Coupled Current-Momentum Relaxation in Reversed Field Pinch Plasmas

1. Coupled Current-Momentum Relaxation in Reversed Field Pinch Plasmas J. C. Triana1, M. Tan2, A. F. Almagri1, J. S. Sarff1, and MST team • 1 University of Wisconsin-Madison • 2 USTC Hefei China RFP Workshop Hefei China 26-29 Oct 2015

2. Motivation • Externally applied E field is toroidally directed, while edge current is poloidally directed, so what drives edge current in the RFP? • Resistive Ohm’s law in an RFP plasma is not balanced.

3. Outline • The Madison Symmetric Torus, MST, device • Tearing instability and magnetic reconnection in MST • Generalized Ohms law and the momentum equation • Early Measurements of Hall and MHD Dynamo and stresses • Both dynamos surge to a large amplitudes at reconnection event • Hall dynamo is primarily produced by the m = 1 modes. • As a consequence to large Hall dynamo, Reynolds and Maxwell stresses also burst to huge amplitudes and remain nearly balanced • NIMROD calculations of the Hall and MHD dynamo show a rich radial structure • Deep Insertion Probe designed to measure the radial profile of the Hall dynamo • Profile of equilibrium magnetic field and currents • Profile of RMS magnetic fluctuations • Hall dynamo measurements at reconnection event.\ • Near term plans • Summary

4. The Madison Symmetric Torus as an RFP • Experimental parameters: • n ~ 1013 cm–3 • Ip ~ 200 kA • Tion ~ Te ~ 200 eV • B ~ 0.1 T • A ~ 1 µs • rion ~ 1 cm • < 12% • S ~ 1 105

5. Tearing instability and nonlinear coupling result in multiple magnetic reconnection sites Tearing resonance: m = poloidal mode number n = toroidal mode number m = 1 are linearly unstable Sawteeth are quasi-periodic impulsive reconnection events m = 0 are linearly stable, nonlinearly driven

6. Ohm’s law and the momentum equation are coupled through the Hall term MHD Dynamo Hall Dynamo Ohms law Momentum equation Maxwell Stress Reynolds Stress Both stress terms, and the dynamo terms burst to large amplitudes during reconnection event.

7. The dynamos and stresses burst to large amplitudes during relaxation events and the stresses remain nearly balanced At r/a ~0.85 (Edge Region) Nearly balanced across the radius T.D. Tharp Phys. Plasma, 2010 Kuritsyn, Phys. Plasma, 2009

8. Dynamo terms have a complex and interconnected radial structure while balancing Ohm’s law is balanced by the Hall and MHD dynamo terms Kuritsyn et al. Phys. Plasmas 16, 055903 (2009)

9. Hall term comes primarily from the m = 1 and n = 6 − 8 modes, which are core resonant At reconnection event T.D. Tharp Phys. Plasma, 2010

10. NIMROD calculations of the Hall and MHD dynamo show a rich radial structure Parameter: King, Sovinec, and Mirnov, Phys. Plasmas 19, 055905 (2012)

11. Deep insertion probe designed to measure all three components of the magnetic field every 1.0 cm In the radial direction • Array of 20 (Br, Bt, Bp) triplets separated by 1 cm in the radial direction are arranged in a linear fashion along a 40 cm BN stalk to form the DIP • In cylindrical coordinate the Hall dynamo can be written as

12. Radial profile of equilibrium magnetic field at reconnection event. • Data averaged around 150ms centered on a reconnection evens. • Equilibrium profiles are used to untangle radial and poloidal fluctuations measured in the lab frame.

13. Profile of equilibrium currents at reconnection even is consistent with previous Rogowski probe measurement

14. Profile of magnetic field RMS fluctuations < 200 kHz at reconnection event are flat inside reversal surface • Need to resolve the n and m spectra using pseudo-spectrum technique • Toroidal fluctuations, (0,1), dominate in the edge

15. Hall dynamo measurements at reconnection event has similar structure to NIMROD calculations See 2015 APS-DPP Triana's poster CP12.00033 “ Measurements of the Hall Dynamo in MST Plasmas”

16. Hall dynamo measurements have been extended further into the plasma Earliest measurements Most recent measurements

17. Hall dynamo measurements have been extended further into the plasma Earliest measurements But we still have a long way to go Most recent measurements NIMROD

18. Hall dynamo measurements have been extended further into the plasma Earliest measurements But we still have a long way to go Next we need to work on the MHD dynamo. But measuring the flow using Mach probe is not compatible with hot core plasma. Most recent measurements NIMROD

19. A deep insertion capacitive probe has been constructed to measure electric field profiles in the plasma A capacitive probe is made of 4 stalks with 10 capacitors each stalk and 1.5 cm radial separation. Visiting grad student from USTC, Mingsheng Tan See 2015 APS-DPP Tan’s poster CP12.00034 “Measurements of Electric Field Fluctuations Using a Capacitive Probe on the MST Reversed Field Pinch”

20. Deep insertion magnetic and capacitive probes can be combined to measure the total dynamo Probe calibration set up MHD Hall Total Raw signal Plasma Potential Calibration

21. Summary • Both dynamos terms surge to a large amplitudes at reconnection event. • Hall dynamo is primarily produced by the m = 1, n = 6, 7, 8 tearing modes. • As a consequence to large Hall dynamo the Maxwel and Reynolds stresses also burst to huge amplitudes but remain nearly balanced. • NIMROD calculations of the Hall and MHD dynamo show a rich radial structure. • Magnetic deep insertion Probe has been used to measure profiles of the Hall dynamo. • Profiles of Equilibrium Magnetic Field and currents are used to constrain MSTFit. • RMS profile of magnetic Fluctuations are flat, need to preform pseudo spectrum. • Hall Dynamo Measurements at reconnection event has structure similar to NIMROD. • Started work on capacitive deep insertion probe to measure the totoal dynamo.

22. Thank you for your attention THE END

23. Thank you for your attention THE END And googol's translation is