Dynamic nonlinearity in large scale dynamos with shear

An explicitly time dependent equation for the alpha-effect in mean field dynamo theory is employed to ensure that the magnetic helicity equation for the total (small and large scale) magnetic field is obeyed exactly. The dependence of the turbulent magnetic diffusivity on the field strength is unconstrained by magnetic helicity conservation and is therefore employed as a free parameter. The approach is applied to mean field models with shear that exhibit migratory dynamo waves. We find that a modest quenching of magnetic diffusivity is compatible with relevant nonlinear turbulence simulations available to date. Whether or not the cycle period remains of the order of the dynamical time scale at large magnetic Reynolds number depends on the assumption made about the turbulent magnetic diffusivity. This is at present not well constrained by the simulations. Subject headings: MHD – turbulence