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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.

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Presentation on theme: "Berkery – Kinetic Stabilization NSTX Jack Berkery Kinetic Effects on RWM Stabilization in NSTX: Initial Results Supported by Columbia U Comp-X General."— Presentation transcript:

1 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

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

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

4 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)

5 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)

6 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.

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

8 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)

9 Berkery – Kinetic Stabilization NSTX Experimental profiles used as inputs

10 Berkery – Kinetic Stabilization NSTX Hu Berkery (DIII-D shot 125701) Our implementation gives similar answers to Hu’s

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

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

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

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

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

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

17 Berkery – Kinetic Stabilization NSTX 121083128717 Stability results are all near marginal

18 Berkery – Kinetic Stabilization NSTX Stability results are all near marginal 128855128856

19 Berkery – Kinetic Stabilization NSTX Stability results are all near marginal 128859128863

20 Berkery – Kinetic Stabilization NSTX Collisionality

21 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)

22 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)

23 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)

24 Berkery – Kinetic Stabilization NSTX 121083 As expected, colisionality decreases stability

25 Berkery – Kinetic Stabilization NSTX 121083 As expected, colisionality decreases stability

26 Berkery – Kinetic Stabilization NSTX 128717 As expected, colisionality decreases stability

27 Berkery – Kinetic Stabilization NSTX 128717 As expected, colisionality decreases stability

28 Berkery – Kinetic Stabilization NSTX 128855 As expected, colisionality decreases stability

29 Berkery – Kinetic Stabilization NSTX 128855 As expected, colisionality decreases stability

30 Berkery – Kinetic Stabilization NSTX 128856 As expected, colisionality decreases stability

31 Berkery – Kinetic Stabilization NSTX 128856 As expected, colisionality decreases stability

32 Berkery – Kinetic Stabilization NSTX 128859 As expected, colisionality decreases stability

33 Berkery – Kinetic Stabilization NSTX 128859 As expected, colisionality decreases stability

34 Berkery – Kinetic Stabilization NSTX 128863 As expected, colisionality decreases stability

35 Berkery – Kinetic Stabilization NSTX 128863 As expected, colisionality decreases stability

36 Berkery – Kinetic Stabilization NSTX Rotation

37 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)

38 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)

39 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)

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

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

42 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128717

43 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128717

44 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 121083

45 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 121083

46 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128855

47 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128855

48 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128856

49 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128856

50 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128859

51 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128859

52 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128863

53 Berkery – Kinetic Stabilization NSTX Using test rotation profiles shows the behavior 128863

54 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.

55 Berkery – Kinetic Stabilization NSTX

56 Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? 121083

57 Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? 121083 stable – high trapped ion contribution

58 Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? 121083 unstable

59 Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? 121083 stable – high circulating ion contribution

60 Berkery – Kinetic Stabilization NSTX

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

62 Berkery – Kinetic Stabilization NSTX 121083, Symmetric 121083, Asymmetric PEST symmetry setting makes a difference

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

64 Berkery – Kinetic Stabilization NSTX Experimental profile errors can make a big difference 128717, With error 128717, Fixed

65 Berkery – Kinetic Stabilization NSTX

66 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

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

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

69 Berkery – Kinetic Stabilization NSTX

70 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

71 Berkery – Kinetic Stabilization NSTX

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

73 Berkery – Kinetic Stabilization NSTX What about a shot that doesn’t go unstable? 128857, Actual128857, Collisionality

74 Berkery – Kinetic Stabilization NSTX 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.

75 Berkery – Kinetic Stabilization NSTX

76 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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