Optimised axially-symmetric kinematic dynamos

The kinematic dynamo problem is a useful simplification of the full dynamo problem. A steady fluid flow is selected, and the magnetic field solved for, seeking steady or growing solutions in time. Unfortunately, the results depend sensitively on the form of the flow chosen. We investigate using optimisation to reduce the ambiguity of the solution. We focus on simple axially-symmetric flows with high symmetry, optimising to minimise the critical magnetic Reynolds number (Rmcrit) required for dynamo action. Defining Rm in terms of a measure of flow velocity, common in geomagnetism, the optimisation does not converge. The problem is better posed when defined in terms of a measure of strain rate. We obtain solutions for Rmcrit within an order of magnitude of a formal lower bound for dynamo action.