SSX summary: helicity balance and Ohms law

1. SSX summary: helicity balance and Ohms law Workshop on Magnetic Self-Organization NSF Center meeting, Aug 4-6, 2004 Michael Brown C. D. Cothran, J. Fung, A. O Murchadha, Z. Michielli, M. Chang Swarthmore College Collaborators: M. Schaffer (GA), W. Matthaeus (Bartol), D. Cohen (Swarthmore), E. Belova (PPPL) Research supported by US DOE grants ER54604 and ER54490

2. Outline A brief tour of the Swarthmore Spheromak Experiment (SSX) Device, diagnostics, plasma parameters Full merging and self-organization to large scale (magnetic helicity conservation, FRC, doublet CT) Local 3D magnetic reconnection studies (generalized Ohms law, Hall terms, energetic ions)

3. Full merging: FRC formation Right-handed Spheromak Left-handed spheromak Large scale structure (FRC)

4. Magnetic structure consistent with FRC/doublet-CT full data • m=0 dominates • Other modes are present

5. Magnetic reconnection in three dimensions

6. Reconnection in SSX-FRC

7. Ensemble average of 36 identical shots

8. PART 1 Helicity balance

9. Spheromak formation

10. Complete merging: FRC formation Right-handed Spheromak Left-handed spheromak FRC Helicity conservation leads to a null helicity structure

11. The SSX Laboratory 10kV/100kA Pulsed power Cylindrical flux conservers and vacuum chamber (=0.40m, L=0.65m) Coaxial magnetized plasma guns on each end (1 mWb)

12. Diagnostics at SSX 600 channel 1.25 MHz data acquisition system Magnetic probe arrays Langmuir triple probe He-Ne quadrature interferometer 0.2 m VUV monochrometer Bolometer Retarding Grid Energy Analyzers (RGEA) Soft x-ray photodiodes (SXR) Directional (Gundestrup) Mach probe

13. Distributed probe array 12 probe stalks: 4 toroidally at three axial positions

14. Magnetic structure consistent with FRC/doublet-CT m=0 (toroidal mode) component • Reversed field • Very little midplane toroidal field • Axially antisymmetric B • 70 G RCC field (on axis)

15. Magnetic structure consistent with FRC/doublet-CT full data • m=0 dominates • Other modes are present

16. Peak poloidal flux and radial flux profile 70 G RCC field (on axis) • Ends reach 3-4 mWb immediately (3-4 amplification) • Midplane flux grows to match ends • Reconnection rate ≈ 0.04 • No private flux after 50s, but toroidal fields remain • Midplane flux profile consistent with RS/√2: high  FRC

17. Poloidal flux = 3 mWb (east and west) Toroidal flux = +/- 3 mWb (east and west) Helicity = 2x10 mWb^2 east – 2x10 mWb^2 west = zero total Rate = 2(1 kV)(1 mWb) x 10 ms = 20 mWb^2 Axisymmetric helicity estimate

18. m=1 component late in time: tilted CT Geometric axis of CT is perpendicular to the flux conserver axis

19. Elena Belova 2D simulation

20. 3D simulation showing tilt instability

21. Full data (70 G on axis)

22. PART 2 Generalized Ohm’s Law and Energetic Ions

23. 3D magnetic reconnection experiments Large slots cut into FC rear walls define the reconnection region 3D magnetic properties Energetic particles RGEAs Magnetic probe array Brown et al Astrophys. J. Lett. (9/02) Brown et al Phys. Plasmas 9, 2077 (2002) Brown et al Phys. Plasmas 6, 1717 (1999) Kornack et al Phys. Rev. E 58, R36 (1998)

24. 3D magnetic probe array 600 coils, 558 array ~2 cm spacing 25 three channel 8:1 multiplexer/integrator boards 10 eight channel 8-bit CAMAC digitizers Full probe readout every 0.8 s

25. Reconnection in SSX-FRC Catch reconnection early (< 32 s) then FRC forms

26. E + vxB = ηJ + (JxB – grad P)/ne + ∂J/∂t Curl (vxB + div P) = ∂B/∂t + Curl ηJ + Curl (JxB)/ne + Curl (∂J/∂t) Generalized Ohms Law and Curl

27. Hall term dominates electric field during shot

28. Ensemble average of 36 identical shots

29. Terms in curl of Ohms law (single shot)

30. E + vxB = ηJ + (JxB – grad P)/ne + ∂J/∂t Ohmic and electron inertia terms are small From near pressure balance and unity b, we know that JxB and grad P are comparable Only grad P can contribute at the neutral line Generalized Ohm’s Law magnitudes

31. In plane magnetic field (ala min variance)

32. Out of plane magnetic field

33. Merger of left and right handed tori

34. Side view

35. Cross section

36. In plane JxB force (ala min variance)

37. Out of plane JxB force (slingshot)

38. Current channel formation correlates with RGEA activity

39. RGEA raw signals

40. Average peak signal for the out-of-plane RGEA Fit to a thermal distribution with drift: T=33±11eV and V=86±20eV

41. Summary • Spheromak merging in SSX forms large scale, • self-organized structure • Reconnection is fully 3D • Merging results in self-organized structure • Helicity conservation implies null helicity • Hall terms dominate electric field in Ohms law • Study dynamics of doublet-FRC • Study flow with Mach probe, ion doppler • Need computational/theoretical support • Local SSX reconnection is fully 3D, generates energetic • particles, flow, and heat

42. Implement IDS at midplane of SSX-FRC (use with Mach probe) Compare flow results with Belova code Helium glow discharge cleaning for density control (lower density, larger c/wpi) Plans for the near future