# Presentation: 875711

## Influence of kinetic effects on ballooning stability in NSTX –KO 1.003

- J. Manickam, C. Kessel and J. Menard
- Princeton Plasma Physics Laboratory
- Special thanks to
- _R. Maingi_, ORNL and S. Sabbagh, Columbia U.
**APS-DPP Annual Meeting**
**Albuquerque, NM**
- October 27, 2003

## OUTLINE

- Motivation:*********-optimization requires stability to low-n kink-ballooning and high-n, ballooning modes. Kinetic considerations could stabilize the high-n ballooning modes and provide a larger window of stability***
- Theory model
- Finite-n corrections, kinetic effects
- Application to optimized high beta studies
- Relevance of ballooning modes in NSTX
- Analysis of experimental data
- Discussion

## Theory model – Ifinite-n corrections

- Solve ballooning equation for the growth-rate, qk)
- Dewar et al. Princeton Plasma Physics Report PPPL-1587 (1979)

- -.2

- 

- 

- n

- 

- 

- BALMSC

- k

- ncrit

- q

- 
- 
- max

- Contour path
- for integration

## Theory model – Ifinite-n corrections

**Theory model – I****finite-n corrections**

- qmax

- k

- 0.8

- 0.5

- 0

- .2

- -.2

- 
- max
- max
- max
- max

- BALMSC

- k

- q

- Vary  and compute ncrit vs. 

## Theory model – IIIon diamagnetic drift stabilization

**Theory model – II****Ion diamagnetic drift stabilization**

**L****p**** = p/p’ **Determines kinetic stabilization

- Kinetic dispersion relation

- 

- 

- n

- 

- Single fluid
- Ideal MHD
- unstable

- n

- 

- 

- Unstable band in *n*

- Kinetically
- stabilized

- 34.4*Lp

- Tang et al. Nuc. Fusion Vol. 22 (1982)

## Kinetic considerations provide a bigger window of stability

- Optimized high- case,n=8, is stable when kinetics are included

- Lp =9m

- High- kink optimized case,(with wall), is unstable to infinite-n ballooning
- Finite-n corrections predict ncrit = 50
- The mode would be stabilized by kinetic effects, unless, Lp ~ 9m
- Observed values of Lp ~ 5m

- Lp=5m

## Ballooning mode analysis of NSTX 

- Survey of NSTX discharges with significant beta, n>3, long flat-top, >150ms, and a variety of ELM behaviours
- Double-null, frequent ELMs
- Lower single-null, sporadic or no ELMs
- Giant ELMs
- Multiple time slices, every 6 ms.
- EFIT equilibrium reconstruction including kinetic data
- No direct measurement of q
- No consideration of rotation

## There is a correlation of saturation with ballooning instability, whenncrit <20

**There is a correlation of ********saturation with ballooning instability, when********n****crit**** <20**

- Note that kinetic effects
-  do not  provide complete
- stabilization

- n vs. t

- Lpmax vs. t

- ncrit vs. t

- ncrit vs. 

## In some cases saturation has no correlation with ballooning stability but may be due to confinement limits 108473

**In some cases ********saturation has no correlation with ballooning stability but may be due to confinement limits 108473**

- n vs. t

- Lpmax vs. t

- ncrit vs. t

- ncrit vs. 

## In some cases rises even when ballooning stability is violated – (108018-ELMy)

**In some cases ********rises even when ballooning stability is violated – (108018-ELMy)**

- n vs. t

- Lpmax vs. t

- ncrit vs. t

- ncrit vs. 

- kinetic effects
-  do not  provide complete
- stabilization

## There is no clear correlation of the giant ELM with ballooning stability

**There is no clear correlation of the giant ELM with ballooning stability**

- n vs. t

- Lpmax vs. t

- ncrit vs. t

- ncrit vs. 

## Discussion

- We have established a procedure for studying ballooning modes, including kinetic effects
- Ballooning stability at n>8 is attainable with optimized profiles
- Analysis of experimental data shows a qualitative correlation between -saturation and ballooning instability with n-crit< 20
- Counter-examples of  rising in the presence of ballooning instability, have been observed
- Uncertainty in the shear of the q-profile, is a major limitation in this study
- Additional issues that need consideration
- Role of rotation
- Correlation with micro-stability and confinement