General Solution of Two-Dimensional Chapman-Ferraro Problem of Magnetospheric Cavity

Abstract

The famous Chapman-Ferraro problem form the determination of the magnetospheric cavity is elucidated for its two-dimensional solutions in mathematical detail. The general solution presented in this paper amounts to a complex variable extension of the well-known Poisson¡¦s intergral formula for the Dirichlet problem for a half-plane or a circle domain. It provides the needed methodology for obtaining desirable solutions that avoid the defects ingerent in the Dungey-Hurley solution, which uses Ferraro¡¦s approximation of pressure balance as the boundary condition.

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