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

MI

I

2i

I

hch h

Regions of stability

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

hch

MI

Variation of the regions of stability

2i

I

h

I

F. Nabais - Vilamoura - November 2004

Regions of stability

I

h

2i

I

MI

hch

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