Steady dynamos in finite domains: an integral equation approach

The paper deals with the integral equation approach to steady kinematic dyn amo models in finite domains based on Biot-Savart's law. The role of the el ectric potential at the boundary is worked out explicitly. As an example, a modified version of the simple spherical alpha-effect dyrlamo model propos ed by Krause and Steenbeck is considered in which the alpha-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 ar bitrary geometry and for an "inverse dynamo theory" are sketched.