On the integral equation approach and some related inverse problems in MHD

Solving the induction equation has become a synonym for kinematic dynamo studies. We present an alternative integral equation method to solve steady and time-dependent kinematic dynamo problems. This method, which relies on Biot-Savart's law, can be efficiently used to handle dynamos in arbitrary domains, for example in rectangular geometry and finite cylinders. The approach serves also as the basis for various inverse problems in MHD at small and large magnetic Reynolds numbers. The solution of such inverse problems is illustrated by the "Contactless inductive flow tomography" and by the inference of flow features in the Riga dynamo experiment from externally measured magnetic field data.