Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas

Abstract

The relaxation theory of a two-species magnetofluid is presented. This generalizes the familiar magnetohydrodynamic (single-fluid) theory. The two-fluid invariants are the self-helicities, one for each species. Their “local” invariance follows from the helicity transport equations, which are derived. The global forms of the self-helicities are examined in a weakly dissipative system. They are shown to pass three tests of ruggedness (“relative” invariance compared with the magnetofluid energy): the cascade test; the selective decay test; and the stability to resistive modes test. Once ruggedness is established, relaxed states can be found by minimizing the magnetofluid energy subject to constrained self-helicities. The Euler equations are found by a variational procedure. Example equilibria are presented that resemble field-reversed configurations (FRCs) and tokamaks. These states are characterized by finite pressure and significant sheared flows. Throughout the analysis it is shown how this more general theory reduces to the magnetohydrodynamic (single-fluid) theory for suitable reducing assumptions.