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Equilibrium and Stability of Oblate Free-Boundary FRCs in MRX

Outline. IntroductionBrief overview of relevant FRC issuesIntroduction to the MRX facilityFRC formation by spheromak mergingOverview of FRC Stability Results in MRXSystematic Studies of FRC Stabilityn=1 tilt/shift instabilities without passive stabilizationn?2 modes often limit lifetime aft

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Equilibrium and Stability of Oblate Free-Boundary FRCs in MRX

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    1. Equilibrium and Stability of Oblate Free-Boundary FRCs in MRX S. P. Gerhardt, E. Belova, M. Inomoto*, M. Yamada, H. Ji, Y. Ren Princeton Plasma Physics Laboratory * Osaka University

    2. Outline Introduction Brief overview of relevant FRC issues Introduction to the MRX facility FRC formation by spheromak merging Overview of FRC Stability Results in MRX Systematic Studies of FRC Stability n=1 tilt/shift instabilities without passive stabilization n?2 modes often limit lifetime after passive stabilizer is installed Modeling of Equilibrium and Stability Properties Equilibrium reconstruction with new Grad-Shafranov code Oblate Plasmas are Tilt Stable from a Rigid-Body Model HYM calculations of Improved Stability Regime at Very Low Elongation Conclusions

    3. FRCs have Potential Advantages as Fusion Reactors

    4. FRCs have Potential Advantages as Fusion Reactors

    5. FRCs have Potential Advantages as Fusion Reactors

    6. FRC Stability is an Unresolved Issue

    7. FRC Stability is an Unresolved Issue

    8. FRC Stability is an Unresolved Issue

    9. MRX is a Flexible Facility for Oblate FRC Studies

    10. Comprehensive Diagnostics For Stability Studies

    11. FRC Formation By Spheromak Merging

    12. Overview of MRX Results

    13. Long-Lived FRC with Large Mirror Ratio & Passive Stabilizer

    14. Passive Stabilizer and Shape Control Extend the Plasma Lifetime

    15. Passive Stabilizer and Shape Control Extend the Plasma Lifetime

    16. Passive Stabilizer and Shape Control Extend the Plasma Lifetime

    17. Systematic Instability Studies Have Been Performed The instabilities have the characteristic of tilt/shift and co-interchange modes. The center column reduces the n=1 tilt/shift amplitude. Co-interchange (n?2) modes reduced by shaping more than by the center column. Co-interchange modes can be as deadly as tilting.

    18. Axial Polarized Mode Appears Strongly in BR

    19. Axial Polarized Mode Appears Strongly in BR

    20. Radial Polarized Mode Appears Strongly in BZ

    21. n=1 Tilt Observed Without Center Conductor

    22. Center Column Reduces Tilt Signature

    23. n=1 Shifting Signature Observed Without Center Conductor

    24. n=1 Shifting Signature Largely Suppressed with Center Column

    25. Lifetime is Strongly Correlated with BR Perturbations

    26. Lifetime is Strongly Correlated with BR Perturbations

    27. Lifetime is Strongly Correlated with BR Perturbations

    28. Lifetime is Strongly Correlated with BR Perturbations

    29. Multiple Tools Used to Model Oblate FRCs

    30. Multiple Tools Used to Model Oblate FRCs

    31. MRXFIT1 Solves G-S Eqn. Subject to Magnetic Constraints

    32. Fields Calculated From Axisymmetric Model With Flux Conserving Vessel

    33. Fields Calculated From Axisymmetric Model With Flux Conserving Vessel

    34. MRXFIT Code Finds MHD Equilibria Consistent with Magnetics Data

    35. Equilibrium Properties Respond to the External Field

    36. Rigid-Body Model Used to Estimate Tilt/Shift Stability

    37. MRX Plasmas Transition to the Tilt Stable Regime

    38. Rigid Body Shift Often Present, But May Be Benign

    39. Rigid Body Shift Often Present, But May Be Benign

    40. Rigid Body Shift Often Present, But May Be Benign

    41. HYM Calculations Indicate Reduced Growth Rates at Larger Mirror Ratio

    42. HYM Calculations Indicate Reduced Growth Rates at Larger Mirror Ratio

    43. Local Mode Stability Improves At High Mirror Ratio

    44. Results Supportive of Proposed SPIRIT* Program Merging spheromaks for formation of oblate FRC. Process has been demonstrated in MRX. Shaping and passive conductors to stabilize n=1 modes. Demonstrated to work with a center column. SPIRIT program calls for conducting shells. Transformer to increase B and heat the plasma. Prototype transformers under construction using laboratory funds. Neutral beam to stabilize dangerous n?2 modes. Need for beam is clearly demonstrated, especially at lower elongation.

    45. Conclusions FRCs formed in MRX under a variety of conditions Large n=1 tilt/shift instabilities observed in MRX plasmas without passive stabilization. Shaping + passive stabilization substantially reduces n=1 modes, but destructive n?2 axial modes often remain. A regime with small elongation demonstrates improved stability to n?2 axial modes and extended lifetime. Equilibrium reconstruction technique has been demonstrated, illustrating FRC boundary control. The improved stability in the small elongation regime is confirmed by a combination of modeling techniques.

    46. Derivation of Formula For Local Mode Growth Rate

    47. Plasma Parameters

    48. Plasma Lifetime Longest At Large Mirror Ratio

    49. Condition For Kinetic Effects

    50. Neon Tilting Suppressed With Center Column

    51. Center Column Reduces Rigid Body Shift Signature

    52. Analytic Equilibrium Model by Zheng Provides Approximation to Current Profile

    53. Spheromak Tilt is Dominated by n=1

    54. Strong n=1 during Tilting Spheromak

    55. Poor FRC with no Passive Stabilizer and Low Mirror Ratio

    56. Lifetime Not Longer with the Stabilizer at Low Mirror Ratio

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