1. Experimental Tests of Two-Fluid Relaxation D. Craig and MST Team University of Wisconsin – Madison General Meeting of the Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas October 5-7, 2005 Princeton, NJ

2. Outline What is two-fluid relaxation? Experimental indications in the literature Signatures of two-fluid relaxation in MST Possible astrophysical venues for two-fluid relaxation

3. Single Fluid / Taylor Relaxation Key Idea: (J.B. Taylor, PRL 33,1139 (1974)) Global magnetic helicity (K m = A B dV) conserved i.e. K m decays more slowly than magnetic energy, U m Relax to minimum magnetic energy holding K m fixed (happens via in MHD) Experiments tend toward Taylor state when fluctuations are strong Repeatable preferred physical states are observed J B/B 2 profile becomes more uniform K m is better conserved than U m Not perfect description of experiment Often see only partial relaxation Some predicted Taylor states not seen (e.g. helical RFP) No predictions for plasma flow

4. Two-Fluid Relaxation Key Idea: e.g. L.C. Steinhauer and A. Ishida, Phys Plasmas 5, 2609 (1998) S.M. Mahajan and Z. Yoshida, PRL 81, 4863 (1998) C.C. Hegna, Phys Plasmas 5, 2257 (1998) Generalized helicity for each species (K s = A s B s dV) conserved where A s = A + (m s /q s ) v s and B s = A s Relax to minimum magnetic + flow energy (via v B and J B) Features of relaxed equilibria: Relaxation (flattening) of both J B/B 2 and nv B/B 2 profiles Parallel current and parallel momentum profiles get coupled Note: Although relaxation of B(r) or J(r) in low systems could be weakly affected by two-fluid effects, relaxation of v(r) and P(r) may be more strongly affected. (And vice-versa for gravitational or very high systems?)

5. E. Kawamori and Y. Ono, PRL 95, 085003 (2005) TS-4 experiment in Japan Merge spheromaks of opposite helicity Find bifurcation to FRC (~ no B toroidal ) or another spheromak Bifurcation occurs at critical value of net magnetic helicity K Spheromak Merging Shows Some Signs Of Two-Fluid Relaxation

6. E. Kawamori and Y. Ono, PRL 95, 085003 (2005) Spheromak Merging Shows Some Signs Of Two-Fluid Relaxation (continued) (# of ion skin depths in plasma) (~ critical net helicity) Observe that critical helicity for forming FRC varies with ion skin depth (FRC more likely for large skin depth) Generation of strong flows also more likely with large ion skin depth

7. FRC Production in Magnetic Mirror May Show Signs of Two Fluid Relaxation 1. Plasmoid formed here 2. Injected into mirror 3. Bounces off ends and relaxes to FRC Repeatable preferred states observed after relaxation Toroidal flows generated, flux conversion Estimated generalized ion helicity, saw ~ 30% drop Drop in total energy is huge (translational E thermal E) H.Y. Guo et al., PRL 92, 245001-1 (2004)

8. Signatures of Two-Fluid Relaxation in MST Conservation of various helicities relative to various energies: Relaxation of parallel flow, alignment of flow along B Important For Two-Fluid Relaxation

9. Flow Contribution to Generalized Helicities is Small in MST 10 -3 10 -5 10 -7 Contribution of v e to K e is even smaller than v i to K i Change in K m at sawtooth crash is ~ 4%, change in U m ~ 10% K cross = v B dV is roughly constant during crash Accurate measurement of K m (i.e. B(r)) is important (all terms are negative for MST)

10. Parallel Flow Profile Appears to Become More Uniform During Relaxation in MST Spectroscopic measurements give core flow Probe measurements give edge flow

11. Poloidal Flow Profile Becomes More Edge Peaked During Crash Array of passive Doppler chords measures line-averaged flow B is also more poloidal in edge alignment of v and B Next step: Localized measurements of flow profile v

12. Possible Astrophysical Cases Where Two-Fluid Relaxation May Apply Jupiter magnetosphere (J. Shiraishi et al., Phys. Plasmas 12, 092901 (2005)) Stellar/accretion disk coronae (S.M. Mahajan et al., ApJ 576:L161 (2002)) Radio lobes Rotating systems (accretion/momentum transport are linked to B from dynamo?) Anywhere two-fluid effects dominate the reconnection layers

13. Summary Two-fluid relaxation theories have been proposed Both v and J undergo relaxation Conserved generalized helicities for ions and electrons These might apply in some astrophysical systems Experimental verification to date is very limited Does two-fluid relaxation occur in MST? Flow profile shows some signatures Too early to tell about generalized helicity conservation This is an area where all CMSO experiments might be able to contribute in a complementary way