DOE F 4650.2 Department of Energy OMB Control No.(10-99) Office of Science (SC) 1910-1400(All Other Editions Are Obsolete) (OMB Burden Disclosure

Face Page Statement on Back)

TITLE OF PROPOSED RESEARCH: High Beta Tokamak Research

1. CATALOG OF FEDERAL DOMESTIC ASSISTANCE #: 8. ORGANIZATION TYPE:81.049 Local Govt. State Govt.

Non-Profit Hospital2. CONGRESSIONAL DISTRICT: Indian Tribal Govt. Individual

Applicant Organization's District: 8 & 15 Other Inst. of Higher Educ. xProject Site's District: 8 & 15 For-Profit

Small Business Disadvan. Business3. I.R.S. ENTITY IDENTIFICATION OR SSN: Women-Owned 8(a)

1355980939. CURRENT DOE AWARD # (IF APPLICABLE):

4. AREA OF RESEARCH OR ANNOUNCEMENT TITLE/#:Office of Science Research Notice 02-19: Innovations in Fusion EnergyConfinement Systems: Innovative Plasma Operations in Support… 10. WILL THIS RESEARCH INVOLVE:

10A Human Subjects No x If yes,5. HAS THIS RESEARCH PROPOSAL BEEN SUBMITTED Exemption No. or

TO ANY OTHER FEDERAL AGENCY? IRB Approval Date Yes No X Assurance of Compliance No:

10B Vertebrate Animals No If yes,PLEASE LIST: IACUC Approval Date

Animal Welfare Assurance No:

6. DOE/OER PROGRAM STAFF CONTACT (if known): 11. AMOUNT REQUESTED FROM DOE FOR ENTIREDr. Charles Finfgeld PROJECT PERIOD $

7. TYPE OF APPLICATION: 12. DURATION OF ENTIRE PROJECT PERIOD:New Renewal X 11/24/02 to 11/23/05Continuation Revision Mo/day/yr. Mo/day/yr.Supplement

13. REQUESTED AWARD START DATE15. PRINCIPAL INVESTIGATOR/PROGRAM DIRECTOR 11/24/02 (Mo/day/yr.)

NAME, TITLE, ADDRESS, AND PHONE NUMBER14. IS APPLICANT DELINQUENT ON ANY FEDERAL DEBT?

Yes (attach an explanation) No XGerald A. NavratilProfessor 16. ORGANIZATION'S NAME, ADDRESS AND CERTIFYINGDepartment of Applied Physics and Applied Mathematics REPRESENTATIVE'S NAME, TITLE, AND PHONE NUMBERColumbia University, S. W. Mudd Bldg Room 209 Columbia University500 West 120th Street Office of Projects and GrantsNew York, NY 10027 500 West 120th St, Rm 254 Eng Terrace

New York, NY 10027Phone: 212-854-4496 Att: Ms. Patricia H. WelchFax: 212-854-8257 Phone: 212-854-6851

SIGNATURE OF PRINCIPAL INVESTIGATOR/ SIGNATURE OF ORGANIZATION'S CERTIFYINGPROGRAM DIRECTOR 5/13/02 REPRESENTATIVE

Date DatePI/PD ASSURANCE: I agree to accept responsibility for the scientific conduct of the project and to CERTIFICATION & ACCEPTANCE: I certify that the statements herein are true and complete to the provide the required progress reports if an award is made as a result of this submission. Willful best of my knowledge, and accept the obligation to comply with DOE terms and conditions if an provision of false information is a criminal offense. (U.S. Code, Title 18, Section 1001). award is made as the result of this submission. A willfully false certification is a criminal offense.

(U.S. Code, Title 18, Section 1001). NOTICE FOR HANDLING PROPOSALSThis submission is to be used only for DOE evaluation purposes and this notice shall be affixed to any reproduction or abstract thereof. All Government and non-Government personnel handling this submission shall exercise extreme care to ensure that the information contained herein is not duplicated, used, or disclosed in whole or in part for any purpose other than evaluation without written permission except that if an award is made based on this submission, the terms of the award shall control disclosure and use. This notice does not limit the Government’s right to use information contained in the submission if it is obtainable from another source without restriction. This is a Government notice, and shall not itself be construed to impose any liability upon the Government or Government personnel for any disclosure or use of data contained in this submission. PRIVACY ACT STATEMENTIf applicable, you are requested, in accordance with 5 U.S.C., Sec. 562A, to voluntarily provide your Social Security Number (SSN). However, you will not be denied any right, benefit, or privilege provided by law because of a refusal to disclose your SSN. We request your SSN to aid in accurate identification, referral and review of applications for research/training support for efficient management of Office of Sciencegrant/contract programs.

Renewal Application for DOE Research Grant DE-FG02-86ER53222Made to the United States Department of Energy

Office of ScienceOffice of Fusion Energy Science

Washington, DC 20545

HIGH BETA TOKAMAK RESEARCH

Submitted in Response toOffice of Science Notice 02-19

Innovations in Fusion Energy Confinement SystemsInnovative Plasma Operations in Support ofPOP, PE, and Burning Plasma Experiments

by

The Trustees of Columbia University in the City of New YorkOffice of Projects and Grants

Box 20, Low Memorial LibraryNew York, NY 10027

Project Period: 24 November 2002 to 23 November 2005Total 3 Year Project Proposed Budget: $3,578,068

1st Budget Period: 24 November 2002 to 23 November 20031st Budget Period Proposed Budget: $1,177,200

2nd Budget Period: 24 November 2002 to 23 November 20042nd Budget Period Proposed Budget: $1,197,755

3rd Budget Period: 24 November 2002 to 23 November 20053rd Budget Period Proposed Budget: $1,203,113

Gerald A. NavratilPrincipal Investigator, Project DirectorDepartment of Applied Physics and Applied Mathematics(212) 854-4496

M. E. MauelChairmanDept. of Applied Physics andApplied Mathematics(212) 854-4455

Morton B. FriedmanVice-DeanFu Foundation School ofEng. and Applied Science(212) 854-2986

Patricia H. WelchAssistant DirectorOffice of Projects & GrantsColumbia University(212) 854-3023

iii

Budget Pages (DOE Forms 4620.1)

iv

Budget Explanations

We request funds to purchase four equipment systems that will extend thecapability of HBT-EP to carry out active mode control studies of both internal andexternal MHD modes in rotating plasmas. These are:

1. An increase in the power of our active mode control system from 6 kW to50 kW to provide a system with improved control capability for externalRWMs integrated with control of internal tearing modes. (Writtenbudgetary estimate from Crown Audio, Elkart, IN.)

2. A high speed Digital Signal Processor (DSP) to convert our present analogactive mode control system to full digital operation. (Written budgetaryquotation from Traquair, Ithaca, NY based on four parallel 8-channelcontrol loops implemented using Virtex-II 1M gate FPGA from Xilinxmounted on PCI board on existing optically-isolated control computer. 12-bit ADCs,14-bit DACs, Simulink software and other development tools)The added flexibility of a DSP will allow the same system to control bothinternal and external MHD modes, as well as provide greatly extendedcapability for testing improved feedback control algorithms. We plan toinstall this system in two stages, with an initial 10 input channel system inthe 1st budget period followed by an upgrade to a 20 channel system in the2nd budget period.

3. Plasma rotation effects on the RWM are a key question to be explored inthe next 3 years. Extension of the single chord measurement of ourDoppler rotation diagnostic to multiple chords in the 2nd budget period willprovide important internal rotation profile information for these studies.

4. To carry out detailed flow field measurements of the plasma rotating inand around magnetic islands we plan to design and install a new rotatingprobe instrumented with an array of Mach probes in the 2nd budget period.

Year 1 Equipment1. 50 kW Feedback Control Upgrade $ 50,0002. High Speed DSP System-10 channel initial system 40,000

Year 2 Equipment1. 10 Chord Doppler Rotation Measurement System $ 20,0002. High Speed DSP System-20 channel upgrade 30,0003. Instrumented Rotating Probe for Island Studies 10,000

Year 3 Equipment$ 0

v

Table of Contents

Face Page (DOE Form 4650.2).............................................................................................iBudget Pages (DOE Forms 4620.1)................................................................................... iiiBudget Explanations ...........................................................................................................ivTable of Contents.................................................................................................................vProject Summary.................................................................................................................viDescription of Proposed Research.......................................................................................1

1. Introduction....................................................................................................................2

2. RWM Physics and Active Control....................................................................................2

3. Tearing Mode Dynamics and Plasma Rotation ..................................................................9

4. Combined Internal and External Mode Control ...............................................................13

5. Research Tool Development ..........................................................................................14

6. Research Schedule ........................................................................................................19

Research Progress Report 2000–2002 .................................................................................11. Introduction....................................................................................................................1

2. Summary and Highlights .................................................................................................1

3. Resistive Wall Mode Control...........................................................................................3

4. Tearing Mode and Rotation Control .................................................................................6

5. Research Tools and Facilities...........................................................................................8

Other Grant Application Forms and Materials ....................................................................1Biographical Sketches.........................................................................................................1

Facilities, Resources, and Collaborations..............................................................................2

Bibliography ......................................................................................................................6

Current and Pending Support.............................................................................................11

Certifications and Assurance of Compliance.......................................................................14

vi

High Beta Tokamak ResearchProject Summary

Department of Applied Physics and Applied MathematicsColumbia Plasma Physics Laboratory, Columbia University, New York, NY

We propose to use the HBT-EP active mode control facility together withimproved analysis capability from the VALEN feedback modeling code to carry out thefirst experimental tests of active mode control near the stabilization limit achieved by aperfectly conducting (ideal) wall, answer critical questions about the role of plasmarotation in active control of internal tearing modes and external resistive wall modes(RWM), investigate the performance of highly modular “reactor relevant” feedbackcontrol configurations, and use optimal configurations to simultaneously control of bothinternal and external modes. The HBT-EP experiment at Columbia University is ideallysuited to investigate this important area of advanced toroidal physics because of itsunique capabilities. HBT-EP has an adjustable conducting wall, an active feedbacksystem with over 50 independent control coils, rotation and internal profile diagnostics,an inside-launch RF heating system, and an established record of mode controlmeasurements of both tearing modes and external kink and wall modes. In addition, our3D, active mode-control model VALEN (without plasma rotation) has been developedand benchmarked on HBT-EP and is being applied to all present (HBTEP and DIII-D)and many prospective (ASDEX, NSTX, FIRE) external mode control experiments.

The RWM has been identified as limiting phenomena in the reversed field pinch,the spherical torus, and in the advanced tokamak. Similar phenomena are expected to beimportant in other toroidally confined plasmas including the spheromak and fieldreversed configuration. Dramatic progress has taken place in control of these modes inthe experiments and modeling on HBT-EP and DIII-D, led by the Columbia MHD group.This proposed research program builds on these accomplishments and addresses criticaloutstanding questions that have emerged as a result of our present studies. These include:How does toroidal plasma rotation effect growth of tearing and resistive wall modes? andHow can MHD control techniques be optimized at the ideal wall limits of stability? Ouranswers will contribute significantly to the scientific basis for the application of modecontrol techniques to a spectrum of toroidal approaches to fusion energy systems.

During the next three years, we propose a four-part program:1. Carry out a quantitative study of rotation stabilization and rotation-

damping effects of the wall stabilized external kink mode (RWM).2. Extend the capabilities of active mode control model, VALEN, to include

multi-mode and rotation effects, benchmark these effects against advancedcontrol configurations on HBT-EP, and continue its role as the primarymode control analysis and design tool in the fusion program.

3. Carry out the first tests of active mode control at the MHD stability limitachieved by an ideal wall and compare observations with predictedstability properties as functions of gain, control coil and passive stabilizercoverage, and feedback control algorithm.

4. Combine active control of both internal and external modes using a high-performance digital control system and optimized feedback control-coilconfiguration to investigate the “ultimate” MHD b limit in wall-stabilizedtokamak plasma.

1

Description of Proposed Research

This section describes HBT-EP research proposed for the program period 2003-2005. The proposed plan executes a comprehensive study of passive and active control oflong-wavelength MHD instabilities using an adjustable conducting wall and externalmagnetic synchronous and asynchronous control techniques. Because of the close tiesbetween the HBT-EP group and the MHD stability groups of the DIII-D and NSTXnational teams, results from HBT-EP are timely and immediately useful. They will defineand test a conceptual “blue-print” for mode stabilization systems that will influence bothinitial and future versions of the feedback systems installed in these devices and futureburning plasma experiments like FIRE or ITER. The proposed research plan alsoaddresses fundamental issues of ideal and non-ideal MHD such as the effects of plasmarotation on tearing mode dynamics, nonlinear interactions between applied and internaland external MHD modes, multimode feedback physics issues, and the optimization ofactive and passive control schemes for toroidal devices in general.

This proposed research plan continues and significantly extends the worksummarized in our report of research progress. With the addition of new diagnostics andcontrol systems during the past grant period, the HBT-EP research facility is in a uniqueposition to address these physics issues. Indeed, the HBT-EP experiment provides theworld’s fusion community with the only facility capable of systematic study of a widevariety of wall and feedback configurations.

The following presentation of our proposed program is organized into sixsubsections. (1) First, we present a brief introduction to the research and physics issuesassociated with active control of long-wavelength MHD. (2) Next, we describe ourongoing investigations of active control of the RWM, which continues into the proposedgrant period. (3) This is followed by a description of our proposed research to investigatecritical non-ideal MHD tearing mode physics relevant to confined toroidal plasmas. (4)Near the end of our proposed program, we plan an integration step. We will evaluatetechniques for combined internal and external mode control leading to the optimization ofplasma stability. (5) Next, we describe some of the critical research tools that will beimplemented this program period to enable our proposed study of MHD control physics.(6) The final subsection presents our proposed research schedule for the upcoming grantperiod. Application supporting material is attached including our report of progress and abrief description of our research facility, resources, and important external collaborationswith the MHD fusion community that contribute to HBT-EP serving as an effective testsite for mode control research.

2

1. Introduction

Control of long-wavelength MHD instabilities using conducting walls and externalmagnetic perturbations is one of the most important routes to improved reliability andimproved performance of magnetic fusion confinement devices. Understanding theinteraction and effect of resonant magnetic perturbations is key to much equilibrium andstability physics issues of toroidal plasma confinement. Magnetic perturbations nearhelical resonance with the equilibrium field lines at the plasma edge can lead to kinkmode formation and resonant field amplification. Magnetic perturbations in resonancewith non-ideal plasma can break flux surface topology and lead to magnetic islandformation and growth. Plasma response to a resonant perturbation depends critically onnon-ideal effects near the mode rational surface not included in the traditional ideal orresistive MHD equations. The HBT-EP research program is directed at understanding thephysics basis of these performance-limiting instabilities and using this knowledge todevelop novel control schemes to advance MHD control science and with it the operatingparameter regimes currently accessible to toroidal confinement systems.

2. RWM Physics and Active Control

Our major research activity in the present three-year grant period has been focusedon the investigation of active feedback control of external kink modes slowed by thestabilizing effect of a nearby resistive wall. It is well known that control of these resistivewall modes, or RWMs, above the no-wall beta limit is essential to achieving bootstrapcurrent sustained steady-state operation of tokamak fusion energy systems. The RWMhas also been identified as limiting phenomena in the reversed field pinch [Bodin,1990]and the spherical torus [Hender,1999;Sabbagh, 2002]. Similar phenomena are expectedto be important in other toroidally confined plasmas including the spheromak and fieldreversed configuration.

We have had dramatic progress in our understanding of and capability to controlthese RWMs in the experiments and modeling on HBT-EP, as described in the report ofprogress attached to this proposal. The proposed research program for the next threeyears, builds on that record of accomplishment and addresses critical outstandingquestions that have emerged as a result of our present studies dealing with the effects oftoroidal plasma rotation on the RWM and optimizing control of MHD at the limits ofstability that can be achieved with a perfect, or ideal, wall. Among the critical questionswe propose to address are:

1. Identification of the plasma rotation stabilization mechanism for the RWMand its scaling to larger devices.

2 . Experimental realization of the feedback control modeling predictions ofstabilization at the ideal wall beta limit with advanced control coilconfigurations.

3. Extension of feedback control to higher toroidal mode numbers as the n=1beta limit for a perfect, ideal wall is approached.

3

Fig. 2-1. Illustration of the HBT-EP adjustable wall and arrayof close-fitting control-coils.

2.1 Description of the Active Feedback Stabilization SystemAt the start of the present three-year grant period, we modified the original

adjustable conducting wall in HBT-EP to allow investigation of the variation of wallsegment resistivity and segment location relative to the plasma edge. Half of the originalthick (1.2 cm) Al wall segments were replaced with thinner (0.2 cm) stainless steel (SS)segments at equally spaced toroidal locations. A “smart shell” active feedback systemwas installed in HBT-EP, consisting of thirty flux loop sensors and thirty control coilsmounted to the SS wall segments on the side not facing the plasma. At each of the fiveequally spaced toroidal locations there are two SS segments, top and bottom. There arethree, overlapping, 15-turn control coils on each segment with a poloidal angular width ofapproximately 55º and spaced 25º apart. Each SS wall segment also has three 20-turnsensor loops in the center of its corresponding control coil. The active feedback system isillustrated in Fig. 1 of Cates andco-workers [Cates, 2000].

Each sensor loop andcontrol coil pair of the activefeedback system is connected toidentical, independent analogfeedback circuits. Each circuitconsists of solid-state amplifiersand passive filters, arranged toform adders and active filters,allowing suppression of up to94% of the mode radial fluxthrough the resistive wall in a30 -co i l “ smar t she l l ”configuration. This smart shellsystem has been found to bequite effective in stabilizing theRWM in HBT-EP when appliedto a series of current-ramp upexperiments (dI/dt ~ 2 MA/s)that produce strong disruptiveRWM activity of 4/1 modes atthe q* ~ 4 transition and 3/1 modes at the q* ~ 3 transition. At the q* ~ 4 transition,plasmas were normally observed to be 50% disruptive, and application of feedback with again of Gp =1.5¥106 V/Weber completely suppressed these RWM induced disruptions. Atthe q* ~ 3 transition, plasmas were normally observed to be 60% disruptive, andapplication of smart shell feedback control at that same gain reduced the RWM inducedplasma disruption rate to about 10%. Sufficient power is available in the 200 W poweramplifiers driving each control coil channel to prevent penetration of radial magneticfields through the SS wall segments of up to 10 G within a bandwidth of 0.4 kHz < w/2π< 11 kHz. While we will continue to use this system at the start of three-year period ofproposed research, we plan to significantly extend the performance of our active controlsystem with purchase of a fully digital high-speed, high-throughput digital control system

4

and with installation of significantly increased control power (2.5 kW per channel) asdescribed in Sec. 5.

Most recently, we have installed in HBT-EP an additional 40 control coils locatedin the toroidal “gaps” between stabilizing wall segments as shown in Fig. 2-1. Thesecontrol coils are presently connected in pairs for the same poloidal angle on each wallsegment to comprise 20 independent control coil channels. The input signal for thefeedback control loop for each control coil channel is provided by a multi-turn poloidalfield sensor located on the inner surface of the stabilizing wall segment at the samepoloidal angle as the nearby paired control coils. This system will be used to implement a“mode control” feedback scheme where a strongly amplified stabilizing response field isapplied by the control coils directly to the plasma surface. Since these poloidal modefield sensors have negligible coupling to the control coil generated radial response field,very high control loop gains can be used. As described in the next section, both singlemode analytic theory and VALEN [Bialek, 2001] model calculations predict that thisadvanced mode control configuration will allow RWM stabilization up to the stabilitylimit that can be achieved for a perfect, or ideal, wall for both current and pressure drivenRWMs.

2.2 Optimized Feedback Control ConfigurationsThe main purpose of placing a conducting wall structure near the plasma surface is

to stabilize the ideal kink mode branch, and then to deal with the greatly slowed growthof the RWM in the range of plasma parameters up to the ideal wall stability limit. For anygiven passive stabilizer configuration in a toroidal device, the objective in the design ofan active mode control system is to stabilize the set of performance limiting MHD modesas close as possible to this ideal wall (i.e. highest possible) stability limit. By applying theVALEN modeling code to a wide variety of tokamak designs several important designprinciples for optimizing the effectiveness of feedback control for kink modes have beenfound:

1) Mode Control is superior to Smart Shell feedback. “Smart shell” feedbackapplies a radial magnetic field response to the passive stabilizer wall to null out the RWMradial field at the wall, thereby making the wall appear as a perfect conductor to theRWM. However, this “smart shell” stabilization technique can only approach theperformance of an ideal wall limited to the area directly under the smart shell controlcoils. In contrast, using a “mode control” feedback control approach, the feedbackresponse is applied to the plasma surface at the highest possible gain, and can, inprinciple, stabilize the mode as if the entire passive stabilizing wall behaves as an idealconductor. Therefore, higher performance can be obtained with far fewer control coils.

2) Poloidal field sensors are superior to radial field sensors. Typical control coilsused for kink mode control produce primarily radial magnetic fields that do not couplesignificantly to poloidal field sensors. The very small control coil/sensor mutual inductivecoupling allows much higher feedback loop gains to be used in realistic feedback systemconfigurations.3) Mode control feedback is most effective when the control coil coupling to the passivestabilizer is minimized. Simple single mode theory predicts that control coils that couplemore strongly to the passive wall than the plasma are not able to reach the ideal wall

5

Fig. 2-2. Photograph of new control coils and the VALENpredictions of feedback performance approaching thestability limit of for an ideal (perfect) wall.

performance limit. As described by Boozer’s single mode description of the activefeedback control problem, the key interactions are the inductive coupling between theperturbed current in the unstable plasma mode and the wall, Mpw, the inductive couplingbetween the feedback coils and the plasma, Mfp, and the inductive coupling between thefeedback coils and the wall, Mfw. We define the coupling constant between the mode andthe wall, c, as (Mpw Mpw)/LpLw, where Lp and Lw are the respective self-inductances for agiven unstable mode. This problem can be modeled analytically for a RWM above theno-wall beta limit to obtain an overall dispersion relation and stabilization conditionusing active feedback control:

a3 g3 + a2 g

2 + a1 g + a0 = 0,

where a0/gwall = - gfeedback + gwall(D + cf)Kproportional; a1 = - gwall + Dgideal + gwall(D + cf)¥ Kdifferential; a2 = D; a3 = D t ; cf = 1 - (Mpw Mwf)/MpfLw; D = c(1 + s)/s – 1; andwith gwall the inverse wall time constant, gfeedback the inverse L/R time of the feedbackcoils, and s the instability “strength” which is related to bN and varies between 0 (at theno-wall limit) and about 1 (at the ideal wall limit). The proportional and differential gainfactors in the active feedback circuit are Kp and Kd respectively, and t is the inherentdelay in the feedback sensor/control loop. From this we can determine a stability criterionthat all four coefficients a0, a1, a2, and a3 must be positive.

This single mode, lumped parameter model has been found to be quite useful todevelop physical insight into thedominant interactions whenfeedback is used to stabilize anMHD kink mode, and is in goodqualitative agreement with thedetailed 3D calculations of theVALEN code. In particular wenote that since by definition D Æ0 at the ideal wall stability limit,this requires that cf ≥ 0 to make itpossible to reach the ideal wallstability limit. Physically thiscondition can only be satisfiedby minimizing the wall/controlcoil coupling, M wf, w h i l emaximizing the plasma/controlcoil coupling, Mpf. Reduction inthe plasma/wall coupling, M pw,to increase the value of cf is not auseful option here since thisdirectly reduces the ideal walllimit. Instead we seek tomaximize the value of M pw,limited only by the practicalconstraints of installing a close

6

fitting passive stabilizing wall in the toroidal system. The advantage of minimizing thecontrol coil coupling to the passive stabilizer in active feedback of MHD modes was firstnoted for control of the n=0 vertical instability by Lazarus, Lister, and Neilson [Lazar,1990] and passes over to the n=1 problem of the RWM as a direct analog.

This projected advantage of minimizing the control coil coupling to the passivestabilizer has been seen in modeling calculations by VALEN for several realisticconfigurations (HBT-EP, DIII-D, NSTX, and FIRE), where ideal wall stability limitswere reached for designs where the control coils could couple directly to the plasma. Inthe case of the advanced control coil system recently installed in HBT-EP this effect canclearly be seen in Fig. 2-2.

The experimental realization of the feedback control modeling predictions ofstabilization at the ideal wall beta limit with advanced control coil configurations is a keymeasurement which must be carried out to provide a sound basis for the projection ofthese design advantages to larger experiments (DIII-D, ASDEX, NSTX, KSTAR) andnext step Burning Plasma options (FIRE and ITER). We propose to carry out the firstexperimental test and comparison to 3D MHD modeling predictions for such an advancedfeedback control system. This will include a systematic study of RWM stabilizationagainst changes in gain, phase, control coil coverage, and unstable mode growth. Theinitial studies will use the present analog feedback system with power upgraded to 2.5kW per channel, followed by a transition in the second year of our proposed research planto a new, more easily configured, high-speed digitally-controlled feedback systemdescribed in Sec. 5.1.

2.3. Rotation Damping and RWM Stabilization StudiesSince the groundbreaking work of Bondeson and Ward [Bondeson and Ward, 1994]

which provided an explanation of the observation in DIII-D that plasma stability againstthe RWM could be maintained above the no-wall limit if the plasma rotation wassufficiently fast, a critical open question is clear experimental identification of thedissipation mechanism in the rotating plasma/mode/wall system that is required forstability. In the 1994 Bondeson and Ward paper, a collisionless “sound wave damping”model was invoked which in numerical simulations with the MARS code indicated thetoroidal plasma rotation rates needed to stabilize the RWM were in the range of 2% to3% of the toroidal Alfvén velocity. Subsequent experiments on DIII-D were consistentwith this rotation level [Garofalo, 1999]. However, we have yet to determine the criticalrotation threshold scaling, the effect of rotation profile and q-profile on the criticalrotation threshold, and to measure in detail the coupling between the RWM mode and therotating plasma, in order to account for the observed slowing down of the plasma rotationwhenever the pressure exceeds the no-wall stability limit. We must solve these problemsin order to confidently scale these rotation effects in next generation experiments. Wepropose to carry out a detailed study of the effect of rotation stabilization in HBT-EP toanswer these open questions.

In the past year a crucial clue was discovered which has led to both a clearer insightinto the rotation stabilization mechanism as well as providing a tool for bettermeasurement of these stabilizing effects on the RWM. This discovery is based on the

7

q* = 2.9 q* = 2.7

Shot # 34054

Shot # 34038

b q (m

=3) (

G)

I coil (

m=3

) (A)

time (msec)1.5 2.0 2.5 3.0 3.5

m=3 plasma response

m=3 applied amplitude

Fig. 2-3. Resonantly amplified RWM response toan applied static external magnetic field observedon HBT-EP.

Fig. 2-4. Full wall and no wall stability limits forthe proposed FIRE experiment.

proposal by Boozer [Boozer, 2001] that theobserved rotation slowdown observed inDIII-D was due to the plasma amplifyingthe resonant ambient error fields in the DIII-D device. Boozer noted that any linearmode near marginal stability (as would bethe case for the rotationally stabilizedRWM) will amplify an applied magneticfield that is resonant with the mode. Sincethe RWM is unique in having very lowfrequency, this could include resonantinteraction with static error fields.

Experiments in HBT-EP were carriedout to measure the effect of an appliedstatic, predominantly m/n=3/1, externalresonant magnetic perturbation on a rotatingsaturated RWM. The results are shown in Fig. 2-3. The observed plasma response has aphase locked growing m=3 poloidal mode structure. This response is observed to beparamagnetic, that is, amplifying relative to the magnitude of the applied vacuum field.The plasma response depends on the stability limit of the resistive wall mode as indicatedby a slower decay of the plasma response to the external resonant magnetic perturbationwhen q* is reduced further below the rational value of 3 where the mode is more weaklydamped. Similar results were obtained in DIII-D [Garofalo, 2002]. Prior to thesemeasurements, it was widely assumed that the RWM stabilization in a rotating plasmawas due to the plasma exerting a torque on the mode and dragging the RWM modestructure through the resistive wall with induced eddy-current decay damping the mode.In fact, in both HBT-EP and DIII-D, the paramagnetic plasma response is observed to belocked in phase to the applied resonant field for many wall decay times, and therefore theRWM damping is not due to the resistive wall effects as assumed, but to dissipationinside the plasma.

Observations of the decay of theparamagnetic response of the plasmawhen the static resonant applied field isremoved provides a very powerful tool todirectly measure the global effect ofparametric changes in the plasma on theRWM damping rate and to understandthe basic physics of RWM stabilization.In HBT-EP we have the capability tovary the q-profile and pressure profilethrough discharge programming, and therotation profile through local probe biasapplied voltage (see Secs. 2.6 and 3.1).We propose to use this new technique ofresonant field response together withobservation of instability threshold and

8

growth rates to complete a detailed study of these profile changes on RWM stability andcompare with candidate models for dissipation in a rotating plasma/RWM system.

2.4. Stability of n ≥ 2 modes combined with n=1 ControlFor most toroidal systems with plasma near the ideal wall stability limits,

destabilization of higher toroidal mode numbers becomes more likely. Shown in Fig. 2-4is the stability for an Advanced Tokamak (AT) plasma in the proposed FIRE burningplasma experiment for n=1, 2, and 3 kink modes with and without an ideal conductingwall. In Fig. 2-4 we see the typical behavior in AT plasmas of a substantial increase inthe stable beta limit for the n=1 mode due to wall stabilization, but a somewhat lowerstable beta limit for the wall stabilized n=2 mode. All our previous experimentalexperience with the RWM in HBT-EP and DIII-D has focused on the n=1 mode. Wepropose to use the wide helicity range for applied static and rotating fields in HBT-EP tocarry out a detailed study of the plasma response to the n=2 RWM when near the idealwall limit for the n=1 mode during active stabilization. As described in Section 2.3, thenew technique of resonant field response of the plasma will also be used with an appliedn=2 field to carry out a detailed study of rotational stabilization effects on the n=2 RWM.In addition, we will create plasmas in HBT-EP projected to be unstable to both the n=1and n=2 RWM, followed by the first experiments on multi-mode active feedbackexperiment of the RWM. To support both the design of the multi-mode feedbackalgorithm as well as for analysis of the observations, the VALEN code will be extendedto multi-mode capability (see also Sec. 4).

2.5. Extension of VALEN analysis to include a several plasma modesA general circuit formulation of RWM feedback stabilization has been developed

by Boozer [Boozer, 1998] and implemented as the basis for the VALEN code using afinite element representation of thin shells to model arbitrary 3D conducting walls. Thismodel of the conducting structure is combined with a circuit representation of stable andunstable plasma modes represented as 2D surface current distributions derived from theDCON MHD stability code. VALEN also models arbitrary sensor and control coilsincluding the feedback logic to provide a complete simulation capability for feedbackcontrol of plasma instabilities. In this way, the mode-wall-feedback coil inductivecouplings are accurately determined.

While all of the 3D modeling of HBT-EP and DIII-D of active mode control byVALEN has used a single unstable plasma mode in the analysis, the circuit formulationof active stabilization of the RWM described by Boozer is general and can be applied toany set of orthogonal plasma modes. We propose to extend the capability of VALEN toinclude in the analysis a set of the spectrum of unstable and stable n=1 and n=2 (andabove if needed) modes as determined by DCON. The first step toward this capability hasalready been achieved with a direct interface between the DCON stability analysis outputfiles and the plasma mode input to the VALEN code.

9

Fig. 3-1. Illustration from [Waelbroeack, 2000]indicating the effect of ion polarization current onthe tearing mode stability parameter.

3. Tearing Mode Dynamics and Plasma Rotation

Understanding the magnetic island dynamics and stability including the effects ofplasma rotation, plasma inertia, and two-fluid diamagnetic drifts remains an outstandingresearch question in toroidal confinement physics. We share the opinions stated byFitzpatrick and Waelbroeck [Fitzpatrick and Waelbroeck, 2001], “active magneticfeedback represents our most direct way of probing the physics of tearing modes.” Theygo on to explain “that a reliable method for limiting tearing mode amplitudes is onlylikely to become a reality once the physics of such modes in toroidal magneticconfinement devices is fully understood. Such an understanding is most likely to emergefrom the interpretation of magnetic feedback data.” To date, HBT-EP experiments haveprobed tearing mode physics by measuring island response to strong magnetic torques, byapplying active feedback, and by direct measurement of the perturbed density and massflow within and around magnetic islands. Additionally, as discussed in Sec. 2, internalmode dynamics and the physics of plasma flow and induced flow shear shouldsignificantly affect RWM control and,as described later, may lead tooperations with enhanced confinement.Consequently, our research plan for theHBT-EP device continues to combinestudies of tearing mode dynamics andplasma rotation as an overall physics-based approach to mode-control ofadvanced tokamak and related toroidalapproaches to high-beta fusionconfinement.

We propose to continue and toexpand our study of tearing modedynamics and driven rotation on HBT-EP magnetic islands. This rotation canbe probed and effected by two distinctexperimental techniques: (1) externalresonant magnetic perturbations, and (2) biased probe driven E¥B edge flow changes.Both are proven techniques that have been previously demonstrated to significantlychange the background natural flow of pre-existing magnetic islands on HBT-EP. Byincorporating both approaches, we bring a unique experimental “knob” with which tostudy island physics on the HBT-EP device. We intend to concentrate our efforts on threespecific topics of the effects of rotation on tearing modes:

1. Continue our study of rotation and ion polarization stability effects.2. Investigate the possibility of driving sheared plasma rotation using islands at two

distinct rational surfaces in the plasma interior.3. Investigate tearing mode suppression using advanced feedback techniques, such

as using “designer error fields” [Fitzpatrick and Rossi, 2001]

10

Fig. 3-2. Example of high-resolution measurements of probe ion-saturation and Mach measurementsmade with synchronous detection. Right: figure reproduced from [Waelbroeck, 2001].

3.1 Island Rotation and Ion Polarization Physics StudiesThe role of ion inertia (i.e. ion polarization current) in tearing mode island

evolution is a very active area of interest in fusion research in relation to neoclassicaltearing mode (NTM) threshold physics [Wilson, 1996] and the so-called long pulsetokamak b limit [Wilson, 1996]. Recent theoretical studies as to the stabilizing ordestabilizing role of the ion polarization term in the Rutherford evolution equation as itdescribes both classical tearing and neoclassical bootstrap driven islands have concludedthat in single fluid MHD the polarization term is in fact destabilizing,

†

¢ D pol > 0[Waelbroeck, 1997]. Recent sheared-slab, drift-MHD theoretical calculations[Waelbroeck, 2000] indicate a complex frequency and profile dependence of thepolarization term,

†

¢ D pol and predict essentially four different rotation regimes, as seen inFig. 3.1, depending upon the island rotation frequency:

1. When

†

w ≥ w*e , the polarization term is destabilizing,

†

¢ D pol > 0,2. When

†

0 £ w £ w*e , the magnetic island emits drift waves and

†

¢ D pol can bepositive or negative depending on the exact value of w,

3. When

†

w*i £ w £ 0 , the polarization term is stabilizing,

†

¢ D pol < 0,and4. When

†

w £ w*i, the polarization term is again destabilizing,

†

¢ D pol > 0.Accurate predictions of ion polarization physics in current and future toroidal devicesrequire knowledge of (1) self-consistent temperature, density, and electrostatic potentialprofiles in the vicinity of the island, (2) the island natural rotation frequency, and (3) theneoclassical enhancement of the effective perpendicular inertia of the plasma due to ionviscosity [Hegna, 2001]. In order to study these critical island physics issues withmaximal impact and connection to other devices a specific set of island profilemeasurements and external rotation perturbations will be used to quantify the dependence

11

Fig. 3-3. Measured change of island rotation upon applicationof bias to the edge probe.

of

†

¢ D pol on island frequency w and local plasma profiles on HBT-EP. We propose thefollowing three-part plan to experimentally address these important questions:

3.2.1 High Spatial Resolution Rotating Probe Island Profile MeasurementsThe rotating probe diagnostic will initially be equipped with Hall sensors to

measure the local magnetic field profiles and Langmuir probe tips for local electrontemperature and density measurements using a harmonic technique developed by ourUCSD collaborators [Boedo, 2000]. This diagnostic, in addition to making equilibriummeasurements, can and will be used to measure local fluctuations of the magnetic field,electron temperature and density induced by propagating magnetic islands in HBT-EP.The spatial resolution of these diagnostics is a function of the probe trajectory andvelocity, magnetic island location and rotation frequency, and the data digitization rate. Asimple estimate of spatial resolution neglecting geometric effects can be made using atypical probe tip velocity, vprobe = 200m/s, and sampling at a rate of 100kHz (readilyachievable) would yield aspatial sampling interval of Dx~ 2mm. For typical HBT-EPm /n = 2/1 magnetic islandswith full widths of W ~ 2 to5cm this translates into 10 to25 spatial points across theisland o-point width. Fasterdigitization rates will yield mmor even sub-mm spatialsampling of the island profiles.These fine spatial and temporalfluctuation measurements willallow us to accurately map 2Dprofiles in the vicinity of HBT-EP islands with unprecedentedresolution. This in turn willallow us to quantify theseimportant self-consistent profile effects as they govern ion polarization phenomena andmagnetic island stability in general for the first time.

The initial rotating probe installed on HBT-EP will include only magnetic andelectron temperature and density diagnostics, and was designed as mainly an equilibriumdiagnostic. After successful installation and operation of this first model rotating probe,an island-specific probe head will be designed and built with our UCSD collaborators toalso measure other important perturbed island profiles including ion flow velocity withMach probe-like Langmuir tips as well as probe measurements of the plasma potential inand around the island structure. These plans will necessarily build on experience andknowledge gained in operation of the first rotating probe on HBT-EP.

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3.2.2. Island Rotation Perturbations to Experimentally Scan Dpol(w)As previously demonstrated on HBT-EP [Navratil, 1998; Maurer, 2000],

magnetic island rotation perturbations are an effective experimental method for observingchanges in island size induced by frequency dependence of

†

¢ D (W ,w) terms that effectisland width. We plan on continuing to use rotating resonant magnetic perturbations tostir HBT-EP islands to study island dynamics in conjunction with our new high-resolution profile diagnostics. In addition, we have recently developed a simple biasedprobe technique as another experimental tool to induce large frequency shifts in edge m/n= 2/1 magnetic islands by driving E¥B rotation. These techniques offer the possibility ofexperimentally determining island amplitude changes in the various frequency bandsindicated by drift-MHD theory.

3.2.3 Comparison to Analytic and Computational Models of Island DynamicsUsing the island profile measurements described above will allow us to make

careful, accurate comparisons to both analytic theory and computational models of islanddynamics in tokamak plasma. We expect to pursue three complementary modeling pathsin order to fully benchmark ion polarization physics and island dynamics on HBT-EP.

1. Comparison of island amplitude and frequency observations with predictions ofthe coupled nonlinear Rutherford differential equations that describe islandamplitude or width and island frequency evolution incorporating the latestpolarization models and interactions with external structures, such as walls andresonant magnetic perturbations [Fitzpatrick and Waelbroeck, 2000].

2. Given the island profile measurements outlined above, we will be able to makedetailed 2D drift-MHD equilibrium reconstructions of rotating magnetic islandson HBT-EP [Connor et al, 2001]. Our measurements of the local magnetic field,density, and temperature profiles (and later, potential and ion flow profiles) willallow us to serve as a useful test-bed for validating these analytic models of islandbehavior for the first time.

3. Finally, we propose to extend our interaction with Dr. Alan Glasser to include thepreparation of well-diagnosed dynamical examples of tearing mode physics thatcan serve as the basis for validation of the developing SEL plasma simulationcode.. The wealth of profile information that will be measured in and aroundHBT-EP magnetic islands will allow detailed comparison to code predictions ofion polarization physics in a relatively modest Lundquist number regime. Thiswill serve as an important benchmark for the simulation code and an exciting toolfor testing two-fluid models of tearing mode dynamics with strong plasma flow.

3.2 Differential Rotation of Multiple Rational SurfacesUsing our high-power saddle coil sets, we have applied local electromagnetic

torques to rational surfaces with pre-existing island chains, and we have inducedsignificant ion fluid rotation on HBT-EP [Navratil, 1998; Taylor, 2000]. We propose toextend our investigations into the effects of driving rotation and rotational shear by (1)driving two distinct rational surfaces in the plasma at different frequencies usingmagnetic perturbations, and (2) utilize the bias probe in combination with single ormultiple helicities of applied control fields to explore sheared plasma flow effects

13

induced by a combination of E¥B and electromagnetic torque. Using these techniques,we intend to study the effects of differential rotation on island stability. As the islanddifferential rotation frequency is varied from positive to negative values the islandsshould begin to strongly interact when they are near co-rotation. Measurements of modeamplitude and phase, as well as rotation profile measurements will aid in quantifyingthese important mode-mode interactions in the presence of sheared plasma rotation.

3.3 Island Suppression with Advanced Control MethodsHBT-EP has successfully implemented and tested a fully digital, high-speed

active feedback system for single-helicity (m/n = 2/1) tearing mode suppression [Nadle2001]. We propose to re-visit the possibility of magnetic suppression of tearing modesbecause of three recent developments. First, Fitzpatrick and Rossi [Fitzpatrick and Rossi,2001] have shown that “designer error fields” containing harmonics of the tearing modemay stabilize or reduce the growth of the phase instability. Second, there has beensignificant advancements in the state-of-the-art of digital signal processing. As explainedin Sec. 5.1, we will build a very high-speed and high-throughput digital feedback systemconstructed from commercial, off-the-shelf components that will have performance morethan an order-of-magnitude higher than our present system. Finally, our magneticcontrol-coils are now installed inside the vacuum vessel at the plasma edge, and they canbe independently powered providing unparalleled flexibility in the application of externalmagnetic perturbations. Our research plan to develop advanced control methods forsynchronous feedback suppression of magnetic islands builds upon the development ofisland physics described in the previous sections. These studies will develop experimentalconfidence of our understanding of the generalized Rutherford equations including ionpolarization effects [Fitzpatrick and Waelbroeck, 2000]. These equations serve as themodel for temporal dynamics of the amplitude and rotation of islands during magneticfeedback. As this work proceeds, we will extend our previous investigations of the gain-dependence of the phase-instability using our new reduced-latency digital feedbacksystem. Secondly, we will experiment with the application of synchronous harmonichelicities. Although it will be difficult to apply more than two harmonics (in addition tothe primary resonant field), the amplitudes of both the fundamental and harmonic fieldscan be large and comparable. Based on the examples computed by Fitzpatrick and Rossi,we expect to be able to observe very significant changes to the dynamical response of theislands during feedback.

4. Combined Internal and External Mode Control

An important long-term objective of the HBT-EP program is to demonstrate thefeasibility of a high-beta tokamak stabilized by a combination of a close-fittingconducting wall, plasma rotation, and active feedback. Realization of this goal requiresthe stabilization of both internal (resistive tearing) modes and external kink and RWMmodes. In our previous work, we have made significant progress on stabilizing bothclasses of performance limiting MHD instabilities, but with separate feedback systemsapplied typically to differently-prepared plasma discharges. We propose here to carry out

14

the first investigations of combined and simultaneous control of external and internalmodes. This will be possible because of the improvements to our control system that willbe made during the next two year and which include the 40-channel internal control coilarray, increased 2.5 kW/channel driving power, and the high-speed digital controlsystem. While the basic control techniques for tearing and kink mode control are similar,there are some important differences that will need to be explored in a combined controlsystem. Chief among these are: (i) The helicities of the dominant internal mode is 2/1,while of the RWM is 4/1 or 3/1. Combined control is inherently multiple-mode, and weneed minimize any adverse effects from helicty sidebands. (ii) The frequencies of the 2/1internal mode is typically higher (7 to 10 kHz) than the RWM (a few kHz). We need abroad-band detection and control system that properly distinguishes between modes. And(iii) the 2/1 tearing mode freely rotates in response to applied fields and exhibits a phaseinstability, while the RWM cannot increase it’s rotation frequency without beingstabilized by wall eddy current effects. We believe the achievement of combinedstabilization of both internal and external modes at the ideal wall stability limit in HBT-EP will be a challenging task. It will likely require both mode structure and frequencydiscrimination of the input mode detection signals and intelligent combination ofdifferent stabilization algorithms creating a combined response signal that is appliedthrough a common array of control coils. These planned investigations of advancedfeedback system will also likely uncover new phenomena and techniques with bothpractically and scientifically valuable.

5. Research Tool Development

The following sections describe several new research tools that are in the processof being developed to enable the HBT-EP program to continue as an effective test-bedfacility for mode control physics issues. A new state of the art high speed digital controlsystem using parallel data pathways containing field programmable gate arrays (FPGA)is being designed to enable experimentation with a variety of mode control algorithms forour current and future control coil sets. The VALEN feedback code is being enhanced byinclusion of important new multi-mode and rotation physics effects. In collaboration withUCSD, we will be installing a rotating magnetic-Langmuir probe apparatus to allowmeasurement of internal profiles on HBT-EP during mode control experiments. We arecurrently implementing a radial position control system to enhance our ability to positionHBT-EP discharges for feedback and magnetic island studies and to help develop andcontrol ICRH target plasmas. We are in the process of planning an upgrade to our currentedge biased probe circuitry to enable the systematic variation of edge plasma flow forRWM and magnetic island rotation studies. These developments are described in moredetail in the following sections.

5.1 High Speed Digital MHD Control SystemPreviously, two advanced methods to control MHD modes with active magnetic

feedback have been demonstrated successfully on HBT-EP. Nadle and co-authors [Nadle,2000] described an optically-isolated, dual-processor digital-signal-processor (DSP) was

15

Fig. 5-1. Schematic of proposed digital active controlsystem.

used for high-power, activefeedback of the m/n = 2/1 tearingmode. Cates and co-authors[Cates , 2000] demonstratedresistive wall mode (RWM)control using a distributednetwork of 30 specially-designedanalog feedback processorsoperating in parallel andindependently. Both systemsachieved their objectives andallowed development and testingof several control algorithms.However, both systems also hadlimitations that can now beovercome because of recentadvancements in the state-of-the-art of digital signal processing technology.

We propose to purchase a new high-speed digital control system built fromadvanced, off-the-shelf DSP components with fully-integrated multi-channel dataacquisition. This system will allow high-speed digital processing of large arrays ofmagnetic and other data, and it will generate up to two-dozen output control signals withlow overall latency. The new system will be based on up to four parallel field-programmable gate arrays (FPGA) fully integrated with dedicated high-speed digital I/O(ADCs and DACs). FPGAs have revolutionized high-speed digital signal processing, andthey have are being used in a variety of commercial markets and especially digital video,coded telemetry, and gigabit-speed frequency modulators/demodulators. As far as weknow, our proposal will implement the first high-speed, high-throughput digital controlsystem incorporating the latest high-density FPGAs. This brings an entirely newtechnology to advanced plasma digital control systems, and we believe our experiencewill benefit future efforts to implement mode control systems on other confinementexperiments, such as DIII-D, NSTX, and burning plasma experiments exploringadvanced tokamak modes.

The new digital mode control system will be capable of both active tearing modecontrol and resistive wall mode control. The system combines the convenience of thedigital programming (used in our present tearing mode feedback system) with the high-data throughput of a distributed analog feedback loops (used in our present RWMfeedback system). Using technology not available a few years ago, the new system willbe deliver nearly an order-of-magnitude improvement over HBT-EP’s present digitalfeedback control system (which uses two ADSP-21062 DSPs each operating at 40 MIPSand capable of peak performance of 120 MFLOPS.) Presently, the DSPs are programmedin assembly language allowing overall latency to be approximately 12 msec.Nevertheless, for a 10 kHz rotating tearing mode, inherent phase accuracy is only slightlybetter than 45 deg. Although the system offers flexibility and relatively ease of digitalprogramming, the limitations of the processor and data acquisition components createproblems at high gain. As explained in Nadle [Nadle, 2000], tearing mode feedback islimited by the phase-instability. At high gain, phase-inaccuracy causes torques to be

16

applied to the island that accelerate rotation and create increasing phase-errors. Webelieve this effect can be overcome by combining novel control logical (such as applying“designer” control fields, see [Fitzpatrick and Rossi, 2001]. and by reducing latency.

Fig. 5-1 illustrates the conceptual design of the new digital control system forMHD mode control. The system consists of four signal pathways each capable of 8-channels of 12-bit ADC and 14-bit DAC at 4 Msps/channel. Extremely fast (pre-programmed) control processing is contained in commercial field-programmable gatearrays (FPGA) from Xilinx clocked at 365 MHz. Working with engineers from Traquair(the U.S. partner with Hunt Engineering), we estimate nearly an order-of-magnitudereduction is I/O latency can be achieved—even when increasing the number of I/Ochannels from I/O = 4/2 to I/O = 20+/20+. We will specify control algorithms using theXilinx development system (essentially a “silicone compiler”) combined withMatLab/Simulink software. Graduate students and research staff will attend tutorialsoffered by Xilinx and by the component distributor.

5.2 Achieving Enhanced Beta in Stabilized DischargesHBT-EP achieves moderately high normalized-beta with ohmic heating by

operating at relatively low toroidal field, high plasma density, high plasma current, andlow electron temperature. This maximizes toroidal beta, energy confinement time, andohmic heating power. In order to obtain repeatable RWMs, plasma discharges with bN ~1.4 are combined with a positive plasma current ramps which steepens the edge currentgradient, broadens the pressure profile, and increases the no-wall growth rate of externalkinks. Although HBT-EP’s ohmic discharges offer a good platform with which toinvestigate instability control in tokamaks, we plan to use research tools already installedto enable study of instability control in discharges with enhanced beta. In addition toincreasing plasma beta in stabilized discharges, these techniques should also prolong thetime-period during which the plasma is above the no-wall stability limit while allowingthe edge current gradients to relax.

We have installed three systems to explore wall stabilization in dischargessignificantly above the no-wall stability limits and to provide greater versatility forchanging discharge parameters. These three systems are: (1) an ICRF auxiliary heatingsystem, (2) a differentially rotating system of resonant magnetic perturbations, and (3) aninternal bias-probe capable of driving strong E ¥ B flows at the plasma edge.

The ICRF heating system was designed and installed in collaboration with PPPLand LANL, and it launches RF waves from the inside, high-field side of a deuteriumplasma containing a large, 10-20%, hydrogen minority. This corresponds to the heatingregime with strong mode-conversion, and it has the desirable feature of significantelectron heating. As described in the progress report, the ICRF antenna and RF oscillatorhas been operated successfully into plasma at full voltage, and we seen evidence ofsignificant plasma loading when the plasma’s edge is positioned immediately in front ofthe RF limiter. The coupling appears to be a strong and sensitive function of the plasma-antenna separation. Our effort to enhance beta with ICRF remains an active workingcollaboration between PPPL and the HBT-EP Team. This includes using the integratedSPRUCE/TRANSP code to calculate the plasma/antenna parameters (such as plasma-antenna separation, k|| spectrum, H/D minority ratio, and edge density) that lead tosignificant beta enhancement, installing and operating addition ICRF diagnostics (such as

17

Fig. 5-2. Drawing of rotating probe diagnostic.

new, optically-isolated data acquisition rack containing a dedicated CAMAC system,complete RF antenna measurements of antenna parameters, a charge-exchange energyanalyzer, a fast neutral particle flux detector, a newly-installed edge triple-probe tomeasure the plasma density near the antenna, and RF pick-up probes to measure coupledRF wave fields), and the operation of our new equilibrium radial position control systemand the investigation of synergistic enhancement of RF coupling when the bias-probe isenergized. We will investigate the use of these two tools to control (and to increase) theplasma density at the antenna

The goal of the differential rotation effort is to apply rotating, resonant magneticperturbations in order to generate large toroidal shear flow at multiple nearby helicitiesand to produce an internal transport barrier. For example, if a resonant (m,n) = (3,2)perturbation is applied while simultaneously rotating a (m,n) = (2,1) magnetic island,large differential rotation may appearbetween the internal 3/2 and 2/1surface. We plan to investigate thispossibility by applying differentially-rotating external fields of multiplehelicities using our active modecontrol system.

Finally, we have recentlydemonstrated an ability to verysignificantly change island rotation byinserting a biased probe just beyondthe plasma’s last closed flux surface.These experiments are modeled afterthe pioneering work described by R.Taylor and co-authors [Taylor, 1989].The bias probe may generate enhancedbeta (or, equivalently, a confinementimprovement) alone or in combinationwith the other beta enhancement techniques. For example, the bias probe may increaseplasma density at the edge and, as a consequence, improve ICRF coupling. Also, we willinvestigate the possibility that internal transport barriers may be more easily obtained bycombining edge probe bias with resonant rotating fields. All three techniques for betaenhancement are interesting and likely to produce noteworthy results and will continue tobe an active part of our research program.

5.3 Rotating Magnetic and Langmuir Probe SystemIn our joint collaboration with Dr. Jose Bodeo of UCSD the final engineering

design of the rotating probe diagnostic has been completed during this past year andUCSD has begun construction and fabrication of the probe shaft and housing structure.This novel probe will provide 2D measurements of the internal magnetic fields andelectron temperature and density profiles of a poloidal cross-section of HBT-EP plasmasenabling us to further characterize the equilibrium and stability of our discharges duringactive control experiments (see Fig. 5-2.). This diagnostic will incorporate several newnovel technologies [Chousal, 2001] including: (1) high magnetic field tolerant Ferro-

18

fluidic rotary motion feedthroughs capable of 2000-3000rpm high vacuum operation, (2)low noise (<1mV/sqrtHz), high rpm rotating contact feedthroughs for signal output, (3)vacuum compatible PCB boards for efficient multi-signal path coupling of diagnostics tosignal outputs, (4) compact, high frequency, solid-state magnetic sensors, and (5) a highfrequency Te measurement using Langmuir probes and a harmonics technique developedat UCSD [Bodeo, 1998]. The initial probe shaft has been designed as mainly anequilibrium diagnostic, but will also be able to measure fluctuating plasma temperatureand density effects and magnetic fields down to the ~1G level. There are six magneticand six Langmuir probe tips along the probe shaft that will enable profiles of B(r,q),ne(r,q), and Te(r,q) to be measured, The typical plasma edge to center residence time is~1.5 to 2.5msec. A typical probe tip velocity is vprobe=157m/s at 2092rpm operation. Thevacuum housing structure, probe shaft, motor drive train, and electronics will tested atUCSD before shipment to Columbia during the summer and fall of 2002.

In preparation for the arrival of the rotating probe diagnostic at Columbia theHBT-EP group has designed a new spool-vacuum chamber segment for the HBT-EPvacuum chamber to accommodate the probe sweep through the plasma. A new couplingchamber piece to mate to the probe housing supplied by UCSD has also been designed.These chamber pieces are currently on bid. Construction is planned during the summer of2001. Installation of these pieces will occur during a winter up-to-air in late 2002.

5.4 Radial Position Control Feedback SystemRadial equilibrium of HBT-EP plasma discharges are maintain by pre-

programmed EF coils and equilibrium eddy currents in the close-fitting conducting shells.To provide additional radial position control, a new radial position feedback system hasbeen designed, and construction is underway. The system consists of six coils, in an up-down symmetric configuration, connected to an existing 5 MW feedback power supplywith 50 kHz response time. This coil system can produce a vertical magnetic fieldsufficient to increase or decrease the total vertical magnetic field at the plasma by 25% inless than 0.5 msec. The coils have been designed to minimize the mutual inductance withthe existing vertical field system and the ohmic transformer. Time resolved electriccircuit modeling using the SPICE software package and realistic models of the threesystems has confirmed that the magnetic coupling between the three systems isnegligible. The mutual inductances and self-inductances were calculated using amagnetostatic code with each coil modeled realistically as a set of circular conductors.

In addition to better control of existing discharge types, the radial feedbackcontrol system will allow us to perform new physics experiments with new dischargescenarios. For example, by carefully changing the major radius during a current rampdischarge, we will be able to keep the edge safety factor constant for an entire discharge,and hence we can study feedback stabilization of a current driven external kink that isunstable during the entire discharge.

The radial feedback control system is also an important complement to our betaenhancement program. During beta enhancement, fast radial position control prevents theplasma from radial expansion. Additionally, the ability to control the radial position willallow optimization of the antenna-plasma coupling by maintaining the plasma edge veryclose to the antenna. During dynamic radial scans of plasma flow (using the fixed Machprobe), edge plasma current and magnetic field (using the fixed magnetic probe), and

19

edge plasma density and temperature, using the newly installed edge triple probe, theradial feedback system will allow us to dynamically change the effective insertion depthof the bias probe. Finally, we believe the radial feedback system will increase ourproductivity by making for more reproducible discharges with a prescribed major radialtime evolution.

5.5 Edge Bias Probe UpgradeThe simple bias probe technique developed to charge the edge plasma and thereby

induce significant mode and plasma rotation is currently configured for positive bias onlyusing a simple SCR switched capacitor bank. We have been able to run the system up to400VDC bias and have drawn currents up ~250A without deleterious plasma dischargeeffects being observed, while generating large mode frequency excursions. To further theprobes effectiveness and utility we are planning on upgrading the bias supply system toallow both positive and negative bias voltages to be applied to HBT-EP plasmas. Inaddition we are contemplating short pulse or full AC capability to modulate the edgerotation as an additional tool in mode and plasma rotation studies.

6. Research Schedule

FY03: RWM Studies at the Ideal Wall Stability Limit

+ Install 2.5 kW/channel upgrade to advanced control coil system+ Install Rotating Probe System for internal profile measurements+ Design and order initial DSP system with 10 input channels+ Carry out a quantitative study of rotation stabilization and rotation

damping effects of the wall stabilized external kink mode (RWM).+ Extend the capabilities of the three-dimensional active mode control

model, VALEN, to include multi-mode and rotation effects.+ Carry out the first tests of active mode control at the ideal wall MHD

stability limit and compare with predicted stability properties as functionsof gain, control coil and passive stabilizer coverage, and feedback controlalgorithm.

+ Investigate rotation control of magnetic islands having different helicities(2/1, 3/2, 5/2) and using our new closefitting control coils.

+ Complete design and evaluation tests for new digital control system.

FY04: Extend System Capability With Digital Control andBroaden Research Focus to Tearing Mode Dynamics

+ Install and operate initial digital control system with 10 input channels+ Install rotating probe upgrade for detailed island flow field studies.+ Extend Doppler rotation system to 10 toroidal chords.+ Upgrade DSP system to 20 input channels+ Study rotation and active stabilization of n=2 RWM.

20

+ Study rotation dynamics of tearing modes compare with generalizedRutherford evolution equations.

+ Perform initial experiments using “designer error fields” to control phase-instability.

+ Benchmark multi-mode analysis in VALEN against performance ofadvanced control configurations on HBT-EP.

FY05: Complete Detailed Physics Study of Tearing Mode Dynamicsand Combine Optimal Control for Maximum b

+ Complete detailed studies of tearing mode dynamics and advancedstabilization techniques, including multiple helicities.

+ Integrate active control of both internal and external modes using a digitalcontrol system and optimized feedback control configuration to investigatethe “ultimate” MHD beta limit in wall stabilized tokamak plasma.

1

High-Beta Tokamak ResearchDOE Grant No. DE-FG02-86ER53222

Research Progress Report 2000–2002May, 2002

1. Introduction

Control of long-wavelength MHD instabilities using conducting walls andexternal magnetic perturbations is one of the most important routes to improvedreliability and improved performance of magnetic fusion confinement devices.Conducting walls stabilize long-wavelength modes because wall eddy currents opposethe helical perturbations created by these instabilities. However, for slowly growinginstabilities, passive wall stabilization can fail when the eddy currents decay due to finitewall resistivity, leading to the growth of resistive wall modes and resistive tearing modes.Because these modes grow on a reduced timescale they are amenable to active control.The HBT-EP research program investigates active control techniques to suppress oreliminate these remaining slowly growing modes. This includes both synchronousfeedback and asynchronous control methods applied using external magneticperturbations that alter and control plasma and mode rotation.

2. Summary and Highlights

During the past grant period, we have executed new studies and analyses of thecontrol of the resistive wall mode (RWM) and the tearing-mode, and we have installedand operated several new research tools at the HBT-EP facility. A summary of progressachieved include the following highlights:

Resistive Wall Mode Control

• Made the first observations of resistive wall mode (RWM) control with usinga distributed array of 30 flux sensors and 30 feedback coils.

• Investigated the role of gain, bandwidth, and control coil coverage on the“smart-shell” method of RWM active control.

• Demonstrated disruption avoidance by suppressing RWM growth for m = 4and m = 3 kink modes.

2

• Observed resonant-field amplification and investigated the response ofexternal kink modes to applied rotating and static resonant magneticperturbations.

• Benchmarked the VALEN active mode control modeling code againstexperimental measurements using unstable mode structure computed by theDCON code.

• Developed and installed a new in-vessel 20 sensor-20 control coil modecontrol feedback system predicted by VALEN to stabilize the RWM up to theideal wall limit in HBT-EP.

Tearing Mode Physics

• Demonstrated tearing mode rotation using our distributed array ofcontrol coils.

• Completed new analysis of tearing-mode suppression and growth induced byrotating external magnetic perturbation torque.

• Completed new analysis of two-dimensional measurements of plasma flowaround and within magnetic islands using a movable Mach probe.

• Demonstrated our ability to significantly modify tearing-mode (and plasma)rotation using a biased edge probe.

New Research Tools

• Optimized “smart shell” feedback loop circuitry using measured resistivewall, sensor, and control coil and amplifier properties.

• Developed a high-speed programmable 32-channel digital waveformgenerator capable of applying external magnetic perturbations using ourfeedback coil sets to study “external kink-mode spectroscopy.”

• In collaboration with PPPL and LANL, installed high-power ICRF oscillatorand antenna system, applied 5 MW of circulating RF power, coupled 50 kWof RF power to the plasma transiently, and initiated studies to optimize plasmaloading and heating.

• In collaboration with Dr. Steven Paul (PPPL), installed and made operationala new impurity-line Doppler monitor using high throughput interferencefilters a the dispersive device.

• Completed our interface design work in collaboration Dr. Jose Boedo for theUCSD rotating magnetic and Langmuir probe system collaboration.

• Constructed a Molybdenum edge bias probe and associated circuitry forplasma and mode rotation studies and H-mode generation.

3

• Made operational our new single point Thomson scattering and charge-exchange diagnostics.

• Built and installed a new 8–channel insertable magnetic probe for equilibriumand kink mode fluctuation analysis.

• Developed and installed a high field side triple probe and magneticdiagnostics to aid in quantifying and optimizing ICRH coupling.

• Completed full data-acquisition system transition from MDS to newMDS-Plus “fusion science standard” software.

In addition to our experimental accomplishments, we have continued to advancethe understanding and application of active mode control by our leadership ininternational workshops and collaborations with other experiments including DIII-D,NSTX, and FIRE. We have presented several invited and contributed presentationsdescribing active mode control, resistive-wall-mode control, and the evaluation of theadvanced tokamak including invited review presentations. (See Publications andPresentations.)

In the following sections, we briefly describe in more detail research progress inthree areas: (1) resistive wall control, (2) tearing mode and rotation control, and (3)installation of new research tools for the HBT-EP facility.

3. Resistive Wall Mode Control

The first observation in a tokamak of the use of active feedback control tosuppress the onset of the n=1 resistive wall mode (RWM) was made in HBT-EP. Theinitial observations appeared in [Cates, 2000]. This work included analysis of the currentprofile evolution that enabled detailed comparisons to be made between observations andthe VALEN electromagnetic feedback code.

The 3D finite element electromagnetic code, VALEN [Bialek, 2001], is a criticalanalysis and design tool for the study, design, and optimization of active feedback controlsystems for the RWM. The use of VALEN for the RWM is based on the theoreticalmodels developed by Boozer [Boozer, 1998]. The code has been carefully benchmarkedagainst analytic cylindrical model calculations and is in good agreement with theexperimental results seen in HBT-EP and DIII-D. Recently, we have used the code tooptimize the feedback coil geometry in HBT-EP and install a second-generation activefeedback coil and sensor system. VALEN calculations predict optimized feedbackgeometries minimize the inductive coupling between the control coils, sensors, andpassive stabilizer. By installing the control coils in the gaps between HBT-EP’s stainless-steel and Aluminum shells, improved feedback performance is predicted to allow HBT-EP to reach ideal wall limit stabilization of current and b driven RWMs for the first timein a tokamak.

During the past year, newly optimized control loop circuitry capable of excluding95% of the penetration of radial magnetic fields through the SS wall segments has

4

Fig. 1. Recent experiments using controlled current ramps toinvestigate the properties and limits of RWM active control.The external m/n = 3/1 RWM grows as the edge safety factor,qa, drops below 3. When feedback is applied (right), theamplitude of the RWM remains at the noise level. Withoutfeedback, the RWM leads to disruption of the discharge.

Fig. 2. Measured rate of disruptions during current ramps with and without active feedback control.

allowed the suppression ofRWM amplitude and inhibitedR W M - i n d u c e d p l a s m adisruptions. Resistive wallmode induced disruptions aregenerated using a plasmacurrent ramp between 1.8 to 2.2MA/s to drive the q* = 3 and 4surfaces through the plasmabounda ry . (D i scha rgesproduced by this technique aresimilar to those described in[Ivers, 1998], and have beenused previously to demonstratepassive wall stabilization ofcurrent-driven external kinks.We have extended thistechnique to p roducedischarges with highernormalized beta, bN (and thathave external kinks modes with amplitudes peaking on the low-field side of the torus) byadjusting the current profile evolution. This has allowed observation and characterizationof a range of unstable plasmas. Fig. 1 illustrates feedback stabilization of an m/n = 3/1RWM excited during a higher-bN current ramp discharge and the avoidance of the earlydisruption.

When these low order rational surfaces enter the vacuum, large amplitude n = 1resistive wall modes are excited that lead to plasma disruption and current termination.

5

Fig. 2. High-speed, 32-channel arbitrarywaveform generator (a) used as inputs tothe high-power solid-state amplifiers (b)that drive the HBT-EP distributed array ofcontrol coils.

Fig. 2 presents the results of feedback inhibition of these wall mode induced disruptionsfor an ensemble of similarly prepared plasmas. By varying the plasma current ramp rateand plasma position either m/n = 4/1 resistive wall modes or m/n = 3/1 resistive wallmodes can be generated. At full-gain/full-coverage q*=3 and q*=4 disruptivity isstrongly affected and plasma operation at lower q* is possible. Energizing only the 10coils above and below the mid-plane is still effective at inhibiting m/n = 3/1 induceddisruptions as seen in Fig. 1. Resistive wall modes are not significantly effected,however, when feedback gain is reduced an order of magnitude. These changes infeedback effectiveness are currently being modeled by VALEN and will serve as animportant benchmark for code validation.

We have been able to suppress RWM disruptions in plasmas with both a currentdriven and pressure driven instability, and have been able to extend the operatingparameter space of HBT-EP using feedback. Current investigations include experimentsto determine the limits of our active feedback system by systematically varying thestrength of the instability and by changing the characteristics of the feedback system (e.g.gain, and the number of active feedback coils.) We are also using our recently upgradedfeedback control loop system to help characterize the RWM instabilities on HBT-EP, forexample by switching off the feedback and monitoring mode growth.

Last year, we also initiated studies with a new 32-channel, high-speedprogrammable waveform generator for the investigation of Alfvén-wave “plasmaspectroscopy” of the kink mode. Our immediate goal is to observe and to characterize theplasma response to external magnetic per-turbation arranged to interact with external kinkmodes. This contrasts with our previous workto interact and to control internal tearingmodes. The computer-controlled waveformgenerator has performed as designed, and wehave performed several experiments. We arestudying the results from these experiments toimprove the performance of the HBT-EP“smart shell”—especially with regard to modeshaving a real rotation frequency. The measure-ment of plasma response to magneticperturbations using this technique can be usedto test developing theories of the rotation andgrowth of resistive wall modes.

When an external magnetic perturbationis stationary in the lab-frame, it is often calledan “error field” because static error magneticperturbations always exist due to coilmisalignment and imperfection. Plasmaresponse to an error field has been found tostrongly influence rotation and RWMdynamics. On HBT-EP, the external magneticperturbation, or error field, is applied by themeans of a distributed array of control coils

6

installed as part of our “smart shell” system. Each control coil is driven by one of the 30independent pre-programmable waveform generator channels and solid-state amplifiers.The large number and substantial surface coverage of the control coil array allows goodcontrol of the toroidal and poloidal spectrum of the applied field. This is an importantrequirement for a system intended to apply resonant perturbations. The plasma responseduring these experiments is measured by a variety of diagnostics available on HBT-EPsuch as shell mounted Mirnov coils, saddle-flux loops, and Fourier-analyzing Rogowskicoils.

Fig. 2-2 shows one example of the response of a high-beta plasma to a resonantperturbation resonant with the external, m/n = 3/1, kink mode. The data from two nearlyidentical discharges are used to identify the stability limits of the RWM. The pre-existingmode rotation rate in these experiments was found to be of the order of the wall timescale. When the external error field was applied, the plasma responded in a coherent waywith the amplitude of the response field changing as the plasmas approached the stabilitylimit of the RWM. The relative phase between the plasma response field and the appliedperturbation can also be measured and used to calculate the torque applied to the RWMby the external magnetic field. Experiments are currently underway to characterize RWMamplification and induced plasma torque as the frequency of the external perturbation issystematically varied to further characterize these important wall mode physics issues.

4. Tearing Mode and Rotation Control

A few years ago on HBT-EP, we demonstrated the suppression of tearing modeamplitude by inducing rapid variations in island rotation by applying external resonantmagnetic perturbations to pre-existing m /n=2/1 saturated magnetic islands. (See[Navratil, 1998].) Suppression was understood to occur as a result of a rotation-dependent

†

¢ D term having a form resulting from ion-polarization currents. This methodof island suppression avoided the problems of the so-called phase instability that limitssynchronous stabilization of tearing modes with magnetic feedback. (See [Nadle, 2000].)

Rapid modulations in mode frequency are generated by applying rotating resonantmagnetic perturbations (RMPs) to pre-existing saturated tearing modes. These rapidmodulations change island size through frequency dependent delta prime terms thatgovern island evolution [Smolyakov , 1996]. These modulations can be large,fo=10kHz+Df=5kHz [Navratil, 1998; Maurer, 2000]. On HBT-EP the tearing modegenerated magnetic islands are observed to rotate with the electron fluid at a speed oforder the electron diamagnetic velocity ~w*e. Closer examination of the frequencylocking experiments later pointed out that magnetic islands can both be suppressed andamplified by inducing these rapid rotations [Maurer, 2000]. Specifically, when HBT-EP2/1 islands are frequency modulated, acceleration of the island induces mode growth,while island deceleration causes island damping or suppression. An example of theunlocking of a 2/1 island and the resultant amplitude behavior is shown in Fig. 3-1. Thisasymmetric response points to a more complicated frequency dependence of thepolarization term than first considered.

7

Fig. 3. Measurement of mode amplitude as a functionof frequency and an illustration of interpretationinterms of ion inertia.

Recently, the sign of the ionpolarization term has been a point oftheoretical controversy. Waelbroeckand Fitzpatrick [Waelbroeck andFitzpatrick,1997], pointed out an errorin the conventional understanding ofion-polarization currents occurring inrotating islands in the resistive MHDlimit. The present theoreticalconsensus is that in resistive MHD, ioninertia (polarization currents) are infact destabilizing, that is, the deltaprime contribution is positive,

†

¢ D pol > 0.(See Fig. 3.) Subsequent theory hasincorporated finite Larmor radius anddiamagnetic drifts effects as discussedin Sec. 3.1. The observed asymmetryin HBT-EP island amplitude responseto rotating magnetic perturbations canbe interpreted as evidence of adestabilizing frequency contribution toisland width dynamics. To understandthis point in relation to ion polarizationphysics, one can consider Fig. 3, whichdepicts a simple quadratic dependence of

†

¢ D (w) given by resistive and finite ion FLRMHD theory. Magnetic islands in resistive MHD propagate at the local E¥B velocityshown in Fig. 4a. In HBT-EP, islands rotate with the electron fluid as mentioned above.This is indicated in Fig. 4b which contains diamagnetic and FLR corrections. Theinduced frequency changes we observe while stirring HBT-EP islands are consistent witha destabilizing ion polarization to the Rutherford equation, since islands grow withacceleration and damp with deceleration. This observation is the first experimentalevidence in support of the destabilizing role of ion polarization currents for magneticisland dynamics in toroidal plasma.

Additionally, we have completed a new analysis of mass flow around and insidethe m/n = 2/1 tearing mode [Taylor, submitted to Phys. Plasmas].) Using a novelsynchronous detection method [Taylor, 1999]), local measurements of the pressure andmass flow perturbations were made using insertable Mach probes. Pressure perturbationsfollowed the magnetic island motion for both naturally rotating and actively controlledislands. The toroidal mass flow was sharply peaked near the center of the 2/1 magneticisland (see Sec. 3.1); however, the magnitude of the flow was only about 30% of themagnetic island velocity (indicating strong diamagnetic effects.) Active rotation controlof the magnetic island also accelerated the ion, but by a lesser degree, and this isattributed to charge-exchange drag. These observations together with new measurementsof central ion flow with our Doppler impurity-line spectrometer will allow progressunderstanding large-island dynamics and detailed comparisons with developing non-idealMHD codes and models.

8

5. Research Tools and Facilities

During the past grant period, we have conducted new investigations madepossible with newly installed research tools. These are described in more detail below.

“Smart-Shell” Feedback and Open Control Loop OptimizationWe have implemented a new feedback control loop analog board with optimized

lag-lead compensation to allow flux suppression up to 95% of the penetration of radialmagnetic fields through the SS wall segments during “smart-shell” RWM feedback. Atwo-pole approximation to the measured stainless–steel shell eddy current response oncontrol and sensor coil impedance and mutual inductance was used in circuit modeling tooptimize the analog board filter. The improved flux suppression is shown in Fig. 3. Thisoptimization has allowed suppression of RWM amplitude and, as a consequence, hasreduced RWM induced disruption frequency. We have also developed a newprogrammable digital function generator able to apply arbitrary signals to our 30independent control coils consisting of two Kinetic Systems V285, 16-channel, 16bit,500kHz digital signal generators in a VXI-1200 crate with VXI-PCI8015 controller.

This system has performed as designed and allowed us to begin our “kink modespectroscopy” studies of the RWM.

VALEN Modeling and Benchmarking of Active Mode ControlA critical analysis and design tool for our work on active feedback control of the

RWM is the 3D finite element electromagnetic code, VALEN [Bialek, 2001] developedin support of HBT-EP. Boozer [Boozer, 1998] has developed a general circuitformulation of the RWM feedback stabilization problem. This circuit formulation hasbeen implemented as the basis for the VALEN code using a finite element representationof thin shells to model arbitrary 3D conducting structures. This model of the conductingpassive structure is combined with a circuit representation of stable and unstable plasmamodes represented as 2D surface current distributions derived from the DCON (Glasserref) MHD stability code. VALEN also models arbitrary sensor and control coils includingthe feedback logic to provide a complete simulation capability for feedback control ofplasma instabilities. In this way, VALEN plasma mode, wall, and feedback inductivecouplings are very accurately determined. The code has been carefully benchmarkedagainst analytic cylindrical model calculations and is in good agreement with theexperimental results seen in HBT-EP as described in the [Cates, 2000]. In addition thecode has been applied to optimize the feedback coil geometry in HBT-EP. The simpleanalytic circuit model of feedback stabilization developed by [Boozer,1998] predicts thatto optimize the feedback geometry, the inductive coupling between the control-coils andthe passive stabilizer should be minimized. This effect has been seen in modeling ofprospective HBT-EP feedback configurations. When the control coils are located in thegaps between the stainless-steel and Aluminum shells, the feedback performance ofHBT-EP is predicted to reach the ideal wall stabilized beta limit. Fig. 6 illustrates test coilarrangements studied by VALEN and prototyped on the bench-top prior to installationinto HBT-EP.

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Beta EnhancementWe are investigating new tools to enhance the beta of HBT-EP plasma in order to

study the limits of active mode control of MHD instabilities. Specifically, we haveconducted experiments using our newly installed (1) dual strap, inside launch ICRFheating system, and (2) a movable edge bias electrode that may enhance beta by reducingturbulent transport [Taylor, 1989]. RF heating is applied at 4.5MHz to deuteriumdischarges with 15 percent hydrogen minority species in order to heat electrons in thestrongly damped mode-conversion regime. More than 5 MW of circulating power hasbeen applied to the antenna, and we have measured transient (100 microsecond) couplingof power to the plasma on the order of 50 kW. Optimization of plasma coupling is anongoing process. Using the integrated SPRUCE/TRANSP code, Dr. R. Budny hasalready verified design choices by showing that monopole phasing of the two-strapantenna (with more energy at low k||) leads to strong central heating while dipole phasingcouples only to the plasma edge. Since ICRF heating improves with increasing edgedensity, probe biasing may improve ICRF coupling. During the past year, we have alsoimproved the insulation of our high-power transmission lines allowing higher-poweroperation, and increased the stored energy within our high-voltage pulse-formingnetwork (as shown in Fig. 4). Also, during a recent up to air we installed a high field sidetriple probe and magnetic pickup coil diagnostic to monitor edge plasma parameters andwave magnetic fields ~1 cm past the antenna RF limiter to aid in optimizing plasmacoupling experiments.

We have also begun investigations to modify the plasma flow shear at the edgeusing a simple mushroom-cap Molybdenum electrode biased by an SCR switchedcapacitor bank. Substantial changes in edge mode rotation have been observed.

Equilibrium Reconstruction and Stability AnalysisAccurate knowledge of the safety factor profile is needed to evaluate MHD

stability for tearing modes and resistive wall modes. In HBT-EP, we reconstruct the timeevolution of the safety factor profile, q(r, t), from equilibrium measurements of externalmagnetic fields and fluxes using our free-boundary equilibrium code, TOKAMAC. Inaddition, a movable internal magnetic probe is used to measure internal magnetic fields tofurther constrain reconstructed equilibria. Fig. 4 shows this newly calibrated internalprobe that will also be used in the future as a cross check on UCSD rotating probeinternal magnetic field measurements.

Dr. Alan Glasser (LANL) visited, installed DCON, and updated the interfacebetween the TOKAMAC and DCON codes. This enables computation of the time-evolution of the instability growth rates and mode structures. Currently we are usingDCON derived mode structure to aid in understanding the stabilization of current and b-driven m/n=3/1 and 4/1 RWMs observed during mode control experiments.

Data Acquisition Performance IncreasedOperation of our new data-acquisition computer and MDS-Plus “fusion science

standard” software as improved analysis efficiency and shortened analysis time. We arenow able to store considerably more data on-line and to process data more quickly.

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Facility Maintenance and UpgradesDuring the past year, the experiment operated without any unscheduled

maintenance periods and achieved high levels of utilization. We installed our second-generation control-coil and sensor system for active mode control experiments along withadditional diagnostics including edge and RF probes.

s-1

Other Grant ApplicationForms and Materials

Biographical Sketches

The curriculum vita of Drs. Navratil, Mauel, Pedersen, Maurer, and Bialek areattached.

GERALD A. NAVRATILPh.D. 1976, Plasma Physics, University of Wisconsin–MadisonM.S. l974, Nuclear Engineering, University of Wisconsin–Madison.B.S. 1973, Physics, California Institute of Technology.EXPERIENCEProfessor of Applied Physics, Columbia University, July 1988 to present.Chairman, Department of Applied Physics and Applied Mathematics, Columbia University,

July 1988 to Dec 1994, January 1997 to June 2000.Associate Professor of Applied Physics, Columbia University, July l983 to June 1988.Assistant Professor of Applied Physics, Columbia University, July l977 to June l983.HONORS AND AWARDS

Alfred P. Sloan Research Fellow in Physics 1984-86.Fellow of the American Physical Society 1989-present.

PROFESSIONAL ACTIVITIESAssociate Editor, Physics of Fluids, 1987-l990.Associate Editor, Physics of Plasmas, 1994-2002University Fusion Association: VP 90; Pres.91; Executive Committee 1986-1988; 2000-2002Chairman of the NSTX Program Advisory Committee, 1996 to 2000; member 2000-present.Member, DOE Fusion Energy Sciences Advisory Committee, 1998-2002Vice-chair, Next Step Options Program Advisory Committee; 2000-2002Member, FESAC Panel on Burning Plasma Science, 2001.Chairman, NCSX Physics Validation Review Panel advising OFES, March 2001.Co-chairman, Fusion Energy Sciences Summer Study 2002, Snowmass, CO July 8-19, 2002.Member, FESAC “Action Panel” on Burning Plasma Experiments, March-Sept. 2002.

SELECTED RECENT PUBLICATIONS“Higher Fusion Power Gain with Pressure Profile Control in Strongly-Shaped DIII-D Tokamak Plasmas,” E. A. Lazarus, G. A. Navratil, C. M. Greenfield, E. J. Strait, et al., Physical Review Letters 77, 2714 (1996).“Active Control of 2/1 Magnetic Islands in a Tokamak,” by G. A. Navratil, C. Cates, M. E. Mauel, D. Maurer, D. Nadle, E. Taylor, Q. Xiao, W. A. Reass, and G. A. Wurden, Phys. Plasmas 5 (1998) 1855.“Stabilization of the External Kink and Control of the Resistive Wall Mode in Tokamaks,” Garofalo, A.M., Turnbull, A.D., Strait, E.J., Austin, M.E., Bialek, J., Chu, M.S., Fredrickson, E., La Haye, R.J., Navratil, G.A., Lao, L.L., Lazarus, E.A., Okabayashi, M., Rice, B.W., Sabbagh, S.A., Scoville, J.T., Taylor, T.S., and Walker, M.L., Physics of Plasmas.6, 1893 (1999).“The Feedback Phase Instability in the HBT-EP Tokamak,” D. L. Nadle, C. Cates, H. Dahi, M. E. Mauel, D. Maurer, S. Mukherjee, G. A. Navratil, M. Shilov, E. D. Taylor, Nuclear Fusion 40, 1791 (2000).“Suppression of Resistive Wall Instabilities with Distributed, Independently Controlled, Active Feedback Coils,” C. Cates, M. Shilov, M. E. Mauel, G. A. Navratil, D. Maurer, S. Mukherjee, D. Nadle, J. Bialek, A. Boozer, Phys. Plasmas 7, 3133 (2000).“Modeling of Active Control of External MHD Instabilities,” James Bialek, Allen H. Boozer, M. E. Mauel, and G. A. Navratil, Phys. Plasmas 8, 2170 (2001).“Sustained Rotational Stabilization of DIII-D Plasmas above the No-Wall Beta Limit” A. M. Garofalo, T. H. Jensen, L. C. Johnson, R. J. LaHaye, G. A. Navratil, M. Okabayashi, J. T. Scoville, E, J, Strait, et al., Phys. Plasmas 9, 1997 (2002).

Michael E. Mauel (May, 2002)

210 S. W. Mudd BuildingColumbia UniversityNew York, New York 10027(212) 854-4455mauel@columbia.edu

Personal Datahttp://www.columbia.edu/~mem4/Born August 3, 1956Citizen of U.S.A.Married to Allison M. Moore, Two daughters

EducationSc.D. (EE) 1983, Massachusetts Institute of TechnologyM.S. (EE) 1979, Massachusetts Institute of TechnologyB.S. (EE) 1978, Massachusetts Institute of Technology

ExperienceChairman, Dept. of Applied Physics and Applied Mathematics, July, 2000 to presentProfessor, Applied Physics, Columbia University, July 1995 to presentVisiting Scientist, MIT, 1999 to presentVisiting Scientist, General Atomics, San Diego, July 1994 – December 1994

Honors and AwardsRose Award for Excellence in Fusion Engineering, Fusion Power Associates, 2000Fellow, American Physical Society, 1995Teacher of the Year, 1994, elected by SEAS undergraduatesCertificate of Appreciation, U. S. Dept. of Energy, 1989I.E.E.E. Fortesque Fellowship (1978 – 1979)Guillemin Prize for undergraduate thesis in Electrical Engineering

Professional ActivitiesChair-Elect, Division of Plasma Physics, American Physical Society, 2002Co-Chair, 1999 Fusion Summer Study, Snowmass, CO, July, 1999.Divisional Associate Editor, Physical Review Letters, 1995-1998.Chair, Physics Advisory Committees, C-Mod, 2002-presentPresident, University Fusion Association, 1997-1998, Secretary/Treasurer, 1992 - 1996, Executive Committee, 1992 - 1994Chairman, Selection Comm., National Fusion Energy Undergraduate Fellows, 1997, 1995, 1994.

Select Publications “Effect of Magnetic Islands on the Local Plasma Behavior in the HBT-EP Tokamak,” E. D. Taylor, et al.,submitted to Phys. Plasmas.

“Modeling of active control of external magnetohydrodynamic instabilities,” J. Bialek, A, Boozer, M. E. Mauel, G.A. Navratil, Phys. Plasmas 8 (2001).

“Suppression of resistive wall instabilities with distributed, independently controlled, active feedback coils,” C.Cates, et al., Phys. Plasmas 7 (2000) 3133.

“The feedback phase instability in the HBT-EP tokamak,” D.L. Nadle, et al., Nuclear Fusion 40 (2000) 1714.

“Nonstationary signal analysis of magnetic islands in plasmas,” E. D. Taylor, et al., Rev. Sci. Instr. 70, (1999).

“Stabilization of Kink Instabilities by Eddy Currents in a Segmented Wall and Comparison with Ideal MHDTheory,” A. M. Garofalo, et al., Nuclear Fusion, 38, no.7, July 1998, pp.1029-42.

“Active control of 2/1 magnetic islands in a tokamak”, G. A. Navratil, et al. , Physics of Plasmas , 5, (1998),pp.1855-63.

“Enhanced Confinement and Stability in DIII-D Discharges with Reversed Magnetic Shear,” E. J. Strait, L. L. Lao,M. E. Mauel, et al., Phys. Rev. Lett. 75 (1995) 4421.

“Wall Stabilization of High Beta Plasmas in DIII-D,” T. S. Taylor, E. J. Strait, L. L. Lao, M. E. Mauel, et al., Phys.of Plasmas 2 (1995) 2390.

“Operation at the tokamak equilibrium poloidal beta limit in TFTR,” M. E. Mauel, G. A. Navratil, S. A. Sabbagh,et al., Nuclear Fusion 32 (1992) 1468.

Curriculum vitae: Thomas Sunn PedersenEducation

1996- 2000: Ph.D. in Plasma Physics, Massachusetts Institute of Technology, Cambridge, MA, USA1990-1995: M. Sc. in Applied Physics Engineering, Technical University of Denmark, Lyngby, Denmark

Research and teaching experience

2000 - present: Assistant professor, Dept. of Applied Physics and Applied Math., Columbia UniversityResearch topics include experimental measurements of plasma quantities, ICRF heating in a tokamak, developmentof feedback systems for plasma control, confinement of plasma in a dipole magnetic field, and development of anovel experiment for confinement of non-neutral plasmas. Teaching graduate and undergraduate level classes, andadvising Ph.D. students on their thesis research. Courses taught: "Plasma Diagnostics", "Plasma Physics I", and"Introduction to Plasma Physics". Ph.D. thesis advisor for two students.2000: Postdoc, Levitated Dipole Experiment, Columbia University/MIT PSFC, Cambridge, MA, USAResponsible for developing diagnostics, testing state of the art superconducting magnet, and designing parts of thesuperconducting magnet system of the levitated dipole experiment (LDX) at MIT. Research on hot plasmaconfinement in a dipole magnetic configuration.1994-1995: Scientific researcher, Risø National Laboratory, Roskilde, Denmark Computational and theoretical plasma physics. Investigation of the connection between particle dispersion, chaos(Lyapunov exponents) and the presence of coherent structures in the turbulent flow.1993, 1994: Research assistant, JET Joint Undertaking, Abingdon, EnglandDeveloped computer algorithms for analysis of experimental data from the Edge LIDAR Thomson Scattering LaserDiagnostic on the Joint European Torus (JET), including a new neural network approach.

5 publications related to this proposal:

T. Sunn Pedersen et al. "Radial Impurity Transport in the H-Mode Transport Barrier Region in Alcator C-Mod",Nuclear Fusion 40 (2000), p. 1795T. Sunn Pedersen and R. S. Granetz, "Simultaneous soft x-ray emissivity profile measurements in poloidallyseparate locations of the Alcator C-Mod edge plasma", Review of Scientific Instruments 71 (2000), p. 3385T. Sunn Pedersen and R. S. Granetz, "Edge X-Ray Imaging Measurements of the Plasma Edge in Alcator C-Mod",Review of Scientific Instruments 70 (1999), p. 586I. H. Hutchinson et al. "Edge transport barrier phenomena in Alcator C-Mod", Plasma Phys. Contr. Fusion 41,March 1999, p. A609T. Sunn Pedersen, P. K. Michelsen and J. Juul Rasmussen "Lyapunov exponents and particle dispersion in driftwave turbulence", Physics of Plasmas 3, 1996, p. 2939

5 other representative publications

T. Sunn Pedersen and Allen H. Boozer, "Non-neutral plasmas confined on magnetic surfaces", Phys. Rev. Letters88, 2002, 205002J. Kesner et al. "Dipole equilibrium and stability", Nuclear Fusion 41 (2001), p. 301D. Mossessian et al. "Studies of EDA H-mode in Alcator C-Mod" Plasma Phys. Contr. Fusion, 42, 2000, p.A263 T. Sunn Pedersen, P. K. Michelsen and J. Juul Rasmussen "Resistive Coupling in drift wave turbulence", PlasmaPhysics and Controlled Fusion 38, December 1996, p. 2143T. Sunn Pedersen, P. K. Michelsen and J. Juul Rasmussen "Analysis of Chaos in Plasma Turbulence", PhysicaScripta T67 (1996), p. 30

DAVID A. MAURER

EducationPh.D. 2000 Department of Applied Physics and Applied Mathematics, Columbia UniversityM.P. 1998 Applied Physics, Columbia UniversityM.S. 1993 Applied Physics, Columbia UniversityB.S. 1991 Nuclear Engineering, University of Wisconsin, Madison

Work ExperienceAssociate Research Scientist, Columbia University, Plasma Physics Laboratory, 2001-presentPostdoctoral Research Assistant, Columbia University, Plasma Physics Laboratory, 2000-2001Research Assistant, Columbia University, Plasma Physics Laboratory, 1993-2000Engineering Technician, University of Wisconsin, Madison, MST Group, 1991-1992

Research ExperienceResearch primarily focused on the interaction of magnetic field perturbations in rotatingplasma and their effect upon magnetic island behavior along with control implications fortokamak performance. Diagnostic experience: designed and constructed single pointNd:YAG based Thomson scattering system; soft x-ray emissivity and magneticdiagnostic analysis of magnetic islands and their properties; experience with Ruby basedThomson scattering systems and basic tokamak facility operation.

Select Recent Publications“Real-time measurement of toroidal rotation”, S.F. Paul, C. Cates, M. Mauel, D. Maurer, G.Navratil, M. Shilov, Review of Scientific Inst., Vol. 72, No. 1, 966, (2001).

“Active feedback control of the wall stabilized external kink mode,” G. A. Navratil, J.Bialek, A. Boozer, C. Cates, H. Dahi, M. E. Mauel, D. Maurer, S. Mukherjee and M. Shilov, toappear in Plasma Physics and Controlled Nuclear Fusion Research, (2001).

“Effect of Rotating Resonant Magnetic Fields on Magnetic Islands in Tokamak Plasma, “D.Maurer, Ph.D. Thesis, Columbia University (2000).

“The feedback phase instability in the HBT-EP tokamak,” D. L., Nadle, C. Cates, M. E. Mauel, D.A. Maurer, G. A. Navratil and E. Taylor, Nuclear Fusion, Vol. 28, No. 6, 1085, (2000).

“Suppression of resistive wall instabilities with distributed, independently controlled, activefeedback coils,” C. Cates, M. Shilov, M. E. Mauel, G. A. Navratil, D. Maurer, D. Nadle, S.Mukherjee, J. Bialek, A. Boozer, Physics of Plasmas, Vol. 7, No. 8, 3133, (2000).

“Nonstationary signal analysis of magnetic islands in plasmas,” E. D. Taylor, C. Cates, M. E.Mauel, D. A. Maurer, D. Nadle, G. A. Navratil and M. Shilov, Review Scientific Inst., Vol. 70, No.12, 4545, (1999).

“Suppression of magnetic islands through synchronous and asynchronous application of resonantmagnetic fields,” M. E. Mauel, J. Bialek, C. Cates, H. Dahi, D. Maurer, G. A. Navratil, D. Nadle, M.Shilov and E. Taylor, in Plasma Physics and Controlled Nuclear Fusion Research, Vol. 2, 197,(1999).

“Active control of 2/1 magnetic islands in a tokamak,” G.A. Navratil, C. Cates, M.E. Mauel, D.Maurer, D. Nadle, E. Taylor, Q. Xiao, W.A. Reass and G. A. Wurden, Physics of Plasmas, Vol. 5,No. 5, 1855, (1998).

James M. BialekCurriculum Vitae

21 Nassau Court March 1999Skillman N.J. 08558 phone 609 466 4479

Education:1968 BS Engineering Science SUNY ( Buffalo )

Magna Cum Laude & Tau Beta Pi1971 MS Math - Stevens Institute of Technology1978 MS Physics - Stevens Institute of Technology1988 Ph.D. Physics - Stevens Institute of Technology

(Thesis: Chaos in Hamiltonian Systems; G.Schmidt advisor )

Experience at Columbia University (Applied Physics ):

I have been employed as a Research Scientist at Columbia University sinceSeptember 1997. My work during this period has been concentrated on modeling thefeedback stabilization of resistive wall modes. This has involved doing computationsthat simulate and predict the behavior of plasma as it interacts electromagnetically withthe surrounding electrical conducting structures. These conducting structures are bothpassive and active. Passive structures are those which react to the electromagneticenvironment by simply being conductors of current. Active structures are those in whichthe changing electromagnetic environment is measured and then some (corrective)response is produced via human designed logic and circuitry. Feedback stabilization hasthe potential to make a major advance in the field of plasma confinement.

Selected References:

"Stabilization of the External Kink and Control of the Resistive Wall Mode inTokamaks" by Garofalo, A.M., et al. Phys. Plasmas.

"Active Control of MHD Modes in a Tokamak," by G. A. Navratil, J. Bialek, A. H.Boozer, M. E. Mauel, D. Maurer, D. Nadle, E. Taylor, Proc. 25th European PhysicalSociety Conference on Controled Fusion and Plasma Science, Prague, Part II, p730,(1998).

"Study of the Resistive Wall Mode in DIII-D," by A. M. Garofalo, J. Bialek, M. S. Chu,E. D. Fredrickson, R. J. Groebner, R. J. La Haye, L. L. Lao, G. A. navratil, B. W. Rice, S.A. Sabbagh, J. T. Scoville, E. J. Strait, T. S. Taylor, A. D. Turnbull, and the DIII-DTeam, Proc. 25th European Physical Society Conference on Controled Fusion andPlasma Science, Prague, Part II, p814, (1998).

"Suppression of Magnetic Islands Through Synchronous and Aynchronous Applicationof resonant Magnetic Fields," M. E. Mauel, J. Bialek, C. Cates, H. Dahi, D. Maurer, D.Nadle, G. A. Navratil, M. Shilov, and E. Taylor, Plasma Physics and Controlled FusionResearch 1998, , (IAEA, Vienna, 1999) paper IAEA-CN-69/EXP3/09 to be published.

"Observation and Control of Resistive Wall Modes," E. J. Strait, M. S. Chu, L.L. Lao, R.J. LaHaye, J. T. Scoville, T.S. Taylor, A.D. Turnbull, M. Walker, A. M. Garofalo, J.Bialek, G.A. Navratil, S. A. Sabbagh, E. Fredrickson, M. Okabayashi, E.A. Lazarus, M.E. Austin, G. McKee, B. W. Rice, Plasma Physics and Controlled Fusion Research 1998,, (IAEA, Vienna, 1999) paper IAEA-CN-69/EXP3/10 to be published.

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Facilities, Resources, and Collaborations

This research will be conducted using the HBT-EP tokamak research facilitylocated within Columbia’s Plasma Physics Laboratory. Established in 1961 by Robert A.Gross, the Plasma Physics Laboratory is one of the major research laboratories on theColumbia University campus. The laboratory has been the research home to ninemembers of the faculty, four-dozen research scientists, and 116 graduate students. Over12 major experimental devices have been built at Columbia’s Plasma Physics Laboratoryproviding the tools to investigate a wide range of basic and applied topics of plasmaphysics. The HBT-EP experimental facility is presently the largest and most productiveexperiment within the laboratory. HBT-EP serves as an overall focus to the ColumbiaUniversity plasma physics program, and HBT-EP provides educational and hands-onresearch opportunities to as many as one dozen undergraduate student interns every year.The HBT-EP experiment is frequently featured in guided tours of the scientific researchfacilities of the School of Engineering and Applied Science.

Columbia University has strongly supported the Plasma Physics Laboratory andthe HBT-EP experiment. The laboratory consists of over 27,000 sq. ft. of research, office,and equipment assembly and fabrication space. We have a full machine shop, anelectronics shop, several mini-computers and workstations, a fiber-optic CAMAC dataacquisition system, direct 100bt internet connections to a 1 Gbs F.O. internet switch, anda new video conference facility. The experiments within the laboratory acquire andprocess data using the MDS/MDS-Plus and IDL software packages.

Overview of the HBT-EP TokamakThe HBT-EP tokamak is the fourth toroidal magnetic experiment constructed

within the laboratory. HBT-EP was designed to demonstrate the feasibility of a high-betatokamak stabilized by a combination of a close-fitting conducting wall, plasma rotation,and active feedback. The specific approach taken by HBT-EP was to investigate thecombined use of a close-fitting conducting wall and modular saddle coils for the purposeof significantly extending the tokamak beta limit.

Descriptions of the HBT-EP device have been published previously. HBT-EP is aunique experiment for the investigation of wall-stabilization because it is the onlytokamak device built with adjustable walls. HBT-EP is also unique because the vacuumchamber is made from several quartz cylindrical breaks. These allow fast penetration ofexternally-applied magnetic perturbations. HBT-EP has been able to accelerate magneticislands to nearly sonic speeds, and the device has been used to access the Troyon-normalized beta limit with ohmic heating alone.

The HBT-EP tokamak is well diagnosed, and we have demonstrated the use ofmodern tokamak equilibrium reconstruction and detailed interfaces between experimentalmeasurements and ideal MHD stability codes. Plasma fluctuations are measuredmagnetically and with soft x-ray arrays. Since the pulse length of the plasma dischargesare relatively short (less than 15 ms), we are able to insert a variety of electrostatic andmagnetic probes into the outer one third of the plasma minor radius. HBT-EP uses

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Fig 4. Cut-away illustration of the HBT-EP experiment showingthe adjustable conduction wall on which are mounted numerousmode sensors and control coils.

microwave interferometry tomeasure line density andThomson scattering forelectron temperature. Wehave built and tested aneutral particle energyanalyzer, and we haverecently installed a two-strap, ICRF antenna, Faradayshield, and RF limiter forpulsed, plasma heating up to200 kW. On a typical plasmashot, we record over 15 MBof digitized data representingmore than 200 diagnosticchannels from 9 CAMACcrates.

A photograph of theHBT-EP device is shown.

CollaborationsAn essential part of

the HBT-EP program is outreach and collaboration within the fusion science and theColumbia University communities. In many respects, HBT-EP acts as an internationalcenter and clearinghouse for expertise and experience with active mode control and itspractical application to a variety of experiments. For several years, we have sponsoredand co-sponsored specialized workshops and forums on MHD phenomena and MHDmode control. Through direct interaction with DIII-D, NSTX, ASDEX-U, and the FIREdesign team, we have participated in the evaluation and implementation of active modecontrol techniques on these major facilities. Additionally, it is noteworthy that HBT-EP isthe largest on-campus physics experiment at Columbia University. HBT-EP plays avaluable role in the training of both graduate and undergraduate students and as avaluable attraction to illustrate fusion science research to a students, parents, and civicgroups in the New York City area. Several area high school students and one high schoolscience teacher have worked in the HBT-EP laboratory. Each semester, we conductseveral tours (accompanied by mini-lectures on fusion science research) to localeducational groups.

While educational outreach is an important and enjoyable service element of ourprogram, our collaborations with experts and with related experimental teams within thefusion program are extremely cost-effective in widening the scientific impact of ourwork. As already explained, HBT-EP’s research program includes the development ofexperimental techniques, the development of theoretical and computation design tools,and the validation and testing of these models and tools through detailed experimentation.Thus, HBT-EP brings relevant experience and proven tools, like the VALEN code, tocollaborations with proof-of-principle, performance extension, and (recently) possibleburning plasma research devices.

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Our collaborations with fusion experts are both informal and formal. Informally,we have had hosted extended visits of leading theorists, Drs. Jensen, Fitzpatrick, andGlasser, that have proven to be invaluable in the generation of new ideas, interpretation,and experiments. These informal theory collaborations contributed to the design of ourthe first-generation “smart-shell” for RWM feedback and to the use of DCON in order tocompute ideal no-wall and ideal-wall stability limits and to compute the precise surfaceRWM eigenfunction needed for accurate VALEN calculations. (In addition, Dr. AllenBoozer has contributed pioneering understanding of plasma rotation and RWM physicswhose value can not be overstated.) Among our formal collaborations, two are supportedthrough the PPPL Off-Site University Support Program, one through the innovativediagnostics initiative, and two involve direct participation by Drs. Navratil and Bailek inthe DIII-D and NSTX programs.

We propose to continue and (hopefully) strengthen our informal and formalfusion science collaborations. Four of these collaborative efforts are briefly describedbelow.

Laboratory Benchmarks for Two-Fluid Toroidal Plasma Simulation Code (Drs. A.Glasser and X. Tang, LANL)

We propose to provide detailed laboratory benchmarks of rotating islanddynamics to aid the development at Los Alamos National Laboratory of a new plasmasimulation code called SEL. SEL is intended to treat some of the most difficult problemsin fusion research: low-frequency, long-wavelength, nearly-singular instabilities and theirnonlinear evolution in toroidal magnetic confinement devices such as the advancedtokamak, spherical torus, spheromak, RFP, and stellarator. The code’s name is derivedfrom its use of high-order spectral elements for spatial discretization. Spectral elementmethods combine exponentially fast convergence and parallelizability. SEL will alsoincorporate dynamic alignment of the computational grid with the evolving magneticfield by means of a variational principle and allow fast, accurate treatment of singularMHD modes. The time step is fully implicit, allowing fast, accurate treatment of multipletime scales, including two-fluid effects and rapid plasma flow. Massively paralleloperation is achieved with the use of the now-standard MPI and PETSc libraries.Efficient linear system solution is achieved with static condensation, combining small,local direct solves with a global, parallel iterative solve on a small skeletal grid.Currently, the code functions correctly (but slowly) in 2D on incompressible magneticreconnection with S =104. 1D adaptive grid packing works perfectly. Static condensationand grid alignment in 2D are expected to be working within 6 months. 3D operationshould be achieved within a year later, and this time-scale is appropriate to the HBT-EPexperimental program.

Real-time plasma rotation diagnostic for measuring small Doppler shifts (Dr. S.Paul, PPPL)

A non-invasive toroidal velocity measurement has been developed and installed inHBT-EP in order to allow real-time measurement of plasma rotation. The novel aspect ofthe technique is that the shift is calculated from the ratio of the light intensity from twodetectors rather than resolving the emission line with a spectrometer. One detector views

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the plasma through an interference filter whose passband has a negative slope and theother channel views through a positive-slope filter. The ratio varies as the line is shiftedacross the passbands the filters. Variations in plasma emission are canceled because thetwo detectors observe the identical volume of plasma, achieved by employing a 'Y'-splitter composed of bundle of randomized optical fibers. The signal ratio does notdepend on any detector or circuit characteristic that remains constant because systematicdifferences are removed by relative calibration of the two channels. Measurements onHBT-EP discharges seeded with 10% He show adequate emission from the He II (n = 4Æ 3) line at 4686 Å. In the absence of any applied perturbation, the toroidal rotation ofthe central He impurity is about 4 km/sec. The noise level of the measurement at a 5 kHzbandwidth corresponds to a rotational accuracy of 0.5 km/sec.

Achieving Enhanced Beta with ICRF for Active MHD Mode Control (Drs. J. R.Wilson and R. Budny)

Our longest on-going formal collaboration has been with the PPPL’s RF groupthat has culminated in the successful high-power, high-voltage operation of the inside-launch ICRF antenna during the past year. During the next period, collaborative activitiesinvolve three tasks: (1) parameterizing ICRF coupling and deposition using the integratedSPRUCE/TRANSP codes, (2) assistance with the installation, interpretation, andoperation of RF diagnostics, and (3) participation in active MHD mode controlexperiments using discharges with enhanced beta.

USCD Rotating Probe Collaboration (Dr. J. Boedo, UCSD)In our collaboration with Dr. J. Bodeo of UCSD involves the final installation and

test of the rotating probe diagnostic that will provide 2D measurements of the internalmagnetic fields and electron temperature and density profiles. Installation of thisdiagnostic will occur in late 2002. Currently, UCSD is completing parts procurement andinitial construction of the vacuum chamber that will house the probe motion and facilitatethe rotating electrical feedthroughs.

Theory of RWM, Plasma Rotation, Helical Fields, and Island Dynamics (Dr. AllenBoozer)

Perhaps the most important and productive collaboration has been with our theorycolleague, A. Boozer. Among Boozer’s many contributions to plasma physics and fusionscience, he has recently developed the precise formulary for the calculation of theeffectiveness of passive and active wall stabilization. Boozer’s formulation is the basisfor the calculations of J. Bialek using his 3D electromagnetic code, VALEN.

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Bibliography

1. HBT-EPE. D. Taylor, C. Cates, M. E. Mauel, D. A. Maurer, D. Nadle, G. A. Navratil, M. Shilov, “Effect ofMagnetic Islands on the Local Plasma Behavior in the High Beta Tokamak – Extended Pulse (HBT-EP)Experiment,” submitted to Phys. Plasmas.

J. Bialek, Boozer, A.H.; Mauel, M.E.; Navratil, G.A., “Modeling of active control of externalmagnetohydrodynamic instabilities,” Phys. Plasmas 8 (2001) 2170.

S. F. Paul, Cates, C.; Mauel, M.; Maurer, D.; Navratil, G.; Shilov, M., “Real-time measurement oftoroidal rotation,” Rev. Sci. Instr 72 (2001) 966.

C. Cates, M. Shilov, M. E. Mauel, G. A. Navratil, D. Maurer, S. Mukherjee, D. Nadle, J. Bialek, A.Boozer, "Suppression of resistive wall instabilities with distributed, independently controlled, activefeedback coils," Phys. Plasmas 7 (2000) 3133.

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Q. Xiao, Effect of Applied Resonant Magnetic Fields on the Measured MHD Mode Structure in aTokamak Plasmas, Ph.D. Thesis, Columbia University (1998).

M. E. Mauel, J. Bialek, C. Cates, H. Dahi, D. Maurer, D. Nadle, G. A. Navratil, M. Shilov, and E.Taylor, Suppression of Magnetic Islands through Synchronous and Asynchronous Application ofResonant Magnetic Fields", Plasma Physics and Controlled Fusion Research 1998 (IAEA, 1998).

Reass WA. Wurden GA. Nadle DL. Mauel ME. Navratil GA., “Operational performance of the twochannel 10 Megawatt feedback amplifier system for MHD control on the Columbia University HBT-EPtokamak,” 17th IEEE/NPSS Symposium Fusion Engineering, vol.1, pp.497-500 (1998).

A. M. Garofalo, Measurement and Interpretation of Eddy Current Induced in a Segmented ConductingWall by MHD Instabilities in a Tokamak, Ph.D. Thesis, Columbia University (1997).

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M. E. Mauel, E.Eisner, A. Garofalo, T.#H.#Ivers, R.Kombargi, D. Maurer, D. Nadle, G. A. Navratil, A.Sainz, M. K. V. Sankar, M. Su, E. Taylor, Q. Xiao, W. A. Reass And G. A. Wurden, “Eddy-CurrentCharacterization and Plasma Rotation Control in Wall-Stabilized Tokamak Discharges,” PlasmaPhysics and Controlled Fusion Research 1996 (IAEA, 1996).

T. H. Ivers, et al., “Passive and Active Control of MHD Instabilities in the HBT-EP Tokamak,” PlasmaPhysics and Controlled Fusion Research 1994 (IAEA, 1994).

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D. Gates, Stabilization of MHD Instabilities Using a Conducting Wall on HBT-EP, Ph.D. Thesis,Columbia University (1993).

2. Recent Mode Control and Tearing Mode Dynamics ArticlesJ. A. Snipes, Granetz, R.S.; Hastie, R.J.; Hubbard, A.E.; “beta limiting MHD activity and mode lockingin Alcator C-Mod” Plasma Physics and Controlled Fusion 44 (2002) 381.

J. A. Malmberg, Brunsell, P.R , “Resistive wall instabilities and tearing mode dynamics in the EXTRAPT2R thin shell reversed-field pinch” Phys. Plasmas 9 (2002) 212.

R. Paccagnella, Schnack, D.D.; Chu, M.S. “Feedback studies on resistive wall modes in the reversedfield pinch” Phys. Plasmas (2002) 234.

S. Takeji, Tokuda, S.; Fujita, T.; et al. “Resistive instabilities in reversed shear discharges and wallstabilization on JT-60U” Nuc Fusion 42 (2002) 5.

A. H. Boozer, “Error field amplification and rotation damping in tokamak plasmas” Phys. Rev. Lett 86(2001) 5059.

C. N. Lashmore-Davies, “The resistive wall instability and critical flow velocity” Phys. Plasmas 8(2001) 151.

M. V. Umansky, Betti, R.; Freidberg, J.P. “Stabilization of the resistive wall mode by flowing metalwalls” Phys. Plasmas 8 (2001) 4427.

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J. B. Taylor, Connor, J.W.; Gimblett, C.G.; Wilson, H.R.; Hastie, R.J. “Resistive wall modes andnonuniform wall rotation” Phys. Plasmas 8 (2001) 4062.

M. Okabayashi, Bialek, J., et al., “Active feedback stabilization of the resistive wall mode on the DIII-Ddevice” Phys. Plasmas 8 (2001) 2071.

J. P. Freidberg, Betti, R. “Stabilization of the resistive wall mode by differentially rotating walls” Phys.Plasmas 8 (2001) 383.

A. M. Garofalo, Chu, H.S.; Fredrickson, E.D., et al., “Resistive wall mode dynamics and activefeedback control in DIII-D” Nucl. Fusion 41 (2001) 1171.

S. C. Guo, Chu, M.S. , “Interaction of an external rotating magnetic field with the tearing mode in aplasma surrounded by a resistive wall” Phys. Plasmas 8 (2001) 3342.

Bondeson, Yueqiang Liu; Fransson, C.M.; Lennartson, B.; Breitholtz, C.; Taylor, T.S. “Active feedbackstabilization of high beta modes in advanced tokamaks” Nuc Fusion 41 (2001) 455.

S.H. Hogun Jhang; Ku, Jin-Yong Kim “An optimum feedback coil position for active stabilization ofresistive wall modes” Phys. Plasmas 8 (2001) 3107.

A.B. Mikhailovskii, Pustovitov, V.D. “Feedback suppression of resistive wall modes in a tokamak”Fizika Plazmy 26 (2001) 512.

C. C. Hegna and S. R. Hudson, Phys. Rev. Letters 87 (2001), p. 035001

D. Gregoratto, Bondeson, A.; Chu, M.S.; Garofalo, A.M. “Influence of rotation profiles on stabilizationof resistive wall modes” Plasma Physics and Controlled Fusion 43 (2001) 1453.

R. J. Buttery, Valovic, M.; Warrick, C.D.; Wilson, H.R. “Controlled seeding of neoclassical tearingmodes in COMPASS-D” Nuc Fusion 41 (2001) 985.

R. Fitzpatrick, Rossi, E.; Yu, E.P. “Improved evolution equations for magnetic island chains in toroidalpinch plasmas subject to externally applied resonant magnetic perturbations” Phys. Plasmas 8 (2001)4489.

R. Fitzpatrick, Rossi, E. “Control of tearing modes in toroidal fusion experiments using "designer" errorfields”, Phys. Plasmas 8 (2001) 2760.

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S. C. Guo, Chu, M.S. “Interaction of an external rotating magnetic field with the tearing mode in aplasma surrounded by a resistive wall” Phys. Plasmas 8 (2001) 3342

R. Coelho, Lazzaro, E. “An innovative interpretation of rotating tearing mode locking to an externalstatic current” Nuc Fusion 41 (2001) 813.

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J. W. Connor, Waelbroeck, F.L.; Wilson, H.R. “The role of polarization current in magnetic islandevolution” Phys. Plasma 8 (2001) 2835.

C. M. Fransson, Lennartson, B.; Breitholtz, C.; Bondeson, A.; Liu, Y.Q. , “Feedback stabilization ofnonaxisymmetric resistive wall modes in tokamaks. II. Control analysis” Phys. Plasmas 7 (2000) 4143.

R. Coelho, Lazzaro, E. , “External field threshold for the unlocking of magnetic islands in the presenceof resistive wall effects and toroidal mode coupling” Physica Scripta 62 (2000) 363.

M. Garofalo, Strait, E.J.; Bialek, J.M.; et al. “Control of the resistive wall mode in advanced tokamakplasmas on DIII-D” Nuc Fusion 40 (2000) 1491.

C. G. Gimblett, Hastie, R.J. “A rotating shell and stabilization of the tokamak resistive wall mode”Phys. Plasmas 7 (2000) 5007.

C. G. Gimblett, Hastie, R.J. “Torque balance and rotational stabilization of the resistive wall mode”Phys. Plasmas 7 (2000) 258.

Y.Q. Liu, Bondeson, A.; Fransson, C.M.; Lennartson, B.; Breitholtz, C. “Feedback stabilization ofnonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model” Phys. Plasmas 7 (2000)3681.

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M. F. F. Nave, Coelho, R.; Lazzaro, E.; Serra, F. “The influence of mode coupling on the non-linearevolution of tearing modes” European Physical Journal D 8 (2000) 287.

R. Fitzpatrick, Waelbroeck, F.L. “Nonlinear dynamics of feedback modulated magnetic islands intoroidal plasmas” Phys. Plasmas 7 (2000) 4983.

3. Other Cited ArticlesA. Bondeson, M. Persson, “Stabilization by resistive walls and q-limit disruptions in tokamaks,” Nuc.Fusion 28 (1988) 1887.

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H.A.B. Bodin, Nuc. Fusion 30, 1717 (1990).

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A. H. Boozer, “Stabilization of resistive wall modes by slow plasma rotation,” Phys. Plasmas 2, 4521(1995); 3, 4620 (1996).

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L. Chousal, R. Hernandez, J. Boedo, J. Chalfant, D.A. Maurer," Novel Probe Diagnostic for FusionPlasmas ", Bulletin of the American Phys Society, Oct 2001, 45 , No 8, pg 65

S. Sabbagh, et al., “Beta-limiting instabilities and global mode stabilization in the National SphericalTorus Experiment”, Phys. Plasmas 9 (2002) 2085.

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Current and Pending Support

Prof. Gerald A. NavratilCurrently supported 0.5 months during the academic year plus 1.0 summer month

by US DOE Grant DE-FG02-99ER54524 and 2.0 months during the academic year plus2.5 summer months by US DOE Grant DE-FG02-86ER53222. Pending this proposal.

Prof. Michael E. MauelCurrently supported 1.0 month academic plus 1.0 summer month by US DOE Grant

DE-FG02-86ER53222, 1.5 month academic year plus 1.5 summer month by DOE GrantDE-FG02-98ER54459, and 0.5 month summer by DOE DE-FG02-00ER54585. Pendingthis proposal and 1 year renewal of DE-FG02-98ER54459.