Relaxation of a Two-Specie Magnetofluid

Abstract

The relaxation theory of an ideal magnetofluid is developed for a multispecie magnetofluid. Its invariants are the self-helicities, one for each specie. Their "local" invariance in the ideal case follows from the helicity transport equation. The global forms of the self-helicities are investigated for a twofluid (ion and electron), and their ruggedness in a weakly dissipative system is defended by cascade and selective decay arguments. In general the two-fluid theory predicts relaxed states with finite pressure and sheared flows. The familiar single-fluid relaxation theory, which admits only force-free states, is a reduced case of the present more general theory. [S0031-9007(97)04375-5] PACS numbers: 52.30.Bt, 47.65. + a, 52.55.DyKnowledge of a system's invariants often leads to an elegant qualitative picture of its behavior, particularly that such constraints cause it to self-organize into relaxed states [1]. An example is ideal magnetohydrodynamics (MHD) where the invariance of the magnetic helicity has fostered successful predictions of self-organization by certain classes of magnetofluid into force-free states, i.e., equilibria with no coupling force between the system's fluid and field elements [2,3]. However, practical magnetofluids in space and in fusion experiments are not generally force free, i.e., they exhibit significant fluid pressure. Further, significant flows (not predicted by the MHD theory) are a nearly ubiquitous feature of practical plasmas. A more realistic formulation of a magnetofluid is a multifluid system, e.g., a two-fluid (ions and electrons). In a multifluid the invariants are the self-helicities (one for each specie), which are canonical composites of the fluid and magnetic momenta. MHD is simply the reduced case of a twofluid in which the ion and electron responses are locked together; and the magnetic helicity is simply the electron self-helicity in the limit of massless electrons.In this Letter we develop the two-fluid theory of relaxation. Helicity transport equations, which govern the "local" form of a helicity, are derived from the equations of motion and Maxwell's equations. This leads to the ideal invariance (dissipationless case) of the self-helicities. The global form of a self-helicity is the integral of its local form over the system volume. The ruggedness of the global self-helicities subject to a weak dissipation is defended by cascade and selective decay arguments. In this analysis, the fluid-field coupling in turbulent fluctuations plays an important role. Finally, relaxed states follow from minimizing the magnetofluid energy subject to constrained self-helicities. Inspection of the resulting Euler equations together with the steady equation of motion shows that non-negligible fluid pressure and sheared flows are common features of relaxed states. Throughout the discussion, we show the relationship of this more general theory to the familiar reduced theory based on MHD.We begin by deriving equations for the evolution of two basic electromagnetic and two (for each speci...

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