Transcript Document

ICRF Group
Emission in the range of Ion
Cyclotron Frequencies on
ASDEX-Upgrade
R. D’Inca – September 2009
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).
Signal acquisition process
Sun
workstation
Acqiris
rack
Low noise
preamplifier
Antialiasing
filter 60Mhz+
+30dB
Digital
processing
FFT
Digitizing
We want to observe the evolution of
the frequencies during the whole shot
Increase SNR
and resolution
limited by 8bits
cards
Remove higher
ICRF harmonics
and other high
frequencies
Tunable reject
filter centered on
ICRF generator
freq.
Remove main
ICRF generator
frequency
Increase SNR
Generates TTL signal:
Trigger
10ms
700 pulses
Raw RF
signal
Specific method for triggering
10ms: effect on time resolution
Time Digital
Controller
RF probe
Digitizing
Acqiris
Card
1500
X 700
points
Effect on FFT resolution
Signal
to
digitize
The solution chosen is
a compromise
between the resolution
in frequency and the
resolution in time
≈1MB must be < Acqiris
memory size
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
(MW)
a) Ion Cyclotron Emission from the plasma edge with NBI
+NI4
+NI8
+NI5
+NI1
NI3
Radiated
power
(s)
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
• 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).
4nd harmonic He3
5th harmonic D
4rd D/3rd He3
• No first harmonic present
3rd harmonic D
2nd harmonic He3
2nd harmonic D
• 2nd and 4th D-harmonics more intense
• Presence of the signature of a fusion
product (He3) in the signal.
(MW)
• No fine structure detected (but
limitation of resolution)
+NI4
+NI8
+NI5
+NI1
NI3
Radiated
power
(s)
• intermittence in the signal
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
Conditions of existence
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
 Relatively low magnetic field and current
It (MA)
0,85
0,82
0,76
High level of power (>8MW)
Density H1 (1e19m-3)
6.24
4,42
3,17
 H-mode with type I ELMs
NI Power (MW)
12
12
8
 Neutral flux > 4.1014
3 – Experimental results
a) Ion Cyclotron Emission from the plasma edge with NBI
Correlation 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
• Experiments both with D and D-T NI
injection.
Typical experimental
parameters
Parameter
value
Ip
3.1MA
Bt
2.8T
Ne(0)
1019m-3
3.6
• 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)
NI Power
13MW
• For f>100MHz, continuum
Te(0)
9.9keV
Ti(0)
18keV
• 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-T
With 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
(MW)
b) Ion Cyclotron Emission from the plasma edge with ICRF
(s)
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
3rd harmonic H
Harmonic Generator
(filtered)
2nd harmonic H
Main frequency
Generator (filtered)
+
(MW)
1st harmonic H
Radiated
power
ICRH
(s)
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
3rd harmonic H
Harmonic Generator
(filtered)
Result of the
modulation
between 1st
harmonic H and
main generator
frequency
2nd harmonic H
Main frequency
Generator (filtered)
(MW)
1st harmonic H
Radiated
power
ICRH
(s)
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
• 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).
3rd harmonic H
Harmonic Generator
(filtered)
• 1st and 3rd H-harmonics more intense
2nd harmonic H
Main frequency
Generator (filtered)
+
1st harmonic H
• Presence of the modulation between
main generator frequency and 1st Hharmonic
(MW)
• Fine structure and evolution of
frequencies observed.
Radiated
power
ICRH
(s)
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
Conditions of excitation
6
This plot the characteristics Power/ edge
Density (average value) for all shots with ICRH
in campaign 2009.
5
The conditions for excitation of frequencies
seem to be a high level of ICRF power (>3MW)
associated with low density plasma.
ICRF Power (MW)
4
3
2
The signal is also sensitive to the presence of
NBI heating.
1
0
0
1
2
3
4
5
6
7
8
9
edge density (10e19m-3)
ICRF
Frequencies observed for minority heating D(H).
Only L-modes (no pure ICRH H-mode at low
density possible due to sputtering problems)
NBI
NBI
ICE
signal
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
Characteristics of the ICE signal
Shot 23294
Generator freq
30MHz
23.5MHz
Bt=-1.99T
Time(s)
Shot 23515
Generator freq
36.5MHz
28MHz
Bt=-2.3T
Time(s)
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
3 – Experimental results
b) Ion Cyclotron Emission from the plasma edge with ICRF
Characteristics 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.
Intermediate
splitting
Large
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 ICRF
Comparison 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.
Without ICE
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.
With ICE
Spectrum with and without ICE [Cottrell00]
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
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.
2nd harmonic D
1st harmonic D
Radiated power
NI3
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
Shot 24631
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.
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
+NI8
NI3
4 – ICE theories and interpretation
Back to outline
4 – ICE Theories
Suprathermal ICE at the edge: overview of the mechanism
1
Source of free energy available at the edge: inversion of fast ion population
V
V
Wedged ring distribution at
the edge for fast ions
2
Eigenmodes localized at the edge
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
3
Resonance condition for energy transfer
The 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:
4 – ICE Theories
1
Fast ions distribution function
Passing
Large
extension
2 constraints on energy and pitch angle
Trapped
TRANSP results for JET: extension of orbit related
to energy and pitch angle [Cottrell95]
V
Fast ions
responsible
for ICE
Trapped/
passing
boundary
Pitch angle
boundary for
edge access
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.
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)
Correlation between ICE power and neutron rate
on JET [Cottrell95]
Power
-> 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
Energy
transfer
fcP
2fcP
3fcP
Doppler
fcD
2fcD 3fcD 4fcD 5fcD 6fcD
fcα
2fcα 3fcα 4fcα 5fcα 6fcα
Theoretical energy spectrum
f
3 – Experimental results
On ASDEX Upgrade
4nd harmonic He3
5th harmonic D
4rd D/3rd He3
(MW)
3rd harmonic D
2nd harmonic He3
2nd harmonic D
+NI4
+NI8
+NI5
+NI1
NI3
Radiated
power
(s)
5 – Interpretation of results
On ASDEX Upgrade
Vertical central line
4 – ICE Theories
2
Determination of eigenmodes
1D case (cylinder):
[Coppi86]
[Gorelenkov95]
[Hellsten04]
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’
[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).
Separatrix
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
4 – ICE Theories
Determination of eigenmodes
Toroidal case, high aspect
ratio, circular profile:
[Coppi85], [Gorelenkov95]
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.
Ray trajectory of contained mode with
toroidal deformation [Coppi85]
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:
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
Growth
Growth
time
time
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:
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.
Fast ions contribution:
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 structure with fast ions
Case without
fast ions
Fast wave
(cold plasma)
ω/ωcα
Bernstein wave
(hot plasma)
Excitation
New component
due to fast ions
k(cm-1)
Wave propagation [Fulop97]
Case with
fast ions
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
We collected some pieces of evidence that the signal measured corresponds to ICE
- 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 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 Detection
R. 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 Gyrokinetics
Berk, 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 Heating
M. 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: 15591570. [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].