A toy model for inverse dynamo theory

For a simple spherically symmetric mean-field dynamo model the radial dependence of $\alpha$ is determined from eigenvalues of some spherical harmonics by means of an evolutionary strategy code. The same code is used for "energetic" optimization as well as for constructing dynamo models with level-crossing. The connection with isospectrality problems in quantum mechanics is outlined. Consequences for a general inverse dynamo theory are discussed.