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Berkery – Kinetic Stabilization NSTX Jack Berkery Kinetic Effects on RWM Stabilization in NSTX: Initial Results Supported by Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec May 30, 2008 Princeton Plasma Physics Laboratory Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

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Berkery – Kinetic Stabilization NSTX RWM Energy Principle – Kinetic Effects (Haney and Freidberg, PoF-B, 1989)

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Berkery – Kinetic Stabilization NSTX RWM Energy Principle – Kinetic Effects (Haney and Freidberg, PoF-B, 1989) (Hu, Betti, and Manickam, PoP, 2005)

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Berkery – Kinetic Stabilization NSTX RWM Energy Principle – Kinetic Effects (Haney and Freidberg, PoF-B, 1989) PEST Hu/Betti code (Hu, Betti, and Manickam, PoP, 2005)

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Berkery – Kinetic Stabilization NSTX RWM Energy Principle – Kinetic Effects (Haney and Freidberg, PoF-B, 1989) PEST Hu/Betti code (Hu, Betti, and Manickam, PoP, 2005)

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Berkery – Kinetic Stabilization NSTX 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.

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Berkery – Kinetic Stabilization NSTX Effects included: Trapped Ions Trapped Electrons Trapped Hot Particles Circulating Ions Alfven Layers The Hu/Betti code calculates δW K

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Berkery – Kinetic Stabilization NSTX Effects included: Trapped Ions Trapped Electrons Trapped Hot Particles Circulating Ions Alfven Layers The Hu/Betti code calculates δW K (Hu, Betti, and Manickam, PoP, 2006)

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Berkery – Kinetic Stabilization NSTX Experimental profiles used as inputs

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Berkery – Kinetic Stabilization NSTX Hu Berkery (DIII-D shot ) Our implementation gives similar answers to Hu’s

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability diagrams: contours of constant Re(γ K τ w )

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Berkery – Kinetic Stabilization NSTX Stability results are all near marginal

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Berkery – Kinetic Stabilization NSTX Stability results are all near marginal

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Berkery – Kinetic Stabilization NSTX Stability results are all near marginal

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Berkery – Kinetic Stabilization NSTX Collisionality

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Berkery – Kinetic Stabilization NSTX Simple model: collisions increase stability increasing * “dissipation parameter” Fitzpatrick simple model Collisions increase stability because they increase dissipation of mode energy. (Fitzpatrick, PoP, 2002)

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Berkery – Kinetic Stabilization NSTX 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)

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Berkery – Kinetic Stabilization NSTX Collisionality should decrease δW K : test with Z eff 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)

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX As expected, colisionality decreases stability

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Berkery – Kinetic Stabilization NSTX Rotation

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Berkery – Kinetic Stabilization NSTX Simple model: rotation increases stability increasing Ω φ 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)

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Berkery – Kinetic Stabilization NSTX 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)

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Berkery – Kinetic Stabilization NSTX 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)

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Berkery – Kinetic Stabilization NSTX Convert to Hu/Betti code form Rotation profiles just before instability

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior

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Berkery – Kinetic Stabilization NSTX 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.

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability?

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Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? stable – high trapped ion contribution

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Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? unstable

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Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? stable – high circulating ion contribution

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX PEST symmetry setting makes a difference Symmetric Asymmetric

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Berkery – Kinetic Stabilization NSTX , Symmetric , Asymmetric PEST symmetry setting makes a difference

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Berkery – Kinetic Stabilization NSTX Experimental profile errors can make a big difference

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Berkery – Kinetic Stabilization NSTX Experimental profile errors can make a big difference , With error , Fixed

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX Caveat: calculated with only trapped ion effect included. (Hu, Betti, and Manickam, PoP, 2005) Previous ITER results also showed complex stabilization

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Berkery – Kinetic Stabilization NSTX Ranges of stability – more complex than simple model

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Berkery – Kinetic Stabilization NSTX (Fitzpatrick and Bialek, PoP, 2006) “simple model” Ranges of stability – more complex than simple model

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX Changes to coding 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 Z eff ≠ 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

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX What about a shot that doesn’t go unstable?

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Berkery – Kinetic Stabilization NSTX What about a shot that doesn’t go unstable? , Actual128857, Collisionality

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Berkery – Kinetic Stabilization NSTX What about a shot that doesn’t go unstable? , Rotation This actually comes closer to instability than the case of , which was observed to go unstable, so certainly the code is not perfect.

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Berkery – Kinetic Stabilization NSTX

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Berkery – Kinetic Stabilization NSTX 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.

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