GS2-T T

1

Tearing Parity Microturbulent Drift Modes on
NSTX

• Martha Redi
• NSTX Results Review
• 9/21/04

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
2




NSTX Low ?i ITG stable from qlt0, ExB, high
beta High ?e core ?tearing
Hi Beta ?i ?e ITG, ?tearing ETG, ?tearing
r/a0.30 lt ?neo gtgt ?i stable ITG stable
r/a0.60 ?neo gtgt?i unstable ?tearing (0.02MHz) damped ?tearing ?
r/a0.80 ??neo gtgt ?i unstable ITG (0.09 MHz) ExB shear stabilized unstable (0.3 MHz)
H-Mode ?i ?e ITG, ?tearing ETG
r/a0.25 lt ?neo gtgt ?i unstable ?tearing (0.02MHz) stable
r/a0.65 lt ?neo gtgt ?i unstable ?tearing (0.02MHz) stable
r/a0.80 lt ?neo gtgt ?i ITG unstable (0.07MHz), ExB shear stabilized Unstable (1.0 MHz)
3
Microtearing modes robust, extensive convergence
tests

• Eigenfunctions of electrostatic
• and electromagnetic fields
• for 0.6 sec and r/a 0.25
• at k??s0.5
• Seventeen 2? extent
• of field line length needed
• to confine eigenfunctions
• Corresponds to a very large
• radial width in the
• simplest approximation
• width of A//?? 1radian
• Resonant trapped particle instability
• at each field period

4
Broad spectrum of unstable modes

• What causes NSTX
• high electron diffusivity?
• GS2gt new microinstability
• with tearing parity.
• Is it responsible for ?e?
• Plasma core
• - Find only long wavelength
• microstabilities
• At 0.65 r/a modes extend
• to shorter wavelengths
• than at 0.25r/a

5
What is the radial width of the ?tearing mode?

• Corresponds to a very large radial width in the
• simplest approximation
• Width of A//?? 1radian. Estimate
  ltkxgtltkygtrq'/q??.
• With ltkygt 0.5/?s, rq'/q 0.15, ??? 1.2
  radians,
• Then ?x2?/ltkxgt84?s84?i.
• Near the plasma core ?i 0.017 m,
• leading to the radial width of the tearing mode
  
• ?rtearing1.4 m gt amid1.2 m, the plasma minor
  radius.
• More detailed calculations are needed
• to properly answer this question.

6




7

NSTX Examine ITG and ETG Microstability
Find tearing parity eigenfunction, with broad
wave vector spectrum g(k?ri) ITG instabilities,
with symmetric eigenfunctions and parabolic
g(k?ri)
t0.6s positive shear
8
Connection with TheoryDrift mode instability at
high beta

• Microtearing instability expected for flat
  density,
• if ?rTigt?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

9
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
  ?rTigt?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/a0.65 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.

10
Nonlinear Simulations

• Nonlinear simulations are in progress on
• NERSCs 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?(2?rq'/q)?Ny?(Lx/Ly)?(Np-1)/2
• when more than one field period for necessary
• eigenfunction connections. Npnumber of 2? field
  periods

11
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?