Detailed derivation of axisymmetric double adiabatic MHD equilibria with general plasma flow

Abstract

We derive a system of equations to describe stationary axisymmetric MHD equilibria characterized by toroidal and poloidal ows as well as plasma anisotropy due to strong magnetic eld and eventual auxiliary heating methods. The system consists of a nonlinear partial di erential equation for the poloidal magnetic ux function and an algebraic Bernoulli-type equation, which relates plasma density with several surface functions. We analyse the ellipticity of the equation and the plasma density bifurcation as the Alfven-Mach n umber is changed.

Adiabatic plasma rotations and symmetric magnetohydrodynamical stationary equilibria: analytical and semi-numerical solutions

“…This is not the only type of motion compatible with mass continuity equation, though. It is possible to show that the most general such motion consists of a combined toroidal and poloidal rotation, although the equations are far more difficult to solve [9,22,23].…”

Stationary MHD equilibria describing azimuthal rotations in symmetric plasmas

“…1,20 The equilibrium equation was applied to anisotropic plasma equilibria by Clemente and Viana. 21,22 A general equilibrium equation with differentially varying radial electric fields was proposed by Tasso and Thromolopoulos, who showed the nonexistence of axisymmetric equilibria with purely poloidal flows or nonparallel flows with isothermal magnetic surfaces and omnigenous equilibria. 23 Dotting (2) with B results in B Á rp ¼ ÀqB Á ðv Á rÞv, which is nonzero for a finite velocity.…”