The influence of non-resonant perturbation fields: Modelling results and

Proposals for TEXTOR experiments

S. Günter, V. Igochine, K. Lackner, Q. YuIPP Garching

• Resistive wall modes and error field amplification• Error field amplification and plasma rotation• Suppression of neoclassical tearing modes by external helical fields

Concept of advanced tokamaks

Non-monotonic current profile

Turbulence suppression

high pressure gradients

large bootstrap current

fBS= N A q 0.8 … 0.9

N 4 … 5

MHD stability ?

Ultimate limit to maximum N is external kink mode

External kink mode can be stabilised by ideal walls

n·B|wall = 0

n·B|wall = 0

For optimised current profiles(avoid double low order rational surfaces of same helicity)

Günter et al., NF 2000

External kink mode in AUG advanced scenarios

Closeness to rational qa destabilising Good agreement between theory and experiment

eigenfunction

Stabilising influence of an ideal conducting wall

Closed wall in distance rw from plasma can be strongly stabilising, especially for:

- broad current and pressure profiles- strong shaping of plasma cross section

3d geometry of ideally conducting walls

CAS3D: First code dealing with 3D wall and 3D plasma:

Destabilising effect of wall resistivity: RWMs

Garofalo et al., PRL 1999

Simple model for RWMs and error field amplification

Fitzpatrick´s (PoP 9(2002) 3459) analytical (inertial layer) model

: stability parameter >0: ideal kink mode stabilised by infinitely conducting wall<0: in absence of rotation plasma is stable

Plasma rotation

Instability driveof plasma mode increases

Effect of rotation for varying wall distance

a rw

rw

ideal („plasma“) mode unstable

detailed shape of marginal curve depends on plasma (dissipation) model

torque balance between mirror current forces and viscous drag (or inertia) determines mode rotation frequency

can be modified by:- distance of wall (0 < <1) at given instability drive

d/dc

increasing wall distance reduces coupling, perturbation can start slipping with respect to wall rotation stabilizes mode

Re() [wall frame]

Effect of rotation for varying instability drive

can be modified by:- variation of the MHD instability drive at given wall distance

rotation destabilizes plasma in MHD stable region:

electromagnetic coupling to wall opens relative velocity plasma-wall to Kelvin-Helmholtz drive (inertia needed)

marginal curve corresponds to error field amplification condition (resistive wall mode can be interpreted to error field amplification of the induced wall-current field)

more unstable plasma has larger ratio of field amplitude in plasma to wall => reduced wall coupling allows slip and rotational stabilization

Numerical treatment of RWMs anderror field amplification

In realistic geometry (coupling to internal resonances):

• MARS (Bondeson)

• VALEN (Bialek, Boozer)

• CASTOR-A (Holties, Kerner)

- response to frequency dependent external perturbation field - modified to include differential plasma rotation, viscosity- resistive wall included (so far high resistivity only)

Numerical results: Error field amplification

Here for comparison with simple analytical theory:• frequency dependent external (3,1) perturbation field (qa < 3)• no internal resonances, no viscosity

Re P

jant B cos ~

(torque onto plasma)

1/

towards marginal stability

Increasing wall distance

1/

/ A

0 0.01 0.02 0.03

Change in plasma stability by varying distance of ideally conducting wall

Numerical results: Error field amplification

Good agreement with analytical model for ideal plasma (scan in wall distance)

~

Maximum of absorbed power

Here for comparison with simple analytical theory:• frequency dependent external (3,1) perturbation field (qa < 3)• no internal resonances, no viscosity

-W~2pl

Numerical results: Error field amplification

Good agreement with analytical model for ideal plasma (scan in N)

Maximum of absorbed power

Here for comparison with simple analytical theory:• frequency dependent external (3,1) perturbation field (qa < 3)• no internal resonances, no viscosity

Numerical results: torque on plasma

Re P

jant B cos ~tor

Torque on the plasma due to external error fields:

1/

~

Maximum torque

Influence of error fields on plasma rotation

reduction in resonant frequency,increasing torque

increase in , mode growth reduction in plasma frequency

59223Saddle current[A]

3.4li

N(%)

br(0o)

br(90o)

Signal which sees no vacuum (or low N) pick-up clearly rises as approaches ideal limit

PNBI[MW]

NB due to low field Bt=1T and high NBI alfven~ 4%

Experiments on error field amplification on JET

Influence of error fields on plasma rotation

Proposals for error field amplification experiments on TEXTOR – comparisons with theory

Frequency dependence in error field amplification:

• discharges with qa<3 (and qa>3 for comparison), low li• scan in N/plasma rotation within one discharge, measure (3,1) amplitude increase compared to vacuum case• repeat for different frequency of antenna current• comparison with code calculations possible

Influence of error fields on plasma rotation:

• compare torque onto plasma with theory (with and without q=3 surface) for different coil current frequencies and plasma pressures

Proposals for resistive wall mode experiments onTEXTOR

Develop scenarios with external (3,1) RWM mode

• vacuum vessel: rw/a = 1.35, w = 14 ms• try to stabilize RWM by rotating external (3,1) perturbation fields (compare required rotation velocity with theory)

Physics of neoclassical tearing modes (NTMs)

jBS p

Magnetic islands driven by the loss of bootstrap current inside island

Helical current parallel to plasma currentdrives magnetic islands unstable

Interaction of NTMs with different helicity

No simultaneous large NTMs of different helicities

Stabilising effect of additional helical field

For finite perpendicular heat conductivity helical field perturbation reducesBS current perturbation caused by single magnetic island

Contour plots of BS current perturbation

Single magnetic island with external perturbation field

Stabilization of NTMs by external error fields

DIII-D: suppression of (3,2) NTM onset successful, but strong reduction in plasma rotation observed

n=3 perturbation field

Stabilization of NTMs by external error fields

On TEXTOR: rotating perturbation fields possible

• (3,2) NTM stabilization by external (3,1) fields

Stabilization of NTMs by external error fields

On TEXTOR: rotating perturbation fields possible

• NTM stabilization by external (3,1) fields for qa < 3

• if perturbation field too small use conditions with error field amplifications

• Influence plasma rotation by external fields, study effect on NTM stability

Conclusions

“Rotating” external perturbation fields of a single helicity opens new possibilities for MHD experiments on TEXTOR:

• error field amplification experiments, comparison with theory - frequency dependence of error field amplification - influence on plasma rotation

• Resistive wall mode studies

• Stabilization of NTMs by external perturbation fields

Newcomb criterion

Cylindrical plasma: pointing vector into vacuum region ~ - ’|r=a

For zero growth rate (ok for RWMs) it describes the energy released from plasma from infinitely slow perturbation (no energy converted to kinetic energy)

wall position

rplasma edge

1

0

r(=0) closer to plasma the larger ’|r=a

(the more unstable the smaller r(=0)

more unstable

Error field amplification influences plasma rotation

Error field amplification reduced plasma rotation RWM growth

Strait et al., IAEA 2002

Critical Rotation Scaling

Strait et al., IAEA 2002