Dynamo Effects in Laboratory Plasmas

1. Dynamo Effects in Laboratory Plasmas S.C. Prager University of Wisconsin October, 2003

2. The lab plasma dynamo does • Generate current locally • Increase toroidal magnetic flux • Conserve magnetic helicity • Act through alpha and other effects • Arise from fluctuations superposed on the mean field • Achieve a nonlinearly saturated steady state (with full backreaction) The lab plasma dynamo does NOT • Generate magnetic field from a small seed field • Increase magnetic energy (it redistributes magnetic field)

3. Dynamo and self-organization occurs in laboratory plasmas with weak toroidal magnetic field The toroidal magnetic field is measured by the safety factor weak field, large fluctuations self-organized strong field, small fluctuations externally controlled q

4. Examples: reversed field pinch (RFP) spheromak The RFP: toroidal plasma with helical magnetic field apply toroidal electric field ET --> jT --> BP --> JP

5. The RFP Today, approximate as cylinder

6. The MST Experiment(Madison Symmetric Torus) T ~ 1 keV; n ~1013 cm-3; I ~ 0.5 MA, S ~ 106

7. The Spheromak a compact torus

8. Outline • Evidence for field generation • The standard MHD model • The backreaction • Measurements of the MHD dynamo • Dynamo effects beyond MHD (measurements) • Open issues and relation to astrophysics

9. Evidence of field generation • Cowling’s Theorem • Toroidal flux generation • Ohm’s law

10. Cowling’s theorem applied to the RFP A time-independent, cylindrically symmetric plasma cannot contain a reversed magnetic field Bz Proof: assume Bz is reversed. at the radius where Bz = 0 r Thus, magnetic flux decays within reversal surface, in constrast to experiment

11. in experiment E|| j|| radius additional current drive mechanism (dynamo)

12. The Standard MHD model • Mean field ohm’s law dynamo effect For high conductivity, Lab: from tearing instability (reconnection) Astrophysics: from convection, rotation…

13. The nonlinear dynamo instability energy source dynamo current diffusion Quasilinear theory: (Bhattacharjee, Hamieri; Strauss;Boozer…..) Nonlinear MHD computation: a complete description

14. yields a collection of spatial Fourier modes (~R/a) Flow vectors z r In poloidal plane: 2 counter-rotating vortices, in toroidal plane: more complicated magnetic field: stochastic

15. Nonlinear MHD Computation radius

16. The Lab Dynamo and the Backreaction The lab dynamo is strong, with the backreaction, self-induced Compare with backreaction theories predicting dynamo suppression(Cattaneo/Vainshtein, Kulsrud/Hahm, Gruzinov/Diamond, Bhattacharjee) From Pouquet et al., for isotropic, homogenous turbulence backreaction

17. Combining two equations, large resistivity small resistivity No obvious suppression, laboratory regime, Astrophysical regime??? -suppression with <B>

18. Measurements of MHD dynamo Measure each term in Ohm’s law In the hot core passive spectroscopy, active spectroscopy (under development) (charge exchange recombination spectroscopy) (den Hartog, Craig, Ennis) Laser Faraday rotation (Ding, Brower, UCLA) Motional Stark effect (Craig, den Hartog, under development In the cool edge Insertable probes: magnetic, Langmuir (E), spectroscopic

19. Active Spectroscopy

20. 3-Wave Polarimeter-Interferometer System Faraday rotation/interferometer system MST R0 = 1.50 m a = 0.52 m Ip = 400 kA ne ~ 1019 m-3 B0 ~ 4 kG

21. Spectroscopic probe

22. Measure quantities during discrete dynamo event Toroidal Magnetic Flux (Wb) MST time (ms)

23. Flow velocity fluctuations

24. Measurement of MHD dynamo 0 Volts m -10 r/a = 0.9 r/a = 0.9 -20 Volts m 0 -10 r/a = 0.8 r/a = 0.8 -20 time (ms) -0.5 0 0.5 time (ms) MHD dynamo dominant at some radii, not everywhere

25. Dynamo Effects Beyond MHD • Hall dynamo • Diamagnetic dynamo • Kinetic dynamo (current transport)

26. Hall dynamo: a two-fluid effect MHD dynamo Hall dynamo Two fluid effects also alter the <v x B> dynamo

27. Quasilinear Theory of Hall Dynamo V. Mirnov Three layer analysis Ideal two-fluid ve ~ vi Resistive two-fluid vi ~ 0 Ideal MHD ve ~ vi dR, de s 0 distance from reconnection layer

28. For experimental parameters de s distance from resonant surface

29. Measuring fluctuations with Faraday rotation Faraday rotation angle Magnetic fluctuations 24 26 time (ms)

30. Time Evolution of Current Density Fluctuation

31. The reconnection “current sheet” m = 1, n = 6

32. Hall Dynamo Measurements W. Ding et al

33. Hall dynamo localized in radius

34. The diamagnetic dynamo parallel component of mean-fields, or, writing yields MHD dynamo diamagnetic dynamo

35. Measurement of diamagnetic dynamo Ji et al TPE-1RM20 RFP Different dynamo mechanisms dominate in different parameter regimes

36. Kinetic Dynamo • Radial transport of parallel current (electron momentum) by particle motion along stochastic magnetic field • Can show, radial flux of parallel current ~ not yet measured

37. Open questions(and relation to astrophysics) Nonlinear aspects of MHD dynamo • Is nonlinear physics of growing field similar to that of steady state dynamo • Does strong dynamo effect in lab have implication for astrophysical dynamo saturation? • What is the role of reconnection in astrophysical dynamos? • Does current (magnetic field) transport play a role in astrophysics? • What is role of nonlinear coupling in altering wave functions near reconnection surface?(Need a nonlinear theory)

38. Non-MHD effects • What are the relative contributions of the various mechanisms? Dependence on parameters? • Does the detailed mechanism matter? • Are non-MHD mechanisms active in astrophysics?