The integral equation approach to kinematic dynamo theory and its application to dynamo experiments in cylindrical geometry

The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed to an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting fluid and to its boundary. This integral equation approach is applied to simulate kinematic dynamos within cylindrical geometry including the von Karman sodium (VKS) experiment and the Riga dynamo experiment. A modified version of this approach is utilized to investigate magnetic induction effects under the influence of externally applied magnetic fields. The computed induced magnetic fields for the VKS experiment show a satisfactory agreement with the experimental results.