emission in the range of ion cyclotron frequencies on asdex-upgrade r. dinca – september 2009 icrf...
TRANSCRIPT
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
3 – Experimental results
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
3 – Experimental results
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
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
+NI4+NI8
+NI5+NI1
NI3
(s)
(MW
)
Radiated power
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
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
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
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
3 – Experimental results
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
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
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
3 – Experimental results
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
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
(s)
(MW
)
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
(s)
(MW
)
1st harmonic H
2nd harmonic H
3rd harmonic H
ICRH
Radiated power
Main frequency Generator (filtered)
Harmonic Generator (filtered)
+
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
(s)
(MW
)
1st harmonic H
2nd harmonic H
3rd harmonic H
ICRH
Radiated power
Main frequency Generator (filtered)
Harmonic Generator (filtered)
Result of the modulation between 1st
harmonic H and main generator
frequency
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
(s)
(MW
)
1st harmonic H
2nd harmonic H
3rd harmonic H
ICRH
Radiated power
Main frequency Generator (filtered)
Harmonic Generator (filtered)
+
• 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.
3 – Experimental results
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)
3 – Experimental results
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
3 – Experimental results
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.
3 – Experimental results
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]
3 – Experimental results
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
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
3 – Experimental results
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.
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
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.
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
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.
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
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
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
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).
3 – Experimental results
b) Ion Cyclotron Emission from the plasma center with NBI
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)
3 – Experimental results
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
Particles/Waves interactions
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
Particles/Waves interactions
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
3 – Experimental results
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
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]
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