Emission in the range of Ion Cyclotron Frequencies on ASDEX-Upgrade

Emission in the range of Ion Cyclotron Frequencies on

ASDEX-UpgradeR. D’Inca – September 2009

ICRF GroupICRF Group

Seminar talk – Advanced plasma courses - IPP

Outline

1 – Motivation ->

2 - Experimental setup ->

3 - Experimental results on ASDEX-Upgrade ->

4 - Overview and interpretation of ICE theories ->

5 - Next steps ->

1 - Motivation

Back to outline

1 – Motivation

ICRF System ASDEX Upgrade and arc detectors

2 – Experimental setup

Back to outline

2 – Experimental setup (1/2)

Two diagnostics are used:

- RF probe in HFS of vacuum vessel, sector 13. (access provided by. M. K-H Schuhbeck)

- Voltage probe in transmission line of ICRF Antenna 4

Side-view Upper-view

Main limitation: the main characteristics of the RF probe are not known (attenuation factor, bandwidth, cut-off frequencies).

2 – Experimental setup (2/2)Signal processing system based on two Acqiris DC265 digitizing cards (8 bits, 500MS/s, 2MB memory/channel, 4x channels).

Sun workstation

Acqiris rack

Low noise preamplifier

+30dB

Antialiasing filter 60Mhz+

Tunable reject filter centered on ICRF generator

freq.

RF probe

Raw RF signalRemove main

ICRF generator frequency

Increase SNR

Remove higher ICRF harmonics and other high

frequencies

Increase SNR and resolution

limited by 8bits cards

DigitizingDigital processing

FFT

Signal acquisition process

We want to observe the evolution of the frequencies during the whole shot

Specific method for triggering

Time Digital Controller

10ms

Generates TTL signal:Trigger Acqiris

Card

10ms: effect on time resolution

1500points

700 pulses

X 700 ≈1MB must be < Acqiris memory size

The solution chosen is a compromise between the resolution in frequency and the resolution in time

Digitizing

Effect on FFT resolution

Signal to digitize

3 – Experimental results

Back to outline


We observe three different types of signals in different conditions:

a) Ion Cyclotron Emission at the plasma edge during NBI heating

b) Ion Cyclotron Emission at the plasma edge during ICRF heating

c) Ion Cyclotron Emission at the plasma center during NBI heating



a) Ion Cyclotron emission at the plasma edge during NBI heating

b) Ion Cyclotron emission at the plasma edge during ICRF heating

c) Ion Cyclotron emission at the plasma center during NBI heating


a) Ion Cyclotron Emission from the plasma edge with NBI

+NI4+NI8

+NI5+NI1

NI3

(s)

(MW

)

Radiated power



2nd harmonic D

2nd harmonic He3

3rd harmonic D

4rd D/3rd He3

+NI4+NI8

+NI5+NI1

NI3

(s)

(MW

)

Radiated power

5th harmonic D

4nd harmonic He3

• We have a good correlation between the FFT of the signal and the theoretical ion cyclotron frequency of Deuterium (or alpha) and He3 in the midplane, 2cm outside the separatrix (r≈2.15m).

• No first harmonic present

• 2nd and 4th D-harmonics more intense

• Presence of the signature of a fusion product (He3) in the signal.

• No fine structure detected (but limitation of resolution)

• intermittence in the signal



Such signal detected only for for three shots (but not all the shots with NI were studied):

Parameter 24539 24541 24546

Bt (T) -1.78 -1,79 -1,72

It (MA) 0,85 0,82 0,76

Density H1 (1e19m-3) 6.24 4,42 3,17

NI Power (MW) 12 12 8

Relatively low magnetic field and current

High level of power (>8MW)

H-mode with type I ELMs

Neutral flux > 4.1014

Conditions of existence


a) Ion Cyclotron Emission from the plasma edge with NBICorrelation with MHD activity

- Interruption of ICE signal correlated with „Giant“ ELM (type I).

- MHD modes detected during ICE signal, interruption also correlated with ELM.

- Neutron rate affected by ELM: fusion reaction rate decrease during ELM (whole plasma affected by the loss of confinement).

- Correct sequence of phenomena still to be determined



Comparison with results from other machines: focus on JET and TFTR: these are the most typical and the most studied.

JET

Parameter value

Ip 3.1MA

Bt 2.8T

Ne(0) 3.6 1019m-3

NI Power 13MW

Te(0) 9.9keV

Ti(0) 18keV

Typical experimental parameters

• Experiments both with D and D-T NI injection.

• ICE measured with ICRF antenna connected to spectrum analyzer

• Frequencies match ΩDl=Ωαl (l: harmonic) at the edge in the midplane (3.9<R<4.1m).

• For l<8, even l-line more intense

• Fine structure appears: split into doublet and triplet (when l increases)

• For f>100MHz, continuum

• Same structure of spectrum both for D NI and T-D NI (No Triton line observed)

• Measured level of ICE power proportional to neutron flux

• ICE disappear with large amplitude ELM.

With D-TWith D







b) Ion Cyclotron Emission from the plasma edge with ICRF

(s)

(MW

)



(s)

(MW

)

1st harmonic H

2nd harmonic H

3rd harmonic H

ICRH

Radiated power

Main frequency Generator (filtered)

Harmonic Generator (filtered)

+



(s)

(MW

)

1st harmonic H

2nd harmonic H

3rd harmonic H

ICRH

Radiated power



Result of the modulation between 1st

harmonic H and main generator

frequency



(s)

(MW

)

1st harmonic H

2nd harmonic H

3rd harmonic H

ICRH

Radiated power



+

• We have a good correlation between the FFT of the signal and the theoretical ion cyclotron frequency of Hydrogen in the midplane, 2cm outside the separatrix (r≈2.15m).

• 1st and 3rd H-harmonics more intense

• Presence of the modulation between main generator frequency and 1st H-harmonic

• Fine structure and evolution of frequencies observed.


b) Ion Cyclotron Emission from the plasma edge with ICRFConditions of excitation

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

edge density (10e19m-3)

ICR

F P

ow

er (

MW

)

This plot the characteristics Power/ edge Density (average value) for all shots with ICRH in campaign 2009.

The conditions for excitation of frequencies seem to be a high level of ICRF power (>3MW) associated with low density plasma.

ICE signal

The signal is also sensitive to the presence of NBI heating.

NBI

ICRF

NBIFrequencies observed for minority heating D(H).

Only L-modes (no pure ICRH H-mode at low density possible due to sputtering problems)


b) Ion Cyclotron Emission from the plasma edge with ICRFCharacteristics of the ICE signal Frequency dependant on the magnetic field and on

the generator frequency.

It is not possible to determine which one has an influence on the ICE frequency since the generator frequency is tuned to the magnetic field to have heating at the center

Shot 23294

Shot 23515

Bt=-1.99T

Bt=-2.3T

Time(s)

Time(s)

23.5MHz

28MHz

36.5MHz

30MHz

Generator freq

Generator freq


b) Ion Cyclotron Emission from the plasma edge with ICRFCharacteristics of the ICE signal Splitting of frequencies.

Two types of splitting are observed:

- A large one: Δf≈900kHz

- An intermediate one: Δf≈100kHz

This kind of splitting is not observed for each shot with ICE.

Large splitting

Intermediate splitting An interesting observation that needs to be

confirmed and explained concerns the relation between splitting and time evolution of frequencies:

-When the ICE frequency does not change in time, there is no splitting: only one frequency is present in the spectrum

- When the ICE frequency changes with time: splitting is observed and we have several frequencies at a time.


b) Ion Cyclotron Emission from the plasma edge with ICRFComparison with Minority Ion Cyclotron Emission on JET [Cottrell00]

This is, to our knowledge, the only documented case of ICE detected with ICRF heating on a tokamak.

The spectrum reveals a frequency corresponding to ion cyclotron frequency of hydrogen (minority species). The ICE signal is correlated with a change of slope in the diamagnetic energy, that means a loss of fast ions in the plasma core.

Spectrum with and without ICE [Cottrell00]

Without ICE

With ICE

ICE correlated with loss of fast ions [Cottrell00]







b) Ion Cyclotron Emission from the plasma center with NBI



Radiated power

2nd harmonic D

NI3

1st harmonic D

When neutral beam is injected into the plasma, a frequency corresponding to the second harmonic of Deuterium at the plasma center appears transiently for a duration of about 80ms.

The level of signal is very low (maximum 150mV) in comparison with the edge ICE.



It the ion beam is modulated in power, the ICE signal reappears at each pulse. The frequency follows very accurately the ion cyclotron frequency at the center of the plasma.



Conditions of observation

This signal appeared for all shots of the campaign 2009 with NBI except for a few ones.

The ICE signal is observed only when tangential beams are injected: the few measurements with radial beams and current drive beams did not reveal any ICE signal. (see shot #24593)

The excitation of the frequency is not linked to a power threshold of the NBI: we can get a signal with only one beam at 2MW.



Characteristics of the signal

Splitting

When NBI is modulated in power, we can observe during some pulses, a ‘splitting’ of the ICE frequency: the main ICE frequency remains but a second frequency appears shifted of about 2MHz.

We haven’t found any correlation with other processes at stake in the plasma. However, the effect of ECE heating is still under investigation because this system is operated when this splitting occurs.

Shot 24631



Characteristics of the signal Intermittencies

There are some cases where NBI delivers steady power and yet, the ICE signal is intermittent and with a total duration of several hundred of milliseconds (instead of 80ms).



Characteristics of the signal Excitation of several harmonics

When adding a second beam to the first one, the second Deuterium harmonic disappear and the thrid one appears.

But we also have cases where 2nd and 3rd harmonics are simultaneously excited.

Jump from2nd to 3rd harmonic

NI3

+NI8

4 – ICE theories and interpretation

Back to outline

4 – ICE Theories

Suprathermal ICE at the edge: overview of the mechanism

Source of free energy available at the edge: inversion of fast ion population

V

V

Wedged ring distribution at the edge for fast ions

1

2 Resonance condition for energy transfer

Essential contribution of bulk ions in cold plasma approximation (even MHD). The wave propagation equation coupled to the plasma geometry makes it possible to compute the localized eigenmodes (CAE Compressional Alfven Eigenmodes). We obtain: position, frequency and k of the modes

3The distribution of fast ions is injected perturbatively in the anti-hermitian part to calculate the growing rate of the eigenmode.

This growing rate is associated with the resonant condition:

Eigenmodes localized at the edge

4 – ICE Theories

Fast ions distribution function

TRANSP results for JET: extension of orbit related to energy and pitch angle [Cottrell95]

1 2 constraints on energy and pitch angle

PassingLarge

extensionTrapped

V

Fast ions responsible

for ICEPitch angle

boundary for edge access

Trapped/passing

boundary V

4 – ICE Theories

Fast ions distribution function

The question is to know which species the fast ions are made of.

Experiments on JET show that the ICE intensity correlates with the neutron rate.

Correlation between ICE power and neutron rate on JET [Cottrell95]

-> protons are the drivers and the Doppler shift due to their large velocity drift is high enough to also excite half harmonics

-> protons are the drivers and half harmonics are excited by non linear mode coupling with energy redistribution between the different harmonics (that would also explain the similarity of spectra with D-T and D-D)

-> alpha particles (secondary products in D-D plasmas) are the drivers: their concentration is very low and the ICE has to be very sensitive to this concentration

f

Power

fcD 2fcD 3fcD 4fcD 5fcD 6fcD

fcP 2fcP 3fcP

fcα 2fcα 3fcα 4fcα 5fcα 6fcα

Energy transfer

Doppler

Theoretical energy spectrum

Primary fusion reactions

D + D -> 3He (0.82MeV) + n (2.45 MeV)D + D -> T (1.0 MeV) + p (3.0 MeV)

Secondary fusion reactions

3He + D -> p (14.6 MeV) + 4He (3.7MeV)T + D -> 4He (3.6MeV) + n (14.0 MeV)


2nd harmonic D

2nd harmonic He3

3rd harmonic D

4rd D/3rd He3

+NI4+NI8

+NI5+NI1

NI3

(s)

(MW

)

Radiated power

5th harmonic D

4nd harmonic He3

On ASDEX Upgrade

5 – Interpretation of results

On ASDEX Upgrade

Vertical central line

4 – ICE Theories

Determination of eigenmodes

1D case (cylinder): It is the simplest case considered but often used. It corresponds to an infinite aspect ratio, i.e., B is only dependent on the radius. Poloidal symmetry => poloidal wavenumber is discrete:

We take the Fast Wave equation in its straight geometry MHD form:‘inverse Fourier transform’

[Coppi86][Gorelenkov95]

[Hellsten04]

2

[Gorelenkov95]

Whispering Gallery modes

5 – Interpretation of results

On ASDEX Upgrade

We took the cylindrical model of eigenmodes presented in the theoretical section and we used a density profile model fitted to the data from the Lithium beam. We notice that we have a peaked profile (the same as in JET).

Comparison model – data for density profile

Solving the 1D field equation gives us the following result: we can have confined modes for high m (poloidal number).

The location of the mode (2.04m) is lower than the one obtained by matching the frequency (2.15). But the model is simple and the basic frequency matching does not take into account any Doppler shift.

Solution of the potential equation

Separatrix

4 – ICE Theories

Determination of eigenmodes

Toroidal case, high aspect ratio, circular profile:

The main tool used here is the eikonal representation:

We have a ε<<1 and 1/m<<1; thus, we can develop the eikonal in powers of 1/m and ε to give corrections due to toroidicity in the eikonal equation which is of the form:

We took here the cold plasma equation in complete cylindrical coordinates.

At the lowest order in 1/m and ε, the equation obtained can be approximated by a 2D harmonic oscillator, which means that the mode is still contained with a slight correction to the cylindrical case. But this is valid only under the condition that:

If we have coupling between radial and poloidal mode, a secular contribution is added and we lose the confinement of the mode.

This is better seen with the geometrical optics approximation (for short wavelength); The following equations are solved numerically:

[Coppi85], [Gorelenkov95]

Ray trajectory of contained mode with toroidal deformation [Coppi85]

Drifting ray trajectory [Coppi85]

4 – ICE Theories

Particles/Waves interactions

The plasma is described by the dielectric tensor:

=> Energy transfer and mode growth rate γ

2 groups of theories

Strong instability Weak instability

time

Growth

time

Growth

4 – ICE Theories


Strong instability The wave electric field is approximately polarized in the plane perpendicular to the magnetic field direction. The dispersion relation is then:

The dielectric tensor contains contributions from electrons (e), bulk ions (i) and energetic ions (α):

4 – ICE Theories

Particles/Waves interactions (3/10)

Maxwellian electron contribution:

Bulk ion contribution:

Fast ions contribution:

This is for the case with quasi-perpendicular propagation. If we add a parallel component to the wave vector, we get the effects of Landau and transit time damping.

It is calculated in the hot plasma case.

ζl represents the relative shift to the ion cyclotron frequency. If >>1, we have the cold plasma approximation. If ~1, hot plasma effects have to be taken into account with damping.

This is the source of the instability. The Π operator applied to the distribution function determines the stability of the interaction (sign of imaginary part).

The resonance condition: two terms play a role: v// and ωD. They determine the Doppler shift

4 – ICE Theories


Fast ions affect both the structure of the wave (real part of the dispersion relation) and the transfers of energy (imaginary part of the dispersion relation). The concentration of fast ions is small, so the growth rate of the excited modes. => use of perturbative analysis

Wave propagation [Fulop97]

Wave structure with fast ions

Case without fast ions

Case with fast ions

Fast wave (cold plasma)

Bernstein wave (hot plasma)

New component due to fast ions

k(cm-1)

ω/ωcα

Excitation


On ASDEX Upgrade

Alfven mode m²/r²·VA

4 – ICE Theories

Particles/Waves interactions (5/10)

Actually, there are two ways to handle the local theory: each leads to different types of excited waves and thus, to different growth rates for each harmonics.

k//=0 approach [Fulop]

Here, the Doppler shift is only due to the toroidal drift of the fast ions. The positive and negative poloidal modes account for the doublet splitting observed on JET ICE.

The alphas are responsible of the excitation and they can excite all harmonics. The growth rate is sufficiently high to be coherent with the local approximation. According to Fulop, it is not the case the k//≠0 approach.

k//<<1 approach [Dendy, Coppi]

Here, the Doppler shift is due to the parallel velocity of the fast ions. Details of the distribution function account for the excitation of all harmonics and the splitting in doublets.

The shape of the spectrum is very dependent on the propagation angle.

5 – Next steps

Back to outline

5 – Next steps

- The signal observed matches well with the ICE frequency.

- The signal is correlated with the global neutron rate

- The signal is correlated with MHD events

We collected some pieces of evidence that the signal measured corresponds to ICE

We have now three targets we aim at:

A- to confirm that the signal is ICE excited by fast ions

B – to use ICE as a tool to investigate fast ions and MHz eigenmodes

C – to manipulate the eigenmodes and their interactions with the fast ions

5 – Next steps

To conclude

This preliminary study shows that the signal observed is very probably the Ion Cyclotron Emission resulting from the interaction between fast ions and compressional alfven eigenmodes.

Further work targets at describing the particles population involved in this interaction and improve the measurement for a better support of the existing theories.

Understanding ICE is important because:

- It can be used as a diagnostics for the fast ions at the edge

- It can perturb the arc detection systems based on frequency signature

- It can enhance the interaction of the ICRF fast waves at the edge with other waves leading to spurious power absorption

Outline

1 – Motivation ->

2 - Experimental setup ->

3 - Experimental results on ASDEX-Upgrade ->

4 - Overview and interpretation of ICE theories ->

5 - Next steps ->

References: ICE

[Batchelor89] Batchelor, D. B., E. F. Jaeger, und P. L. Colestock. 1989. Ion cyclotron emission from energetic fusion products in tokamak plasmas---A full-wave calculation. Physics of Fluids B: Plasma Physics 1, no. 6 (Juni 0): link. [Belikov95] Belikov, V.S., Ya.I. Kolesnichenko, und O.A. Silivra. 1995. Resonance destabilization of fast magnetoacoustic eigenmodes by trapped particles and ion cyclotron emission in tokamak reactors. Nuclear Fusion 35, no. 12: 1603-1608. link. [Cauffman95a] Cauffman, S., und R. Majeski. 1995. Ion cyclotron emission on the Tokamak Fusion Test Reactor. In Proceedings of the tenth topical conference on high temperature plasma diagnostics , 66:817-819. link.[Caufman95b] Cauffman, S., R. Majeski, K.G. McClements, und R.O. Dendy. 1995. Alfvenic behaviour of alpha particle driven ion cyclotron emission in TFTR. Nuclear Fusion 35, no. 12: 1597-1602. link. [Coppi93] Coppi, B. 1993. Origin of radiation emission induced by fusion reaction products. Physics Letters A 172, no. 6 (Januar 18): 439-442. link. [Coppi86] Coppi, B., S. Cowley, R. Kulsrud, P. Detragiache, und F. Pegoraro. 1986. High-energy components and collective modes in thermonuclear plasmas. Physics of Fluids 29, no. 12 (Dezember 0): 4060-4072. link. [Cottrell00] Cottrell, G. A. 2000. Identification of Minority Ion-Cyclotron Emission during Radio Frequency Heating in the JET Tokamak. Physical Review Letters 84, no. 11 (März 13): 2397. link. [Cottrell93] Cottrell, G.A., V.P. Bhatnagar, O. Da Costa, R.O. Dendy, J. Jacquinot, K.G. McClements, D.C. McCune, M.F.F. Nave, P. Smeulders, und D.F.H. Start. 1993. Ion cyclotron emission measurements during JET deuterium-tritium experiments. Nuclear Fusion 33, no. 9: 1365-1387. link. [Dendy92] Dendy, R. O., C. N. Lashmore-Davies, und K. F. Kam. 1992. A possible excitation mechanism for observed superthermal ion cyclotron emission from tokamak plasmas. Physics of Fluids B: Plasma Physics 4, no. 12 (Dezember 0): 3996-4006. link. [Dendy93] Dendy, R. O., C. N. Lashmore-Davies, und K. F. Kam. 1993. The magnetoacoustic cyclotron instability of an extended shell distribution of energetic ions. Physics of Fluids B: Plasma Physics 5, no. 7 (Juli 0): 1937-1944. link. [Dendy94a] Dendy, R. O., C. N. Lashmore-Davies, K. G. McClements, und G. A. Cottrell. 1994. The excitation of obliquely propagating fast Alfv[e-acute]n waves at fusion ion cyclotron harmonics. Physics of Plasmas 1, no. 6 (Juni 0): 1918-1928. link. [Dendy94b] Dendy, R. O., K. G. McClements, C. N. Lashmore-Davies, R. Majeski, und S. Cauffman. 1994. A mechanism for beam-driven excitation of ion cyclotron harmonic waves in the Tokamak Fusion Test Reactor. Physics of Plasmas 1, no. 10 (Oktober 0): 3407-3413. link. [Dendy95] Dendy, R.O., K.G. McClements, C.N. Lashmore-Davies, G.A. Cottrell, R. Majeski, und S. Cauffman. 1995. Ion cyclotron emission due to collective instability of fusion products and beam ions in TFTR and JET. Nuclear Fusion 35, no. 12: 1733-1742. link. [Fraboulet97] Fraboulet, D., und A. Becoulet. 1997. Energy description of wave-plasma interaction in the ion cyclotron range of frequency: Application to fast wave absorption and emission in tokamaks. Physics of Plasmas 4, no. 12 (Dezember 0): 4318-4330. link. [Fredrickson04] Fredrickson, E. D., N. N. Gorelenkov, und J. Menard. 2004. Phenomenology of compressional Alfv[e-acute]n eigenmodes. Physics of Plasmas 11, no. 7 (Juli 0): 3653-3659. link. [Fulop00] Fulop, T., M. Lisak, Ya. I. Kolesnichenko, und D. Anderson. 2000. The radial and poloidal localization of fast magnetoacoustic eigenmodes in tokamaks. Physics of Plasmas 7, no. 5 (Mai 0): 1479-1486. link. [Gorelenkov95a] Gorelenkov, N. N., und C. Z. Cheng. 1995. Excitation of Alfv[e-acute]n cyclotron instability by charged fusion products in tokamaks. Physics of Plasmas 2, no. 6 (Juni 0): 1961-1971. link. [Gorelenkov02a] Gorelenkov, N. N., C. Z. Cheng, und E. Fredrickson. 2002. Compressional Alfven eigenmode dispersion in low aspect ratio plasmas. Physics of Plasmas 9, no. 8: 3483-3488. link. [Gorelenkov95b] Gorelenkov, N.N., und C.Z. Cheng. 1995. Alfven cyclotron instability and ion cyclotron emission. Nuclear Fusion 35, no. 12: 1743-1752. link. [Gorelenkov02b] Gorelenkov, N.N., C.Z. Cheng, E. Fredrickson, E. Belova, D. Gates, S. Kaye, G.J. Kramer, R. Nazikian, und R. White. 2002. Compressional Alfvén eigenmode instability in NSTX. Nuclear Fusion 42, no. 8: 977-985. link. [Heidbrink06] Heidbrink, W.W., E.D. Fredrickson, N.N. Gorelenkov, T.L. Rhodes, und M.A. Van Zeeland. 2006. Observation of compressional Alfvén eigenmodes (CAE) in a conventional tokamak. Nuclear Fusion 46, no. 2: 324-334. link. [Hellsten06] Hellsten, T., K. Holmstrom, T. Johnson, T. Bergkvist, und M. Laxaback. 2006. On ion cyclotron emission in toroidal plasmas. Nuclear Fusion 46, no. 7: S442-S454. link. [Hellsten03] Hellsten, T., und M. Laxaback. 2003. Edge localized magnetosonic eigenmodes in the ion cyclotron frequency range. Physics of Plasmas 10, no. 11 (November 0): 4371-4377. link. [Kolesnichenko98] Kolesnichenko, Ya.I., T. Fulop, M. Lisak, und D. Anderson. 1998. Localized fast magnetoacoustic eigenmodes in tokamak plasmas. Nuclear Fusion 38, no. 12: 1871-1879. link. [Kolesnichenko00] Kolesnichenko, Ya.I., M. Lisak, und D. Anderson. 2000. Superthermal radiation from tokamak plasmas caused by cyclotron magnetoacoustic instability. Nuclear Fusion 40, no. 7: 1419-1427. link. [Mahajan83] Mahajan, S. M., und David W. Ross. 1983. Spectrum of compressional Alfven waves. Physics of Fluids 26, no. 9: 2561-2564. link. [McClements99] McClements, K. G., C. Hunt, R. O. Dendy, und G. A. Cottrell. 1999. Ion Cyclotron Emission from JET D-T Plasmas. Physical Review Letters 82, no. 10 (März 8): 2099. link. [Penn98] Penn, G., C. Riconda, und F. Rubini. 1998. Description of contained mode solutions to the relevant magnetosonic-whistler wave equations. Physics of Plasmas 5, no. 7 (Juli 0): 2513-2524. link.

Back to outline

http://link.aip.org/link/?PFB/1/1174/1

http://www.iop.org/EJ/abstract/0029-5515/35/12/I23

http://link.aip.org/link/?RSI/66/817/1


http://www.sciencedirect.com/science/article/B6TVM-46X9N8C-T/2/d78ce21251db99d7c8de5f3f0bff0a90

http://link.aip.org/link/?PFL/29/4060/1

http://link.aps.org/abstract/PRL/v84/p2397




http://link.aip.org/link/?PHP/1/1918/1









http://www.iop.org/EJ/abstract/0029-5515/42/8/306/

http://www.iop.org/EJ/abstract/0029-5515/46/2/016

http://www.iop.org/EJ/abstract/0029-5515/46/7/S07/





http://link.aps.org/abstract/PRL/v82/p2099


References: miscellaneous

Arc DetectionR. D'Inca, A. Onyshchenko, F. Braun, G. Siegl, V. Bobkov, H. Faugel, J.-M. Noterdaeme, Characterization of arcs in ICRF transmission lines, Fusion Engineering and Design, Volume 84, Issues 2-6, Proceeding of the 25th Symposium on Fusion Technology - (SOFT-25), June 2009, Pages 685-688 [link]R. D'Inca, S. Assas, V. Bobkov, F. Braun, B. Eckert, and J.-M. Noterdaeme, Comparison of Different Arc Detection Methods during Plasma Operations with ICRF Heating on ASDEX Upgrade AIP Conf. Proc. 933, 203 (2007) [link]

Fast ions[GarciaMunoz09] Garcia-Munoz – MHD induced fast-ion losses on ASDEX Upgrade – Nucl. Fusion 49 (2009) [link][Mantsinen07] Mantsinen et al. - Analysis of ICRF-Accelerated Ions in ASDEX Upgrade - Radio Frequency Power in Plasmas: 17th Topical Conference on Radio Frequency Power in Plasmas – AIP 933 [link]W.W. Heidbrink and G.J. Sadler, The behaviour of fast ions in tokamak experiments, Nuclear Fusion, April 1994 Volume: 34 Start Page: 535 [link]

Generalized GyrokineticsBerk, H. L., C. Z. Cheng, M. N. Rosenbluth, und J. W. Van Dam. 1983. Finite Larmor radius stability theory of ELMO Bumpy Torus plasmas. Physics of Fluids 26, no. 9: 2642-2651. doi:10.1063/1.864456. [link].Chen, Liu, und Shih-Tung Tsai. 1983a. Linear oscillations in general magnetically confined plasmas. Plasma Physics 25, no. 4: 349-359. [link].Chen, Liu. 1983b. Electrostatic waves in general magnetic field configurations. Physics of Fluids 26, no. 1 (Januar 0): 141-145. doi:10.1063/1.863992. [link].Lee, X. S., J. R. Myra, und P. J. Catto. 1983. General frequency gyrokinetics. Physics of Fluids 26, no. 1 (Januar 0): 223-229. doi:10.1063/1.864011. [link].

ICRF HeatingM. Porkolab et. 1998. Recent progress in ICRF physics. Plasma Physics and Controlled Fusion 40, no. 8A: A35-A52. [link].Becoulet, A., D. J. Gambier, und A. Samain. 1991. Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas. Physics of Fluids B: Plasma Physics 3, no. 1 (Januar 0): 137-150. doi:10.1063/1.859951. [link].Eester, D. Van. 1999. Trajectory integral and Hamiltonian descriptions of radio frequency heating in tokamaks. Plasma Physics and Controlled Fusion 41, no. 7: L23-L33. [link].Eriksson, L.-G., und P. Helander. 1994. Monte Carlo operators for orbit-averaged Fokker--Planck equations. Physics of Plasmas 1, no. 2 (Februar 0): 308-314. doi:10.1063/1.870832. [link].Eriksson, L.-G., M. J. Mantsinen, T. Hellsten, und J. Carlsson. 1999. On the orbit-averaged Monte Carlo operator describing ion cyclotron resonance frequency wave--particle interaction in a tokamak. Physics of Plasmas 6, no. 2 (Februar 0): 513-518. doi:10.1063/1.873195. [link].Hellsten, T., T. Johnson, J. Carlsson, L.-G. Eriksson, J. Hedin, M. Laxaback, und M. Mantsinen. 2004. Effects of finite drift orbit width and RF-induced spatial transport on plasma heated by ICRH. Nuclear Fusion 44, no. 8: 892-908. [link].Johnson, T., T. Hellsten, und L.-G. Eriksson. 2006. Analysis of a quasilinear model for ion cyclotron interactions in tokamaks. Nuclear Fusion 46, no. 7: S433-S441. [link].Kaufman, Allan N. 1972. Quasilinear Diffusion of an Axisymmetric Toroidal Plasma. Physics of Fluids 15, no. 6 (Juni 0): 1063-1069. doi:10.1063/1.1694031. [link].Kerbel, G. D., und M. G. McCoy. 1985. Kinetic theory and simulation of multispecies plasmas in tokamaks excited with electromagnetic waves in the ion-cyclotron range of frequencies. Physics of Fluids 28, no. 12 (Dezember 0): 3629-3653. doi:10.1063/1.865319. [link].Koch, R., P. Descamps, D. Lebeau, A. M. Messiaen, D. Van Eester, und R. R. Weynants. 1988. A comparison between ICRF theory and experiment. Plasma Physics and Controlled Fusion 30, no. 11: 1559-1570. [link].Koch, R., P. U. Lamalle, und D. Van Eester. 1998. Progress in RF theory: a sketch of recent evolution in selected areas. Plasma Physics and Controlled Fusion 40, no. 8A: A191-A214. [link].Lamalle, P. U. 1997. On the radiofrequency response of tokamak plasmas. Plasma Physics and Controlled Fusion 39, no. 9: 1409-1460. [link].


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Emission in the range of Ion Cyclotron Frequencies on ASDEX-Upgrade