SYMMETRY OF MAGNETOHYDRODYNAMIC FLOWS

Stationary magnetohydrodynamic flows permit a bewildering variety of s olutions. Since no theory exists to limit the choice to more or less p hysically significant hows, the best one can do at present is to organ ize the different possibilities according to their symmetry properties , using group theory. In this paper we consider stationary compressibl e hows with translation symmetry. We pay special attention to the para metrization of the equations and reduce them to the most compact form possible which clearly reflects the different physical mechanisms at w ork. This is done in analogy with studies of static tokamak equilibria . Of course, the latter is a very special and simplified limit of the much wider class of stationary MHD flows. Nevertheless, non-trivial re duction of the number of parameters is both interesting and useful sin ce it prevents redundant parameter scans in the computations. Differen t classes of solutions are considered. By means of symmetry arguments, the original nonlinear partial differential equations are reduced to nonlinear ordinary differential equations, The latter are solved expli citly, both analytical and numerical, and the solutions are analyzed w ith respect to their singularities, fixed points, periodicities, etc. The theory is applicable to both astrophysical and laboratory plasmas.