QUASI-EQUILIBRIA - A SPECIAL-CLASS OF TIME-DEPENDENT SOLUTIONS OF THE 2-DIMENSIONAL MAGNETOHYDRODYNAMIC EQUATIONS

A special method is presented to construct exact time-dependent solutions of the two-dimensional ideal magnetohydrodynamic (MHD) equations for which plasma elements experience no acceleration. The momentum equation then contains the time merely parametrically and assumes the structure of an equilibrium equation. For a special form of the pressure profile p(A), for which the corresponding quasi-equilibrium equation is a completely integrable non-linear elliptic equation that is invariant under conformal transformations, these invariance properties are then used to determine the possible time-dependences of the solutions. Contrary to the common use of the term quasi-equilibrium arbitrarily large plasma velocities are allowed in the present treatment. In polar coordinates, the time evolution turns out to be self-similar in the radial coordinate, but it is in general not self-similar in the azimuthal coordinate. The adiabatic exponent of the plasma is found to he equal to one, which means that the plasma is isothermal. Explicit examples of solutions are discussed. (C) 1995 American Institute of Physics.