Turbulent relaxation of compressible plasmas with flow

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Abstract
Relaxation of compressible plasmas to an equilibrium with flows is studied. The magnetohydrodynamic (MHD) equations with large parallel thermal conductivity and ergodic field lines show that ∫v⋅B is an invariant even with compression. Also, S=∫ρ ln( p/ργ) is the only entropy‐like invariant of the MHD equations with infinite parallel thermal conductivity; S increases in time with finite thermal conductivity. The other invariants are energy, helicity ∫A⋅B, mass ∫ρ, and possibly angular momentum. Equilibria are found by extremizing energy while conserving these invariants or by maximizing entropy with the energy and other invariants as constraints. These invariants are complete in the sense of generating all equilibria that form after relaxation with ergodic field lines. For parallel flows, there are three classes of solutions characterized by the sign of dρ/dB2 and the mirror mode parameter. A sufficient condition for stability is derived. This condition is never satisfied by the class with dρ/dB2>0, indicating the possibility of unstable resistive interchanges. The class with dρ/dB2<0 is stable if generalizations of the local firehose and mirror criteria are satisfied, and if generalized Taylor helicity eigenvalues exceed those of the equilibrium. A comparison of these conditions with those of Frieman and Rotenberg is discussed.