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

摘要

It is shown that a special class of time-dependent solutions of the ideal two-dimensional magnetohydrodynamic equations, which has been found for pressure profiles with exponential dependence on the flux function, can be generalized to pressure profiles with arbitrary dependence on the flux function. Particular properties of the solution class are vanishing plasma acceleration and an adiabatic index gamma=1. It is also shown that the plasma temperature does not have to be uniform in space as assumed in the derivation for the exponential solution class, but that it can vary across field lines. This allows a much wider range of solutions than previously thought, because any numerical or analytical solution of the time-independent Grad-Shafranov equation can be transformed into a time-dependent solution of the magnetohydrodynamic equations. (C) 2000 American Institute of Physics. [S1070-664X(00)02507-6]. [References: 9]