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

Abstract

Plasma rotation appears in many problems of fusion (neutral beam injection) and astrophysical (magnetic stars) interest. In the case of a time-independent plasma velocity it is possible to describe a stationary magnetohydrodynamical (MHD) equilibrium by a set of infinitely nested flux surfaces. Maschke and Perrin have obtained an equation describing stationary MHD equilibria for azimuthal (toroidal) plasma rotations, when the entropy is constant on magnetic flux surfaces. In the present paper we express their equation in curvilinear coordinates, both in orthogonal and non-orthogonal cases, provided there is an ignorable quantity. This equation is presented in some coordinate systems of plasma physics interest. We consider approximated analytical and semi-analytical solutions for plasma configurations in cylindrical and spherical coordinates.