QUASI-EQUILIBRIA - A SPECIAL-CLASS OF TIME-DEPENDENT SOLUTIONS OF THE2-DIMENSIONAL MAGNETOHYDRODYNAMIC EQUATIONS

A special method is presented to construct exact time-dependent soluti ons of the two-dimensional ideal magnetohydrodynamic (MHD) equations f or which plasma elements experience no acceleration. The momentum equa tion then contains the time merely parametrically and assumes the stru cture of an equilibrium equation. For a special form of the pressure p rofile p(A), for which the corresponding quasi-equilibrium equation is a completely integrable non-linear elliptic equation that is invarian t under conformal transformations, these invariance properties are the n used to determine the possible time-dependences of the solutions. Co ntrary to the common use of the term quasi-equilibrium arbitrarily lar ge plasma velocities are allowed in the present treatment. In polar co ordinates, the time evolution turns out to be self-similar in the radi al 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 o f solutions are discussed. (C) 1995 American Institute of Physics.