Generalization of a special class of time-dependent solutions of the two-dimensional magnetohydrodynamic equations to arbitrary pressure profiles

It is shown that a special class of time-dependent solutions of the ideal t wo-dimensional magnetohydrodynamic equations, which has been found for pres sure profiles with exponential dependence on the flux function, can be gene ralized to pressure profiles with arbitrary dependence on the flux function . Particular properties of the solution class are vanishing plasma accelera tion and an adiabatic index gamma=1. It is also shown that the plasma tempe rature does not have to be uniform in space as assumed in the derivation fo r the exponential solution class, but that it can vary across field lines. This allows a much wider range of solutions than previously thought, becaus e any numerical or analytical solution of the time-independent Grad-Shafran ov equation can be transformed into a time-dependent solution of the magnet ohydrodynamic equations. (C) 2000 American Institute of Physics. [S1070-664 X(00)02507-6].