Numerical solutions of three-dimensional pressure-bounded magnetohydrostatic flux tubes

We present a three-dimensional technique for the solution of the magnetohyd rostatic equations when we are modeling structures bounded by a current she et that is free to move to satisfy pressure balance. The magnetic field is expressed in terms of Euler potentials and the equations are transformed to flux coordinates, greatly simplifying the problem of locating the free bou ndary. Multi-grid techniques are used to rapidly solve the resulting nonlin ear elliptic partial differential equations. The method is tested against L ow's (1982) exact solution of a bipolar plasma loop. It is shown that fast, accurate solutions can be found.