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. Hi Beta  i  e ITG,  tearing ETG,  tearing r/a=0.30  neo  i stable ITGstable 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)

3. Microtearing modes robust, extensive convergence tests Eigenfunctions of electrostatic and electromagnetic fields for 0.6 sec and r/a= 0.25 at k   s =0.5 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? GS2=> 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 = ·rq'/q· . With = 0.5/  s, rq'/q = 0.15,  = 1.2 radians, Then  x=2  / =84  s ~84  i. Near the plasma core  i = 0.017 m, leading to the radial width of the tearing mode:  r tearing ~1.4 m > a mid =1.2 m, the plasma minor radius. More detailed calculations are needed to properly answer this question.

7. NSTX: Examine ITG and ETG Microstability Find: tearing parity eigenfunction, with broad wave vector spectrum  (k   i ) ITG instabilities, with symmetric eigenfunctions and parabolic  (k   i ) t=0.6s positive shear

8. Connection with Theory: Drift mode instability at high beta Microtearing instability expected for flat density, if  r T i >  r T e 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  r T i >  r T e. 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.

10. 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 k y modes ≤ 0, 161 k x modes, after dealiasing. Generalize rule for determining the number of k x modes: N x  (2  rq'/q)  N y  (L x /L y )  (N p -1)/2 when more than one field period for necessary eigenfunction connections.N p =number 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?