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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 ) 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 Stability results are all near marginal

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

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

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 As expected, colisionality decreases stability

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

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

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

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

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

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

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

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

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

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

35 Berkery – Kinetic Stabilization NSTX 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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

59 Berkery – Kinetic Stabilization NSTX Which components lead to stability/instability? 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 , Symmetric , 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 , With error , 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? , Actual128857, Collisionality

74 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.

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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