f. nabais - vilamoura - november 2004 internal kink mode stability in the presence of icrh driven...
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F. Nabais - Vilamoura - November 2004
Internal kink mode stabilityin the presence of ICRH driven
fast ions populations
F. Nabais, D. Borba, M. Mantsinen, M.F. Nave,
S. Sharapov and JET-EFDA contributors
F. Nabais - Vilamoura - November 2004
Outline
Internal kink mode n=1, m=1Effect of ICRH driven populations on
HOTMHDMHD WWW
Perturbative method
Variational method
Quantitative results(F. Porcelli et al. Phys.
Plasmas,1 (3), 470 (1994))
Sawteeth
FishbonesSawteeth,
(R. White et al. Phys. Fluids B 2, 745 (1990))
Qualitative results
MHD energy functional
Fast ions energy
functional
Fast ions
Objective : Explain experimental observations in JET
F. Nabais - Vilamoura - November 2004
HOTI
P
F
c
ZedPdEd
mW adHOT 2
22
Perturbative method
HOTMHD WWW
eigenfunction perturbation
(F. Porcelli et al. Phys. Plasmas,1 (3), 470 (1994))
Relevant equations, which include Finite Orbit Width effects,
Adiabatic part - destabilizing
naHOT
adHOTHOT WWW
F. Nabais - Vilamoura - November 2004
k
HOTHOT E
W
Re
2
1D
Perturbative method
CASTOR-K HOTW
Non-adiabatic part - stabilizing
p b
p
bnaHOT pn
Y
E
FndPdEd
mW
2
2
22
Sawteeth
Safety factor on axis
Fast ions temperature
Location of the ICRH resonant layer
Fast ions radial profile
F. Nabais - Vilamoura - November 2004
adHOTW
HOTW
Non-adiabatic
Adiabatic part of(Preliminar results)
Destabilizing
increases with THOT
HOT
Effect of the ICRH fast ions on sawteeth
Blue regions: stabilizing
Red regions: destabilizing
as function of q0 and THOT
on-axis heating
F. Nabais - Vilamoura - November 2004
Experiments with low plasma densities
THOT ~PICRH
ne
Sawteeth destabilization occurred when:
ICRH power increases Plasma density decreases
Application to experiments
Non-adiabatic HOT as function of THOT
F. Nabais - Vilamoura - November 2004
The stabilizing effect of the non-adiabatic part of decreases as THOT increases, so this mechanism for
sawtooth stabilization is weakened.
The destabilizing effect associated with the adiabatic part of is increased.
Numerical results show:
HOTW
HOTW
Application to experiments
The non-adiabatic part of HOTW is dominant.
Sawteeth destabilization coincides with an increase in THOT
F. Nabais - Vilamoura - November 2004
Variational method
0
41
4582/34/9
212/3
A
iHOTMHD
iWW
Solutions of the internal kink
dispersion relation:
Low frequency
High frequency
Kink Branch
Ion Branch
Fishbone Branch
Sawteeth
Low frequency (diamagnetic) fishbones
High frequency (precessional) fishbones
(R. White et al. Phys. Fluids B 2,
745 (1990))
(B. Coppi and F. Porcelli P. R.L, 57,
2272 (1986))ω ≈ ω*i
ω ≈ <ωDhi>
(L. Chen et. al P. R.L, 52, 1122 (1984))(Ideal limit)
F. Nabais - Vilamoura - November 2004
2
1
2
3
2
32
1
Re2
1
4
3
DDDDD
i
DDI Z
2
5
/2
1
214
3
DD
i
DDD
Ah
De
Marginal equation ω=real, ideal limit, ICRH population
Iih
Stability governed mainly by
Ideal (MHD) growth rate
Diamagnetic frequency
Fast particles beta
Determination of the regions of stability
MHDAI W
F. Nabais - Vilamoura - November 2004
Magnetic spectrogram from JET
Precessional Fishbones
Diamagnetic Fishbones
Hybrid Fishbones
Sawtooth Crash
F. Nabais - Vilamoura - November 2004
I
i
h
Increases
Increases
Decreases during a burst
Increases between bursts
In between crashes the q=1 surface expands
In between crashes the ion bulk profile peaks
if : 3 kHz 20 kHz
Variation of the relevant parameters
F. Nabais - Vilamoura - November 2004
Ion branch
Fishbone branch
βh decreases during the burst
Diamagnetic behaviour
Precessional
behaviour
Coalescent Ion-Fishbone
branch
h
0
(R. White et al. Phys. Fluids B 2, 745 (1990))
Solutions of the dispersion relation
ω*i2
ω*i1
ω*i1< ω*i2
F. Nabais - Vilamoura - November 2004
Time (s)
Ma
gn
etic
pe
rtu
rba
tio
n
Magnetic perturbation for an hybrid fishbone
F. Nabais - Vilamoura - November 2004
Ion mode
Fishbone mode
Coalescent ion-fishbone mode
Low frequency fishbones
High frequency fishbones
Hybrid fishbones
Both types of fishbones occuring simultaneously
(Gorolenkov et al. “Fast ions effects on fishbones and n=1 kinks in JET simulated by a non-perturbative NOVA-KN code, this conference)
Modes and regimes
F. Nabais - Vilamoura - November 2004
Summary
Perturbative Method- Accurate calculation of HOT for a realistic geometry- Only for the “kink mode”
Variational Method- All branches of the dispersion relation
- Simplified geometry and fast ions’ distribution function, suitable only for a qualitative approach
- Predicts changes in instabilities behaviour knowing the relevant parameters
Stabilizing term vanishes for high fast ions temperatures
Hybrid fishbones and both types of fishbones occuring simultaneously
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