Ellipticity of axisymmetric equilibrium with flow and pressure anisotropy in single-fluid and Hall MHD

The ellipticity criteria for the partial differential equations of axisymmetric single-fluid and Hall magnetohydrodynamic (MHD) equilibria with flow and pressure anisotropy are investigated. The MHD systems are closed with cold ions and electron pressures derived from their parallel heat flux equations, a closure that reproduces the corresponding kinetic dispersion relation. In the single-fluid model, which differs from the double-adiabatic Chew-Golberger-Low (CGL) model, it is verified that the elliptic region boundaries occur at poloidal flow velocities equal to wave velocities from the kinetic dispersion relation. For Hall MHD, a set of anisotropic-pressure equilibrium equations is derived and an ellipticity condition corresponding to a poloidal flow velocity slightly smaller than the ion sound velocity is obtained. (author)