# Presentation: 683881

**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

** **

** **

| 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 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

## 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

## 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 *<k**x**>=<k**y**>·rq'/q·****.*
- 	With *<k**y**> = 0.5/****s*, *rq'/q =* 0.15, **= 1.2 radians,
- 	Then ***x=2****/<k**x**>=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 > 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 (ki)
- ITG instabilities, with symmetric eigenfunctions and parabolic (ki)

- 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.

## 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(2rq'/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?