Nearby-fluids equilibria. I. Formalism and transition to single-fluid magnetohydrodynamics

The nearby-fluids model is an improvement of the basic two-fluid flowing equilibrium system developed elsewhere [L.C. Steinhauer, Phys. Plasmas 6, 2734 (1999)]. The two-fluid system is a singular perturbation problem in which the usually small ion-inertia length (ion skin depth) gives rise to a small parameter. This has frustrated attempts to find practical equilibria. The nearby-fluids ordering assumes that the ion and electron flow surfaces are close to (“nearby”) each other but do not coincide exactly. This eliminates the singularity and “softens” the stiff differential equations, thus facilitating numerical solution. Previous treatments of two-fluid equilibria did not find a smooth transition to the single-fluid magnetodynamics (MHD) model in the small ion-inertia-length limit. This difficulty is only partly eliminated by recognizing that the electric field is ordered “large” in MHD. A small but nonzero ion-inertia length produces several important effects, including the appearance of a transition lay...

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