarios lead to the ISS04 scaling law which confirmed ISS95 but also revealed clearly the necessity to incorporate configuration descriptive parameters. In other words, an extension beyond the set of regression parameters used for ISS95/ISS04 appears to be necessary and candidates, such as the elongation are investigated. Since grouping of data is a key-issue for deriving ISS04, basic assumptions are revised, e.g. the dependence on the heating scheme.

Moreover, an assessment of statistical approaches is investigated with respect to their impact on the scaling. A crucial issue is the weighting of data groups which is discussed in terms of error-in-variable techniques and Bayesian model comparison. The latter is employed for testing scaling ansatzes depending on scaling invariance principles hence allowing the assessment of applicability of theory-based scaling laws on stellarator confinement.

1. ISCDB resources are jointly hosted by NIFS and IPP, see http://iscdb.nifs.ac.jp and http://www.ipp.mpg.de/ISS

IT-23

143

Self-sustained detachment observed in LHD

J. Miyazawa1, S. Masuzaki1, R. Sakamoto1, H. Arimoto2, K. Kondo2, N. Tamura1, M. Shoji1,

M. Nishiura1, S. Murakami3, H. Funaba1, B.J. Peterson1, S. Sakakibara1, M. Kobayashi1,

K. Tanaka1, K. Narihara1, I. Yamada1, S. Morita1, M. Goto1, M. Osakabe1, N. Ashikawa1,

T. Morisaki1, K. Nishimura1, H. Yamada1, N. Ohyabu1, A. Komori1, O. Motojima1, and

LHD experimental Group

1 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan 2 Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan 3 Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan

Self-sustained detachment has been obtained in the Large Helical Devise (LHD). Strong

hydrogen gas puffing of ~200 Pa·m3/s for ~0.1 s after a density feedback phase shrinks the

plasma column and then the plasma detaches from the divertor plate. After the detachment

takes place, high electron density of over 1 × 1020 m-3 is sustained without gas puffing until the

heating beam stops. The minor radius of the hot plasma column shrinks to ~90 % of the last

closed flux surface, which corresponds to the ι = ι/(2π) = 1/q = 1 rational surface, throughout

the detachment phase. Correspondingly, m/n = 1/1 MHD turbulence is destabilized, where m

and n denote the poloidal and toroidal mode number, respectively. This new state has been

dubbed the “Serpens mode”, for self regulated plasma edge ’neath the last closed flux surface.1

During the Serpens mode phase, large spikes are observed in the ion saturation current on the

divertor tiles, Hα, and CIII signals. These spikes are related to the rotating radiation belt on the

plasma surface, which looks like a big snake and named “Serpent”. Global energy confinement

of the Serpens mode is compared with the international stellarator scaling 1995 (ISS95) and

recently developed scaling for high-density LHD plasmas (HD scaling)2-3, where shrinking

confinement volume and shallow penetration of the heating beams are taken into account.

Although the energy confinement of the Serpens mode seems degraded compared with ISS95,

as is the case of high-density attached plasmas, it well matches with the HD scaling. This

suggests that the energy confinement property of the detached plasmas is similar to that of

high-density attached plasmas.

1. J. Miyazawa et al., J. Plasma Fusion Res. 81, 331 (2005).

2. J. Miyazawa et al., Plasma Phys. Control. Fusion 47, 801 (2005).

3. J. Miyazawa et al., 32nd EPS (Tarragona, Spain), P1.047 (2005).

IT-24

144

New Classes of Quasi-Axisymmetric Configurations

L. P. Kua and P. R. Garabedianb

aPrinceton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USAbCourant Institute of Mathematical Sciences, New York University, NY, NY 10012, USA

We have identified and developed new classes of quasi-axially symmetricconfigurations which have attractive properties from the standpoint of both near-term physicsexperiments and long-term power producing reactors. These new configurations weredeveloped as a result of surveying the aspect ratio-rotational transform space to identifyregions endowed with particularly interesting features. These include configurations with verysmall aspect ratios (~2.5) having superior quasi-symmetry and energetic particle confinementcharacteristics, and configurations with strongly negative global magnetic shear from externallysupplied rotational transforms so that the overall rotational transform, when combined withthe transform from bootstrap currents at finite plasma pressures, will yield a small butpositive shear, making the avoidance of low order rational surfaces, hence the existence of highquality flux surfaces, at a given operating beta, possible. Additionally, we have foundconfigurations with NCSX-like characteristics1 but with the improved integrity of fluxsurfaces and confinement of energetic particles. For each new class of configurations, we havedesigned coils to ensure that the new configurations are realizable and engineering-wisefeasible. The coil designs typically have coil aspect ratios R/∆min(C-P) ≤ 6 and coil separationratios R/∆min(C-C) ≤ 10, where R is the plasma major radius, ∆min(C-P) and ∆min(C-C) are theminimum coil to plasma and coil to coil separations, respectively. The maximum magneticfield strength in the coil body is about twice as large as the field strength on the magnetic axisfor conductors having cross sectional areas 0.2 m2. These coil properties allow powerproducing reactors of major radii less than 9 meters be designed with DT fuels and with a fullbreeding blanket. The good quasi-axisymmetry limits the energy loss of α particles to below10%.

1. G. H. Neilson, M. C. Zarnstorff, L. P. Ku, et al., Proc. 19th Int. Conf. On Fusion Energy, IAEA-CN-94/IC 1, Lyon, 2002.

* This work was supported by the United States Department of Energy Contract No. DE-AC02-76-CHO-3073 and DE-FG02-86ER53223.

IT-25

145

Nonlinear evolution of MHD instability in LHD

H. Miura1��2�, N. Nakajima1��2�, T. Hayashi1��2� and M. Okamoto1��2�

1)National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, JAPAN2)The Graduate University for Advanced Studies (SOKENDAI),

322-6 Oroshi, Toki, Gifu 509-5292, JAPAN

Direct numerical simulations of fully three-dimensional, compressible magnetohydrody-namic (MHD) equations are carried out in order to clarify nonlinear saturation mechanism ofpressure-driven instabilities in the Large Helical Device (LHD). A special attention is paid toimportance of the toroidal flows and compressibility, which are often discarded in the linearanalysis and/or reduced MHD simulations. We refer to these effects as full-MHD effects. Inrecent LHD experiments under inward-shifted configurations, plasma is confined relativelywell even though it passes through Mercier unstable region. Inspired by the experimentalresults, we aim to inspect influences of the full-MHD effects to the stability of the system.

We solve the equations of continuity, momentum, pressure and magnetic field numeri-cally by the 6th-order compact finite scheme and 4th-order Runge-Kutta-Gill scheme in ourDNS code MINOS. Starting from the initial condition with β0 � 4% equilibrium which wascalculated by the HINT code, the plasma kinetic energy grows exponentially. The growthis studied by decomposing the field quantities into Fourier modes in the Boozer coordinate.Having the peaked initial pressure profile, the initial equilibrium has very unstable nature.The poloidal (m) and toroidal (n) Fourier mode m�n � 2�1 is predominant over the othermodes. It is shown that the toroidal flow contributes as much as the polodal flow compo-nents to the growth of the kinetic energy. Though the poloidal components of the velocityfield grows earlier than the toroidal component, the latter exceeds the former when the growthis saturated because of the nonlinearity of the MHD equations.

By inspecting detailed views of the toroidal flow generation, it is shown that the toroidalflow generation contributes to reduce the impact of the instability to the confinement bydistributing the energy obtained from the pressure gradient not only to the poloidal directionbut also to the toroidal direction.

An influence of the compressibility is explored by studying the right-hand-side terms ofthe budget equation of the kinetic energy. It is well known that the divergence of the dis-placement vector ξξξ contributes to suppress the linear growth, because the term is positivedefinite in the energy-principle-formulation of the linear analysis. It is shown that the com-pressible term in the kinetic energy budget equation has 50%�80% magnitude of that of thedriving term in our simulations. It indicates that the linear growth rate is suppressed to 1/2to 1/5 of that value estimated under the incompressible assumption.

Time evolutions of the flow field, pressure and magnetic field are observed closely bymaking use of visualization technique. Generation of the toroidal flow, compressibility willbe discussed in the context of vortex generation associated with the growth of the pressure-driven unstable Fourier modes.

Recent numerical results starting from a stabler equilibrium will also reported.

IT-26

146

On the role of turbulence on momentum redistribution in fusion devices

C. HidalgoLaboratorio Nacional de Fusión, Euratom-Ciemat, Spain

The mechanisms underlying the generation of plasma flows play a crucial role inunderstanding key issues on transport in magnetically confined plasmas. It is wellknown the importance of driving shear in plasma rotation in the development oftransport barriers. Rotation can be driven by external forces such as momentum fromNeutral Beam Injection (NBI). However, in large scale devices like ITER (where theavailable NBI power is limited and the energy of injected neutrals must be high to reachthe core plasma region) the NBI driven rotation will be limited. Then, it is important tostudy the possible role of other mechanisms which can drive plasma rotation.The amplitude of parallel flow measured in the scrape-off layer (SOL) is significantlylarger than those resulting from simulations [1]. Recent experiments have pointed outthe possible influence of turbulence in explaining a component of the anomalous flowsobserved in the plasma boundary region [2, 3].In the plasma core region, evidence of anomalous toroidal momentum transport hasbeen reported [4, 5, 6]. Different mechanisms have been proposed to explain theseresults, including neoclassical effects [7], turbulence driven models [8, 9] and fastparticle effects. The response of toroidal rotation to near-perpendicular NB injection onJT-60U has been interpreted on the basis of the influence of loss of high-energyparticles [10]. The flow reversal observed in the CHS stellarator can be explained by thespontaneous flow driven by large radial electric fields [11]. Neoclassical effects can alsoplay an import role [12].Recent experiments in the TJ-II stellarator have shown that the generation ofspontaneous perpendicular sheared flows requires a minimum plasma density. Near thiscritical density, the level of edge turbulent transport and the turbulent kinetic energysignificantly increases in the plasma edge [13,14]. Experimental results also showsignificant turbulent parallel forces at plasma densities above the threshold value totrigger perpendicular ExB sheared flows [15]. These findings provide the firstexperimental evidence of the important role of parallel turbulence forces on edgemomentum dynamic in fusion devices. [1] K. Erents et al., Plasma Phys. Control. Fusion 42 (2000) 905.[2] C. Hidalgo et al., Phys. Rev. Letters 91 (2003) 065001.[3] B. Labombard et al., Nuclear Fusion 44 (2004) 1047.[4 ] S. D. Scott et al., Phys. Rev. Lett. 64 (1990) 531.[5] W. D. Lee et al., Phys. Rev. Lett. 91 (2003) 205003.[6] J.E. Rice et al., Nucl. Fusion, 44 (2004) 339[7] A. L. Rogister et al., Nucl. Fusion 42 (2002) 1144.[8] B. Coppi, Nucl. Fusion 42 (2002) 1.[9] X. Garbet et al., Phys. Plasmas 9 (2002) 3893[10] Y. Koide et al., in Plasma Physics and Controlled Nuclear Fusion Research 1992 (Proc. 14th Int.Conf. Wurzburg, 1992), Vol. 1, IAEA, Vienna (1993) 777.[11] K. Ida et al., Phys. Rev. Lett. 86 (2001) 3040.[12] K. Ida et al., Nucl. Fusion 45 (2005) 391.[13] M.A. Pedrosa et al., Plasma Phys. Control Fusion 47 (2005) 777.[14] C. Hidalgo et al., Phys. Rev. E 70 (2004) 067402.[15 ] B. Gonçalves et al., Phys. Rev. Lett. (2005) (submitted)

IT-27

147

148

149

IAEA TECHNICAL MEETING ONINNOVATIVE CONCEPTS ANDTHEORY OF STELLARATORS

11th & 12th October

150

151

PROGRAMME OF IAEA-TM, 2005

Monday 10th

8:45 Welcome

9 J. Nührenberg“Global Neoclassical Transport simulation in stellarators”

9:30 H. Maaβberg“Extended Ordering Scheme for Neoclassical Theory”

10 C. Beidler“Effects of the Quasi-Neutrality Condition on Neoclassical Transport inStellarators”

10:30 Coffee Break

11 M. I. Mikhailov“Bootstrap Current Minimization in Quasi-isodynamic Configurations withLarge Number of Periods”

11:30 W. Kernbichler“Computation of neoclassical transport in stellarators with finite collisionality”

12 Y. Turkin“Development of Transport Package for Simulation of Stellarator Plasmas”

12:30 V. G. Kotenko“Magnetic surface configuration with plane magnetic axis in l=2 torsatron withadditional toroidal magnetic field”

13 A. Cooper“Three-Dimensional Anisotropic Pressure Equilñibrium Model Based on a bi-Maxwellian distribution function”

13:30 Lunch

15 Discussion on Neoclassical Transport International Collaboration18 End of the day

Tuesday 11th

9 C. Nührenberg“Global ITG turbulence in screw-pinch geometry”

9:30 Ya. I. Kolesnichenko“Effects of fast-ion-orbit width on Alfvén instabilities in stellarators: a generaltheory and its application to a W7-AS experiment”

152

10 Yu. V. Yakovenko“Properties of the high-frequency part of the Alfvén continuum andeigenmodes in stellarators”

10:30 Coffee Break

11 D. Spong“Particle-based calculations of viscous stress and closure relations forstellarators and broken-symmetry tokamaks”

11:30 N. B. Marushchenko“Kinetic modelling of ECRH and ECCD”

12 S. Kasilov“Kinetic modelling of the nonlinear ECRH in stellarators”

12:30 Closing

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153

Extended Ordering Scheme for Neoclassical Theory

H. Maaßberg and C.D. Beidler

Max-Planck-Institut fur Plasmaphysik,IPP-EURATOM Association, TI-Greifswald, Germany

In the traditional neoclassical ordering, the distribution function is expanded in 1st orderwith an unshifted Maxwellian in 0th order where the density, the temperatures and the (elec-trostatic) potential are assumed to depend only on the flux surface label. In the 1st order driftkinetic equation, the derivatives with respect to radius, � , and velocity, � , are neglected andthe poloidal

�����rotation is treated in the incompressible approach. In this limit, the radial

derivatives of the density, the temperature and the potential are the only thermodynamic forcesdriving the fluxes via the transport matrix.

The collision operator is approximated by the Lorentz form and acts only on the pitch,�� �� ��� , thus violating momentum conservation for like-particle collisions. Within a momentapproach [1,2], the particle, the parallel momentum and the energy balance are fulfilled leadingto a complex energy convolution algorithm of the mono-energetic 1st order distribution functionestimated from the simplified drift kinetic equation. In both formulations, however, the toroidalplasma rotation is omitted, the poloidal rotation is incompressible, and density and potentialvariations within the flux surfaces are neglected.

Three driving mechanisms for density and potential variations on the flux surfaces arediscussed: the radial fluxes [3], the compressibility of the

�����poloidal rotation (for large

���),

and the centrifugal and Coriolis forces of a toroidal rotation (this might be important for quasi-axisymmetric configurations with NBI). The generalisation of the moment equation approach[1,2] with respect to these additional effects is analysed.

[1] M. Taguchi, Phys. Fluids B 4 (1992) 3638[2] H. Sugama and S. Nishimura, Phys. Plasmas 9 (2002) 4637[3] C.D. Beidler and H. Maaßberg, this IAEA-TM (2005)

154

Effects of the Quasi-Neutrality Conditionon Neoclassical Transport in Stellarators

C.D. Beidler, H. MaaßbergMax-Planck-Institut fur Plasmaphysik, IPP–EURATOM Ass., Greifswald, GERMANY

crb@ipp.mpg.de

In this contribution, the implications which the quasi-neutrality condition has for neo-classical transport in stellarators are investigated using a numerical solution of the ripple-averaged kinetic equation which has been extended to account for variations of the electrostaticpotential,

�, on flux surfaces. Solutions of the kinetic equation for ions and electrons which

simultaneously satisfy the conditions of (local) quasi-neutrality and ambipolarity of the (flux-surface-averaged) radial particle fluxes are determined iteratively using standard methods forsolving systems of non-linear equations. Comparisons are made with “standard” neoclassicaltheory (in which only ambipolarity is enforced) for various magnetic-field configurationsassuming plausible density and temperature profiles. Significant differences are found forconventional heliotron/torsatron devices. Especially in the plasma periphery, where strongdensity and temperature gradients exist, the magnitude of the “ion” root is reduced significantlyleading to increased particle and energy fluxes. For strongly drift-optimized stellarators,however, bulk plasma transport is much less affected.

The influence of the results on impurity transport are also considered. It is demonstratedfor fully ionized carbon in the tracer approximation that impurity transport coefficients arestrongly affected by the quasi-neutrality-induced variation of

�on flux surfaces. This is true

for all stellarators, whether classical or drift-optimized, and the effects are further accentuatedfor high- � impurities.

155

Bootstrap Current Minimization in Quasi-isodynamic Configurationswith Large Number of Periods

M.I. Mikhailov�

� W.A. Cooper�

� M.Yu. Isaev�

� V.N. Kalyuzhnyj�

� S.V. Kasilov�

�

W. Kernbichler�

V.V. Nemov�

� C. Nuhrenberg�

� J. Nuhrenberg�

� V.D. Shafranov�

�

A.A. Subbotin�

� R. Zille�

�Russian Research Centre ”Kurchatov Institute”, Moscow, Russia

�CRPP, Association Euratom-Confederation Suisse, EPFL, Lausanne, Switzerland

�Institute of Plasma Physics, National Science Center ”Kharkov Institute of Physics and

Technology”, Kharkov, Ukraine�

Max-Planck-Institut fur Plasmaphysik, IPP-EURATOM Association, Germany�

Institut fur Theoretische Physik, Technische Universitat Graz, Austria

It was shown earlier that in quasi-isodynamic (qi) stellarators [1,2] with moderate numberof periods it is possible to make the bootstrap current negligible [3], so that the change inrotational transform profile does not lead to appearance of low-mode number resonancesand to kink-mode instability [4]. With increasing number of periods the stability

�limit

becomes higher [5], so that for the same value of structural factor of bootstrap current thevalue of the current increases. The increase of aspect ratio related to increasing numberof periods leads to a stronger change of the rotational transform for the same net toroidalcurrent. On the other hand, the stellarator rotational transform becomes larger and the low-mode-free gap in rotational transform becomes wider with increasing number of periods. Inthe present paper results of minimization of bootstrap current for qi configurations with large

�and large number of periods will be presented.

1. Gori S., Lotz W. and Nuhrenberg J. 1996 Theory of Fusion Plasmas (International School ofPlasma Physics) (Bologna: SIF) p. 335.2. M.I. Mikhailov et al, Nuclear Fusion 42 (2002) L23.3. A.A. Subbotin et al, 30th EPS Conf. Contr. Fusion and Plasma Phys. St. Petersburg 2003. ECAVol. 27 A, P-4.16.4. Anthony Cooper et al, Plasma Phys. Control. Fusion 44 (2002) B357-B373.5. J. Nuhrenberg et al, ”Report on INTAS Projecr No. 592: Novel Approaches to Improve Confine-ment in 3D Plasma Magnetic Systems”, 14th International Stellarator Workshop, September 2003,Greifswald.

156

Computation of neoclassical transport in stellarators with finite

collisionality ∗

W. Kernbichler1, S.V. Kasilov2, G.O. Leitold1, V.V. Nemov2, K. Allmaier1

1 Institut für Theoretische Physik - Computational Physics, Technische Universität Graz,

Petersgasse 16, A–8010 Graz, Austria2 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and

Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine

A new numerical method is presented which allows for an efficient evaluation of neoclas-sical transport coefficients and of the bootstrap coefficient in stellarators for the case there isno radial electric field. In this method, the approach [1] used in code NEO to compute the 1/ν

transport coefficient during integration along the magnetic field line is generalized to arbitrarycollisionality regimes.

In more detail, the linearized steady-state drift kinetic equation (DKE) is solved by a finite-difference method. The solution of the DKE is described in terms of the phase space fluxdensity throughs= constcuts, wheres is the distance measured along the magnetic field line.The phase space is split into "ripples" which cover finite intervals overs and extend into thevelocity space. Within such a ripple, the problem is discretized by introducing levels over theperpendicular action. The distribution of these levels is specific for the ripple. The DKE isapproximated by a coupled set of ordinary differential equations overs for the integrals of thephase space flux density over bands between the levels. The general solution of the kineticequation for a single ripple is then expressed in terms of a set of matrix relations betweenthe discretized phase space flux densities of particles entering and leaving the ripple troughits boundaries. The whole set of these matrices is called a "propagator". The final solution isobtained after subsequent joining of these propagators using their group property.

The method has similar advantages as the NEO code, such as high speed, good conver-gence in low collisionality regimes as well as the possibility of computations for magneticfields given in magnetic and real space coordinates, in particular, for magnetic fields resultingdirectly from the Biot-Savart law and from new equilibrium codes such as PIES and HINT.

References[1] V.V. Nemov, S.V. Kasilov, W. Kernbichler and M.F. Heyn, Phys. Plasmas6, 4622 (1999)

∗This work has been carried out within the Association EURATOM-ÖAW and with funding from the AustrianScience Fund (FWF) under contract P16797-N08. The content of the publication is the sole responsibility of itspublishers and it does not necessarily represent the views of the Commission or its services.

157

Development of Transport Package for Simulation of Stellarator Plasmas

Yu. Turkin, H. Maaßberg, and W7-X Team

Max-Planck-Institut für Plasmaphysik, EURATOM-Association,D 17491 Greifswald, Germany

Our present long-term goal is to develop the software tools specifically directed for thecomputer modeling of transport phenomena in stellarators. The new code will be used forprediction and analysis of experiment in the W7-X stellarator, studying of time-dependentprocess, and plasma control in steady-state operation. The transport code is based on a systemof equations, which consists of particle and power balance equations augmented by partialdifferential equations for the radial electric field and the toroidal current density. Along withthe developing and extending of the transport code we start modeling of the physicalprocesses in the W7-X stellarator1, 2.

In this report following topics will be discussed:– Software architecture;– Data base needed for the code to run: magnetic configuration DB, neoclassic DB,

profile DB, geometry(vessel and components) DB;– Capability of coupling with other codes;– Main modules and kinetic codes which must be included;– Distributed computing technique;– Design approach: object oriented, platform independent, heterogeneous;– International collaboration.

1. Yu. Turkin et al. 31st EPS Conf. on Plasma Phys. London, 28 June - 2 July 2004 ECA Vol.28G, P-1.1982. Yu. Turkin et al. Current control by ECCD for W7-X, 15th International Stellarator Workshop 2005, Madrid,

3 - 7 October 2005.

158

Magnetic surface configuration with plane magnetic axis in l=2 torsatronwith additional toroidal magnetic field

V. G. Kotenko, V. I. Lapshin, D. V. Kurilo, Yu. F. Sergeev, Ye. D. VolkovInstitute of Plasma Physics, National Science Center “Kharkov Institute of Physics and

Technology”, Kharkov, 61108, Ukraine

Numerical studies were undertaken to elucidate the properties of magnetic surfaceconfiguration in a model of l=2 torsatron with plane shifted inward magnetic axis. Suchconfigurations are interesting owing to the increase of energy confinement time observedexperimentally in the torsatron/heliotron plasmas [1-3]. It is not impossible that the increasecan be associated with a decrease of field ripples on the magnetic surfaces when spatialmagnetic axis is transformed into a plane one [4]. The design characteristics of torsatron U-2M with additional toroidal magnetic field [5] were chosen as the base parameters for thecalculation model. The calculations were performed with taking into account some technicaldetails of the U-2M helical winding. It is shown in particular, that in the torsatron U-2Mmagnetic system the controllable spacing between the region of closed magnetic surfaces(plasma confinement region) and vacuum chamber wall is possible. This issue is important inview of the development of the conception of the research fusion reactor (RFR) [6,7].

1. N.I. Nazarov, V.V. Plyusnin, T.Yu. Ranyuk, et al, Fizika Plasmy, v.15, 1027(1989) (in Russian).2. S. Okamura, K. Matsuoka, R. Akijama, et al. Nucl.Fusion, 39 (1999) 1337.3. H. Yamada, K. Y. Watanabe, K. Yamazaki, et al. Nucl.Fusion, 41 (2001) 901.4. V.Kotenko, E.Volkov, K.Yamazaki. Plasma Devices and Operations, 12, 2, (2004)143.5. O. S. Pavlichenko. A Collection of Papers Presented at the IAEA Technical Committee Meeting onStellarators and Other Helical Confinement Systems at Garching, Germany 10-14 May 1993, IAEA,Vienna,Austria, 1993, p.60.6. Kotenko V.G., Volkov E.D., Yamazaki K. In: 30th EPS Conf. on Contr. Fusion and Plasma Phys. St.Petersburg, 7—11 July, 2003, ECA, vol. 27A, P-3.1.7. V.G.Kotenko, Ye.D.Volkov, K.Yamazaki. VANT, Ser. Termoyaderny Sintez, Moscow, 2004, 3, p.29 (inRussian).

159

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160

Global ITG turbulence in screw-pinch geometry

C. Nuhrenberg1, R. Hatzky2, S. Sorge1

Max-Planck-Institut fur Plasmaphysik, EURATOM Association,1Wendelsteinstraße 1, D-17491 Greifswald,

2Boltzmannstraße 2, D-85748 Garching,Germany

The present version of the gyrokinetic electrostatic global non-linear particle-in-cell codeTORB1 is used to investigate the turbulence in a straight cylinder with finite rotationaltransform near unity, i.e. in a situation appropriate as a first strongly simplified model forthe one in the W7-X stellarator. Turbulence issues, zonal flows, and energy conservationwill be discussed.

1S. Sorge, Plasma Phys. Control. Fusion 46 (2004) 535.

161

Effects of fast-ion-orbit width on Alfvén instabilities in stellarators: a general theory and its application to a W7-AS experiment

Ya.I. Kolesnichenko1, V.V. Lutsenko1, A. Weller2, A. Werner2, H. Wobig2,

Yu.V. Yakovenko1, J. Geiger2, and S. Zegenhagen2

1Institute for Nuclear Research, 03680 Kyiv, Ukraine 2Max-Planck-Institut für Plasmaphysik, D-17489 Greifswald, Germany

Finite orbit width of the energetic ions causing Alfvén instabilities can considerably influence the instability growth rate in tokamaks. The effect of finite orbit width, b∆ , on Alfvén

instabilities in stellarators is not studied yet. This motivated the fulfilment of the present work aimed to develop a stellarator-relevant theory for finite b∆ and apply the developed theory to an experiment

on Wendelstein 7-AS (W7-AS). In this work, a general expression for the growth rate of Alfvén instabilities driven by

toroidally passing (and poloidally passing or trapped) energetic ions in stellarators is derived, which generalizes that obtained in Ref. [1] by taking into account finite b∆ . This expression is suitable for

a description of the destabilization of all types of Alfvén Eigenmodes (AE) including those which are absent in tokamaks (various Helicity-induces AEs, Mirror-induced AEs). It takes into account peculiarities of the particle orbits and resonances of the wave-particle interaction in stellarators. A code GAMMA-O calculating the growth rate on the basis of the new theory is developed.

It is found that new physics associated with finite orbits can be considered as a result of additional resonances induced by finite b∆ : The mentioned resonances involve low-energy ions,

which decreases the instability growth rate; on the other hand, these resonances can lead to instabilities in the case when the wave-particle interaction for 0=∆b is not possible. It is shown that

the instability growth rate decreases with the poloidal mode number, m , as 1−∝ mγ when the orbit

width well exceeds the mode width. This is different from the dependence 2−∝ mγ obtained for Toroidicity-induced AE in tokamaks [2], which possibly can be explained by different radial structure of AEs in tokamaks [where the magnetic shear is large ( 1~s )] and low-shear systems ( 1ˆ <<s ), e.g., Wendelstein-line stellarators, considered in this work. It is concluded the drive is maximum when mrb /~∆ (like in tokamaks). This fact can be used for analysis of experiments

where the mode numbers cannot be inferred from experimental data. They can also be used for predictive calculations of Alfvén instabilities in Wendelstein7-X and other machines.

The developed theory is applied to a particular shot (shot #34723) of W7-AS, which enabled to explain different characters of Alfvénic activity at 70≤ω kHz and 40≥ω kHz, i.e., at the beginning and the end of the instability bursts (more about this experiment to be reported in Ref. [3]).

1. Ya.I. Kolesnichenko, S. Yamamoto, K. Yamazaki et al., Phys. Plasmas 11 (2004) 158. 2. B.N. Breizman, S.E. Sharapov, Plasma Phys. Contr. Fusion 37 (1995) 1057. 3. Ya.I. Kolesnichenko, V.V. Lutsenko, A. Weller et al., 15th ISW (Madrid) 2005.

162

Properties of the high-frequency part of the Alfvén continuum and eigenmodes in stellarators

Yu. V. Yakovenko1, Ya. I. Kolesnichenko1, A. Weller2, H. Wobig2, and O. P. Fesenyuk1

1Institute for Nuclear Research, 03680 Kyiv, Ukraine 2Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, D-17489 Greifswald,

Germany

The Alfvén eigenmodes (AE) in tokamaks and stellarators are of interest because of

their ability to be destabilized by fast ions. The resulting instabilities may be harmful, causing fast ion losses. On the other hand, they can be utilized for plasma diagnostics. The Alfvén spectra in stellarators are much more complicated than in tokamaks. Due to the lack of axial symmetry, new gaps appear in the high-frequency (HF) part of the Alfvén continuum (AC), with new types of eigenmodes (the so-called mirror-induced and helicity-induced Alfvén eigenmodes, MAE and HAE) residing in these gaps.1-3 Calculations of AC in various stellarators with the AC code COBRA2 show that these gaps are rather wide and relatively close to each other. As a result, some continuum bands in this frequency range are compressed into extremely narrow bands. The Fourier structure of the continuum wave functions in this range is very complicated. Therefore, one can expect that, when studying HF AEs, like HAEs and MAEs, one should take account of a large number of harmonics, which makes this task rather difficult task for both numerical and analytical methods.

Recently a new analytical approach to analysis of the AC was suggested,4,5 which is based on multiple-scale expansion and WKB techniques. Such an approach can be used to analyse the HF part of the stellarators AC since it can treat multi-harmonic interactions. In the mentioned references, the AC in the vicinity of two closely interacting gaps was studied, including the case when the gaps cross at a certain radial point. It was shown that the gaps “annihilate” at the crossing point, i.e., the width of the joint gap at the crossing point is the difference of the widths of the two separate gaps. The structure of the AC near this point turned out to resemble narrow electron energy zones in a crystal.

In this work, the theory4,5 is extended. An analytical WKB theory of the continuum near the crossing point is developed to treat the case of several interacting gaps. In particular, it is shown that the continuum wave functions in the HF range are trapped in the poloidal angle. Results of the theory are compared with continua calculated with COBRA for W7-AS and W7-X configurations. To investigate the structure of AEs of the discrete spectrum in this frequency range, the ballooning formalism is employed. The developed WKB technique is applied to the obtained ballooning equation.

1. N. Nakajima, C. Z. Cheng, M. Okamoto, Phys. Fluids B 4 (1992) 1115. 2. Ya. I. Kolesnichenko et al., Phys. Plasmas 8 (2001) 491. 3. C. Nührenberg, in ISSP-19 “Piero Caldirola”, Theory of Fusion Plasmas (2000), p. 313. 4. Yu. V. Yakovenko, Ya. I. Kolesnichenko, A. Könies, A. Weller, A. Werner, S. Zegenhagen, “Peculiarities

of the Alfvén continuum in stellarators”, Report at the IAEA TC Mtg on Innovative Concepts and Theory of Stellarators (Greifswald, 2003).

5. Yu. V. Yakovenko, Ya. I. Kolesnichenko, V. V. Lutsenko, A. Weller, A. Werner, S. Zegenhagen, J. Geiger, 20th IAEA Fusion Energy Conf. (Vilamoura, 2004), Report IAEA-CN-116/TH/P4-48.

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Particle-based calculations of viscous stress and closure relations forstellarators and broken-symmetry tokamaks

D. A. Spong, E. A. D’Azevedo, S. P. Hirshman, D. del-Castillo-Negrete, R. T. Mills, M. R.Fahey

Oak Ridge National Laboratory, Oak Ridge, TN 37831-6169

Collisional Monte Carlo methods have proven attractive for the calculation of plasmaneoclassical transport properties at low collisionality in three-dimensional configurations. Aproblem of recent interest has been the analysis of plasma flows in such systems and closurerelations for moments methods calculations. For stellarators, these topics are motivated by theinter-relation of sheared flows with enhanced confinement regime access, and the need forbetter predictions of bootstrap current. In the case of broken-symmetry tokamaks, calculationof closure relations in the vicinity of neoclassical tearing mode islands is an importantingredient for the development of extended MHD models of such instabilities. We havedeveloped a δf method that extends the usual approach by first partitioning off both theMaxwellian plus the l = 1 parallel particle and heat flow portions; particle methods are thenused to calculate the remaining components of f. Both equilibrium/surface-averaged and time-varying/local viscosity tensor components can then be obtained by taking appropriatemoments of the resulting distribution function. A number of computational improvements toour DELTA5D Monte Carlo model and access to massively parallel vector architectures (suchas the Cray X1) have also facilitated such calculations. These include vectorized 3D-splineroutines used for the magnetic field evaluation, multi-level time-stepping, quiet restarts,conversion to cylindrical coordinates, and data compression/noise reduction techniques. Thismodel is applicable both to systems with nested closed flux surfaces as well as those withmagnetic islands.

Acknowledgements – Research sponsored by the Laboratory Directed Research andDevelopment Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, forthe U. S. Department of Energy and by the U.S. Department of Energy under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

164

Kinetic modelling of ECRH and ECCD

N.B. Marushchenko, H. Maaßberg, M. Schmidt

Max-Plank-Institut fur Plasmaphysik, EURATOM-Association,Greifswald, Germany

For high power ECRH and ECCD, kinetic models must include the electron momentumand energy balance, at least in some phenomenological way. Despite of high accuracy of theFokker-Planck models for the velocity space dynamic (heating, thermalisation, etc), capabilityof them for the neoclassical effects is very poor. From other side, Monte-Carlo methods arewell suited for description of moments in 5D phase space, e.g. radial fluxes, but have ratherpoor resolution for the velocity space processes, especially for high

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Axisymmetry in tokamaks gives a general possibility to reduce the 5D drift kinetic equation(DKE) up to 3D bounce-averaged Fokker-Planck equation with quasi-linear RF diffusion andcollisional thermalisation and transport included . Since the heating in tokamaks is balancedmainly by anomalous radial diffusion, typically the width of electron banana can be neglected,and the bounce-averaging procedure is strongly simplified. The Fokker-Planck codes , devel-oped in this approach, cover a large area of tasks, but excluding all the neoclassical effects.

In stellarators, in contrary, neoclassical transport is dominating, at least in the central (heated)region, and the energy transport has a convective nature. There is a number of different classesof trapped particles, which have to be included into the model. In a rigorous way the DKE canbe reduced to a set of coupled 4D equations, and it does not give any computational advan-tage compared to Monte-Carlo methods. In some special cases the Fokker-Planck modellingis surely applicable, with a careful formulation of the power balance term. This was done forW7-AS for on-axis ECRH deposition with a simplified power sink simulating the energy trans-port � .

As the next step, the advanced �� Monte-Carlo scheme, recently proposed and well testedfor NBI � , is discussed. The basic idea is to use the steady state solution of the specified Fokker-Planck problem for the marker equation. The application for the ECRH problem is more com-plex, and requests the use of a more advanced (non-linear) Fokker-Planck solver, fulfilling thepower balance. The Fokker-Planck problem can be formulated as a set of magnetic surfaceaveraged equations with the power balance terms, which describes the neoclassical losses � .The Monte-Carlo solver “corrects” the shape of the distribution function by fast convection ofthe trapped particles. This hybrid scheme combines the advantages of Fokker-Planck models(getting the distribution function with a high accuracy), and Monte-Carlo simulation (precisedescription of the spatial fluxes).

1. F.S. Zaitsev, M.R. O’Brien and M. Cox, Phys. Fluids B 5 (2), 509 (1993)2. R.W Harvey, M.G. McCoy, in Proc. of the IAEA Technical Committee Meeting, Montreal, 1992

(IAEA, Vienna,1993) 4983. M.Rome´et al, Plasma Phys. Control. Fusion 39 (1997) 1174. M. Schmidt et al, 31st EPS Conference Plasma Phys., London, 28 June - 2 July 2004 ECA Vol.28G,

P-1.200 (2004)

165

Kinetic modelling of the nonlinear ECRH in stellarators ∗

S.V. Kasilov1, W. Kernbichler2, R. Kamendje2, M.F. Heyn2

1 Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and

Technology”, Akademicheskaya Str. 1, 61108 Kharkov, Ukraine2 Institut für Theoretische Physik - Computational Physics,Technische Universität Graz,

Petersgasse 16, A–8010 Graz, Austria

At power levels typical for the present day ECRF heating experiments in tokamaks and stel-larators, the quasilinear and nonlinear effects of heatingon the electron distribution functioncan be important. This is especially true in scenarii with 2nd harmonic X-mode heating withnear-perpendicular injection of the microwave beam. In this case, both, the nonlinear effectsof the wave-particle interaction and the distortion of the electron distribution function are sig-nificant. A method for the kinetic description of these effects on ECRH and ECCD within aMonte Carlo modelling have been developed and applied to tokamak geometry in [1,2].

In stellarators, an additional complexity is introduced bythe absence of axial symmetry ofthe device which results also in new effects such as generation of convective supra-thermalelectron radial fluxes by ECRH. In order to meet the requirements of ECRH modelling inthese cases, a specific Monte Carlo method, a stochastic mapping technique (SMT), which hasmuch higher efficiency than the conventional Monte Carlo method, has been developed in [3].There, the convective electron fluxes have been modelled assuming that ECRH provides a pointsource of supra- thermal electrons in the phase space. In thepresent report methods of Refs.[1-3] are combined into a consistent model which is applied to a stellarator with parameterstypical to W-7AS.

References[1] R.Kamendje, S.V. Kasilov, W. Kernbichler, and M.F. Heyn, Phys. Plasmas10, 75 (2003)

[2] R.Kamendje, S.V. Kasilov, W. Kernbichler, I.V. Pavlenko, E. Poli, and M.F. Heyn, Phys.Plasmas12, 12502 (2005)

[3] S.V. Kasilov, W. Kernbichler, V.V. Nemov and M.F. Heyn, Phys. Plasmas9, 3508 (2002)

∗This work has been carried out within the Association EURATOM-ÖAW and with funding from the AustrianScience Fund (FWF) under contract P16797- N08. The content of the publication is the sole responsibility of itspublishers and it does not necessarily represent the views of the Commission or its services.

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