Rotating toroidal equilibria of quasi-neutral and non-neutral plasmas

Starting from the fundamental ion and electron fluid equations, a “master” equilibrium equation set is constructed for axisymmetric toroidal plasmas. These equations retain the effects of different ion and electron densities, temperatures, sheared rotation, and electric forces. The master equation is then examined in various limits including the non-neutral plasma limit. An ordering is assumed which makes the effects of the Reynolds stress, pressure, magnetic stress, and electric field stress all comparable emphasizing the natural transition from the non-neutral case to the quasi-neutral one. For sub-relativistic flows, charge separation effects are only significant for nearly force-free plasmas. A set of equilibrium equations are derived for three different cases: (A) n i ≈n e , (B) n i ≠n e ≠0 , and (C) n i =0 and n e ≠0 . In the pure electron plasma case, the resulting equilibrium equation includes the effects of toroidal rotation, poloidal magnetic field, and electron pressure extending the equation of Daugherty and Levy [Phys. Fluids 10, 155 (1967)].