Treatment of the Prager Problem of Potential Theory by the Integral Equation Method

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Abstract
The Prager problem deals with the derivation of source-free vector fields from vector potentials of vortices. Necessary and sufficient conditions are given for the requested volume and surface vortex distribution in multiply connected three-dimensional regions. Further examinations are made for the vectorial Fredholm integral equation of the second kind holding for the surface vortex density. For the numerical treatment of this integral equation in arbitrary doubly connected three-dimensional regions an iteration method is developed, which requires the knowledge of a qualified approximate solution of the adjoint homogeneous equation. Integrating by the trapezoidal rule, the numerical calculation is executed for a torus and a special stellarator.

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