Analytic study of MHD-equilibria of plasmas with non-circular cross-sections

MHD-equilibria of plasmas with various half-axis ratios a/b are studied by conformal mapping in a sharpboundary model with surface currents (upper limit for compression ratio κb) and a conducting wall. Plasma surface and wall are co-ordinate surfaces. First, an exact equilibrium solution for a semi-infinite plasma slab between parallel walls is derived (a/b → ∞). It is found that κb is only 2, and that the plasma end is almost semi-circular in shape. Then a class of mapping functions is determined for various a/b that yields sufficiently accurate equilibria and flux lines in the vacuum field region (computing time of only a few seconds). The asymptotic value (a/b → ∞) of the κb-versus-a/b curve is the semi-infinite-slab result.