Tearing Parity Microturbulent Drift Modes on NSTX

Martha Redi

NSTX Results Review9/21/04

W. Dorland, U. Maryland, J. Baumgaertel, U. Washington (SULI)S. Kaye, R. Bell, D. Gates, G. Hammett, S. Ethier, K. Hill,

B. LeBlanc, J. Menard, D. McCune, D. Mikkelsen, G. Rewoldt, PPPL

C. Bourdelle, Association Euratom-CEA, France The NSTX National Team

Hi Beta i e ITG, tearing ETG, tearing

r/a=0.30 neo i stable ITG stable

r/a=0.60 neo i unstable tearing (0.02MHz) damped tearing ?

r/a=0.80 neo i unstable ITG (0.09 MHz)

ExB shear stabilized

unstable (0.3 MHz)

NSTX: Low i : ITG stable from q<0, ExB, high beta High e : core tearing

H-Mode i e ITG, tearing ETG

r/a=0.25 neo i unstable tearing

(0.02MHz)stable

r/a=0.65 neo i unstable tearing (0.02MHz)

stable

r/a=0.80 neo i ITG unstable (0.07MHz),

ExB shear stabilized

Unstable

(1.0 MHz)

Microtearing modes robust, extensive convergence tests

• Eigenfunctions of electrostatic and electromagnetic fieldsfor 0.6 sec and r/a= 0.25 at ks=0.5

• Seventeen 2 extent of field line length neededto confine eigenfunctions

• Corresponds to a very large radial width in thesimplest approximationwidth of A//= ~1radian

• Resonant trapped particle instabilityat each field period

Broad spectrum of unstable modes

• What causes NSTXhigh electron diffusivity?

GS2=> new microinstability with tearing parity.

Is it responsible for e?

• Plasma core: - Find only long wavelength

microstabilities:

• At 0.65 r/a modes extendto shorter wavelengths than at 0.25r/a

What is the radial width of the tearing mode?

• Corresponds to a very large radial width in thesimplest approximation

• Width of A//= ~1radian. Estimate <kx>=<ky>·rq'/q·. With <ky> = 0.5/s, rq'/q = 0.15, = 1.2 radians, Then x=2/<kx>=84s~84i.

• Near the plasma core i = 0.017 m, leading to the radial width of the tearing mode: rtearing~1.4 m > amid=1.2 m, the plasma minor radius.

• More detailed calculations are needed to properly answer this question.

NSTX: Examine ITG and ETG Microstability

Find: tearing parity eigenfunction, with broad wave vector spectrum (ki)ITG instabilities, with symmetric eigenfunctions and parabolic (ki)

t=0.6s positive shear

Connection with Theory:Drift mode instability at high beta

• Microtearing instability expected for flat density,

if rTi>rTe

Connor, Cowley, Hastie (PPCF 1990)

- Find good agreement with GS2 linear instability predictions

• High beta can destabilize collisionless ETG for steep density and temperature gradients

Joiner, Cowley EPS-2004

- Test on high beta (~34%) NSTX shot 112600

Connor Condition Satisfied for Linear Instabilities

Connor, Cowley, Hastie (PPCF 1990) examined linear instability conditions

for tokamak microtearing mode in the intermediate collisionality regime

For e,i=, instability occurs only if rTi>rTe. Dispersion relation:

Broad spectrum: weak, well converged modes with tearing parity

k=0.1 to 0.8 at r/a =0.25 at 0.6 sec and

k= 0.1 to 1.0 at r/a=0.65 at both 0.4 sec and 0.6 sec.

Well converged, unstable modes with mixed parity

at higher wavevectors, up to k at r/a =0.65 at 0.4 and 0.6 sec.

At 0.4 sec, unstable growth rates at r/a =0.25 are smaller

and the modes, aside from k do not have tearing parity.

Connor condition is satisfied in NSTX core where find tearing parity modes,

Not at r/a =0.25 at 0.4 sec, where tearing parity mode not found.

(

*e

T )

1ˆ C n

2ˆ C

e

*e

T

3ˆ C

e

*e

T

4ˆ C *e

T e

Nonlinear Simulations• Nonlinear simulations are in progress on NERSC’s IBM SP RS/6000 supercomputer,

using 336 processers on 42 nodes, with 4MB memory per processor and GS2 compiled for 64 bit addressing

• Computational domain: 758 million meshpoints in a rectangular box (at the outside plasma midplane) with 15 in the x direction and 63 in the y direction.

• Nonlinear terms evaluated on a grid with 243 points in x and 27 points in y

for 9 ky modes ≤ 0, 161 kx modes, after dealiasing.

• Generalize rule for determining the number of kx modes: Nx(2rq'/q)Ny(Lx/Ly)(Np-1)/2 when more than one field period for necessary eigenfunction connections. Np=number of 2 field periods

Questions

• What is important in destabilizing the tearing mode,If we stabilize it does e decrease?

• Is microtearing destabilized at low beta in ST?

• What is the width of tearing mode?

• Are nonlinear transport predictions possible?How do they compare with transport analysis?

• Can Joiner/Cowley ETG microtearing mode be destabilized?