Steady dynamos in finite domains: an integral equation approach
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The paper deals with the integral equation approach to steady kinematic dynamo models in finite domains based on Biot-Savart's law. The role of the electric potential at the boundary is worked out explicitly. As an example, a modified version of the simple spherical $α$-effect dynamo model proposed by Krause and Steenbeck is considered in which the $α$-coefficient is no longer constant but may vary with the radial coordinate. In particular, the results for the original model are re-derived. Possible applications of this integral equation approach for numerical simulations of dynamos in arbitrary geometry and for an ''inverse dynamo theory'' are sketched.
18 pages, submitted to Astron. Nachr
18 pages, submitted to Astron. Nachr