Toroidal MHD equilibria and classical diffusion in complex magnetic configurations

Abstract

Ideal MHD equilibrium for toroidal plasma situated in a magnetic field with single non-planar magnetic axis with variable torsion and curvature is investigated. The plasma is taken to have a non-circular cross section (elliptically or triangularly deformed) through which a longitudinal current with a flat profile flows. Equilibria of the Tokamak or French Harmonica types are examined as special cases of the general class and it is shown that for a given longitudinal current and torsion of the magnetic axis the effect of triangular deformation on the limiting value of beta (the ratio of kinetic to magnetic pressure) is weak and can be neglected. Vertically elongated elliptical deformation of the plasma cross section is shown to lead to an increase in the limiting value of beta relative to that of a circular cross section. Moreover, classical diffusion of non-axisymmetric toroidal plasma is examined with the result that vertical elongation tends to decrease diffusion while triangular deformation appears to show an effect only at high beta .