High-Beta Axisymmetric Equilibria with Flow in Reduced Single-Fluid and Two-Fluid Models

Abstract

Reduced single-fluid and two-fluid equations for axisymmetric toroidal equilibria of high-beta plasmas with flow are derived by using asymptotic expansions in terms of the inverse aspect ratio. Two different orderings for the flow velocity, comparable to the poloidal Alfvén velocity and comparable to the poloidal sound velocity, are considered. For a poloidal-Alfvénic flow, the two-fluid equilibrium equations with hot ion effects are shown to have a singularity that is shifted by the gyroviscous cancellation from the Alfvén singularity found in singlefluid magnetohydrodynamics (MHD) when the poloidal flow velocity equals the poloidal Alfvén velocity. For a poloidal-sonic flow, a reduced single-fluid model is used to derive a set of equilibrium equations that includes higher-order terms. The singularity at a poloidal flow velocity equal to the poloidal sound velocity is recovered in the higher order equations.