An inverse glance at MHD

We give an overview about our recent activities to solve inverse problems appearing in various branches of MHD. The very general problem, the full reconstruction of velocity or turbulence parameters of fluid flows with arbitrary magnetic Reynolds numbers from externally measured magnetic fields varying in space and time, is tackled from two different corners. First, we explore the restricted inverse dynamo problem of determining, from a limited number of spectral data, the radial profile alpha(r) of an isotropic alpha^2 dynamo model. Among our results is the construction of oscillatory dynamos of this type, which might be of some interest for stellar dynamos. Second, we consider the topic of contactless velocity reconstruction in industrial applications with moderate magnetic Reynolds numbers from the measured deformation of two different external magnetic fields.