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Experimental Tests of Two-Fluid Relaxation

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. Outline. What is two-fluid relaxation?

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Experimental Tests of Two-Fluid Relaxation

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  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, PRL33 ,1139 (1974)) • Global magnetic helicity (Km= AB dV) “conserved” i.e. Km decays more slowly than magnetic energy, Um • Relax to minimum magnetic energy holding Km fixed (happens via in MHD) • Experiments tend toward Taylor state when fluctuations are strong •  Repeatable preferred physical states are observed • JB/B2 profile becomes more uniform • Km is better conserved than Um • 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 Plasmas5, 2609 (1998) • S.M. Mahajan and Z. Yoshida, PRL81, 4863 (1998) • C.C. Hegna, Phys Plasmas5, 2257 (1998) •  Generalized helicity for each species (Ks=AsBs dV) “conserved” • where As = A + (ms/qs) vs and Bs = As •  Relax to minimum magnetic + flow energy (via vB and JB) • Features of relaxed equilibria: • Relaxation (flattening) of both JB/B2 and nvB/B2 profiles • Parallel current and parallel momentum profiles get coupled • Note: • Although relaxation of B(r) or J(r) in low b 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 b systems?)

  5. Spheromak Merging Shows Some Signs Of Two-Fluid Relaxation • TS-4 experiment in Japan • Merge spheromaks of opposite helicity • Find bifurcation to FRC (~ no Btoroidal) or another spheromak • Bifurcation occurs at critical value of net magnetic helicity K E. Kawamori and Y. Ono, PRL95, 085003 (2005)

  6. (~ critical net helicity) (# of ion skin depths in plasma) Spheromak Merging Shows Some Signs Of Two-Fluid Relaxation (continued) • 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 E. Kawamori and Y. Ono, PRL95, 085003 (2005)

  7. FRC Production in Magnetic Mirror May Show Signs of Two Fluid Relaxation H.Y. Guo et al., PRL92, 245001-1 (2004) 1. Plasmoid formed here 3. Bounces off ends and relaxes to FRC 2. Injected into mirror • 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)

  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 10-7 10-5 10-5 10-3 (all terms are negative for MST) • Contribution of ve to Ke is even smaller than vi to Ki • Change in Km at sawtooth crash is ~ 4%, change in Um ~ 10% • Kcross =  vB dV is roughly constant during crash • Accurate measurement of Km (i.e. B(r)) is important

  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 vq Next step: Localized measurements of flow profile

  12. Possible Astrophysical Cases Where Two-Fluid Relaxation May Apply • Jupiter magnetosphere (J. Shiraishi et al., Phys. Plasmas12, 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

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