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 into 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 first employed to simulate kinematic dynamos excited by Beltrami-like flows in a finite cylinder. The impact of externally added layers around the cylinder on the onset of dynamo actions is investigated. Then it is applied to simulate dynamo experiments within cylindrical geometry including the “von Kármán 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 which is also important to measure the proximity of a given dynamo facility to the self-excitation threshold.