Self-Consistent Method for Determining the Boundary Shape between a Plasma and a Magnetic Field

A calculational method of determining the boundary surface between a plasma and a magnetic field is described. The method consists of neglecting the curvature of the surface and approximating the magnetic field adjacent to the boundary by a sum of the field due to the local surface current and the plasma-independent magnetic field source. This field is used in the boundary equations to compute the boundary surface. The resulting surface is then used to compute the magnetic field due to the curvature of the surface and the computation of the boundary surface is repeated. Reiteration of the calculational steps is continued until a self-consistent solution is obtained in which the magnetic field resulting from the curvature of the previous surface is used to obtain a surface whose shape does not differ from the previous surface by more than the imprecision of the calculation of the magnetic field. The method is illustrated by application to three simple problems of (1) a line dipole immersed in a plasma exerting a constant pressure on the boundary, (2) a point dipole immersed in plasma exerting constant pressure, and (3) a line dipole in a plasma stream exerting a pressure in only one direction (parallel to the stream velocity).