# Presentation: 552729

## Kinetic Effects on RWM Stabilization

_**Kinetic Effects on RWM Stabilization**_
_**in NSTX: Initial Results**_

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- May 30, 2008
- Princeton Plasma Physics Laboratory

*Department of Applied Physics and Applied Mathematics, **	*
*Columbia University, New York, NY, USA*

## RWM Energy Principle – Kinetic Effects

- (Haney and Freidberg, PoF-B, 1989)

## RWM Energy Principle – Kinetic Effects

- (Haney and Freidberg, PoF-B, 1989)

- (Hu, Betti, and Manickam, PoP, 2005)

## RWM Energy Principle – Kinetic Effects

- (Haney and Freidberg, PoF-B, 1989)

- PEST

- Hu/Betti code

- (Hu, Betti, and Manickam, PoP, 2005)

## RWM Energy Principle – Kinetic Effects

- (Haney and Freidberg, PoF-B, 1989)

- PEST

- Hu/Betti code

- (Hu, Betti, and Manickam, PoP, 2005)

## Outline

- Introduction
- The Hu/Betti code
- Results: stability diagrams
- Kinetic theory predicts near-marginal stability for experimental equilibria just before RWM instability.
- Collisionality
- Kinetic theory predicts decrease in stability with increased collisionality.
- Rotation
- Experimental rotation profiles are near marginal. Larger or smaller rotation is farther from marginal.
- Unlike simpler “critical” rotation theories, kinetic theory allows for a more complex relationship between plasma rotation and RWM stability – one that may be able to explain experimental results.

## The Hu/Betti code calculates δWK

- _The Hu/Betti code calculates __δ__W__K_

## The Hu/Betti code calculates δWK

- _The Hu/Betti code calculates __δ__W__K_

- (Hu, Betti, and Manickam, PoP, 2006)

## Experimental profiles used as inputs

## Hu

- Berkery

- (DIII-D shot 125701)

- _Our implementation gives similar answers to Hu’s_

## Stability diagrams: contours of constant Re(γKτw)

## Stability diagrams: contours of constant Re(γKτw)

## Stability diagrams: contours of constant Re(γKτw)

## Stability diagrams: contours of constant Re(γKτw)

## Stability diagrams: contours of constant Re(γKτw)

## Stability diagrams: contours of constant Re(γKτw)

## 121083

- 128717

- _Stability results are all near marginal_

## Stability results are all near marginal

- 128855

- 128856

## Stability results are all near marginal

- 128859

- 128863

## Collisionality

## Simple model: collisions increase stability

- increasing *

- “dissipation parameter”

- Fitzpatrick simple model
- Collisions _increase_ stability because they increase dissipation of mode energy.

- (Fitzpatrick, PoP, 2002)

## Kinetic model: collisions decrease stability

- collision frequency (note: inclusion here is “ad hoc”)

- Fitzpatrick simple model
- Collisions _increase_ stability because they increase dissipation of mode energy.
- Kinetic model
- Collisions _decrease_ stability because they reduce kinetic stabilization effects.

- (Hu, Betti, and Manickam, PoP, 2006)

## Collisionality should decrease δWK: test with Zeff

- collision frequency (note: inclusion here is “ad hoc”)

- Fitzpatrick simple model
- Collisions _increase_ stability because they increase dissipation of mode energy.
- Kinetic model
- Collisions _decrease_ stability because they reduce kinetic stabilization effects.

- (Hu, Betti, and Manickam, PoP, 2006)

## 121083

- _As expected, colisionality decreases stability_

## 121083

- _As expected, colisionality decreases stability_

## 128717

- _As expected, colisionality decreases stability_

## 128717

- _As expected, colisionality decreases stability_

## 128855

- _As expected, colisionality decreases stability_

## 128855

- _As expected, colisionality decreases stability_

## 128856

- _As expected, colisionality decreases stability_

## 128856

- _As expected, colisionality decreases stability_

## 128859

- _As expected, colisionality decreases stability_

## 128859

- _As expected, colisionality decreases stability_

## 128863

- _As expected, colisionality decreases stability_

## 128863

- _As expected, colisionality decreases stability_

## Rotation

## Simple model: rotation increases stability

- increasing Ωφ

- toroidal plasma rotation

- Fitzpatrick simple model
- Plasma rotation _increases_ stability and for a given β there is a “critical” rotation above which the plasma is stable.

- (Fitzpatrick, PoP, 2002)

## Kinetic model: rotation/stability relationship is complex

- E x B frequency

- Fitzpatrick simple model
- Plasma rotation _increases_ stability and for a given β there is a “critical” rotation above which the plasma is stable.
- Kinetic model
- Plasma rotation _increases or decreases_ stability and a “critical” rotation is not defined?

- (Hu, Betti, and Manickam, PoP, 2006)

## Kinetic model: rotation/stability relationship is complex

- E x B frequency

- Fitzpatrick simple model
- Plasma rotation _increases_ stability and for a given β there is a “critical” rotation above which the plasma is stable.
- Kinetic model
- Plasma rotation _increases or decreases_ stability and a “critical” rotation is not defined?

- (Hu, Betti, and Manickam, PoP, 2006)

## Rotation profiles just before instability

- Convert to Hu/Betti code form

- _Rotation profiles just before instability_

## Using test rotation profiles shows the behavior

## Using test rotation profiles shows the behavior

- 128717

## Using test rotation profiles shows the behavior

- _Using test rotation profiles shows the behavior_

- 128717

## Using test rotation profiles shows the behavior

- 121083

## Using test rotation profiles shows the behavior

- 121083

## Using test rotation profiles shows the behavior

- 128855

## Using test rotation profiles shows the behavior

- 128855

## Using test rotation profiles shows the behavior

- 128856

## Using test rotation profiles shows the behavior

- 128856

## Using test rotation profiles shows the behavior

- 128859

## Using test rotation profiles shows the behavior

- 128859

## Using test rotation profiles shows the behavior

- 128863

## Using test rotation profiles shows the behavior

- 128863

## Conclusions

- Kinetic Stabilization
- Analysis of multiple NSTX discharges from just before RWM instability is observed predicts near-marginal mode growth rates.
- Collisionality
- The predicted effect of collisionality is as expected from the kinetic equation.
- Rotation
- Increasing or decreasing the rotation in the calculation drives the prediction farther from the marginal point in either the stable or unstable direction.
- Unlike simpler “critical” rotation theories, kinetic theory allows for a more complex relationship between plasma rotation and RWM stability.

## Slide 55

## Which components lead to stability/instability?

- 121083

## Which components lead to stability/instability?

- 121083

- stable – high trapped ion contribution

## Which components lead to stability/instability?

- 121083

- unstable

## Which components lead to stability/instability?

- 121083

- stable – high circulating ion contribution

## PEST symmetry setting makes a difference

- _PEST symmetry setting makes a difference_

- Symmetric

- Asymmetric

## 121083, Symmetric

- 121083, Asymmetric

- _PEST symmetry setting makes a difference_

## Experimental profile errors can make a big difference

## Experimental profile errors can make a big difference

- 128717, With error

- 128717, Fixed

## Previous ITER results also showed complex stabilization

- Caveat:
- calculated with only trapped ion effect included.

- (Hu, Betti, and Manickam, PoP, 2005)

- _Previous ITER results also showed complex stabilization_

## Ranges of stability – more complex than simple model

## Ranges of stability – more complex than simple model

- (Fitzpatrick and Bialek, PoP, 2006)

- “simple model”

- _Ranges of stability – more complex than simple model_

## Changes to the code

- Changed from IMSL library integration to NAG library integration so it can run on PPPL computers.
- Removed all hard-wired numbers - put in input files.
- Automatic removal of rational surfaces and calculation of Alfven layer contributions.
- Surface magnetic field doesn’t have to be monotonic from Bmin to Bmax.
- etc...
- Changes to physics
- ln(Λ) ≠ constant
- Zeff ≠ 1
- No small-aspect ratio assumption for κ·ξ.
- Automatically finds smallest mode frequency ω that doesn’t give integration error.

- _Changes to the code_

## What about a shot that doesn’t go unstable?

## What about a shot that doesn’t go unstable?

- 128857, Actual

- 128857, Collisionality

## What about a shot that doesn’t go unstable?

- 128857, Rotation

- This actually comes closer to instability than the case of 128863, which was observed to go unstable, so certainly the code is not perfect.

## Sontag’s results

- (Sontag et al, NF, 2007)

- High collisionality correlated with lower rotation at collapse.
- Simple model interpretation: collisionality _increases_ stability, leading to a lower “critical” rotation.
- Possible kinetic model interpretation: collisionality _decreases_ stability, meaning the lower rotation plasma, which would otherwise be stable, is now unstable.
- More analysis is required.