Steady dynamos in finite domains: an integral equation approach

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 $\alpha$-effect dynamo model proposed 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 arbitrary geometry and for an ‘‘inverse dynamo theory’’ are sketched.