Abstract

Mean-field approaches to long wavelength dynamo instabilities have until recent years focused on the kinematic case where the velocity field is prescribed and the small-scale magnetic fields are driven by interactions between the flow and the large-scale magnetic field. However this approach will not work when there is an equilibrated small-scale dynamo with dynamically active small-scale magnetic fields, since then the evolution of any long-wavelength disturbances involves simultaneous consideration of the induction and momentum equations. I will show how a formalised theory can be developed for such instabilities if they exist, and discuss conditions under which this can give meaningful information on the long time evolution of the system. I will also discuss the related general question of the effects on disordered dynamical systems of small symmetry-breaking perturbations. Joint work with David Hughes (Leeds) Joanne Mason (Exeter) and Alastair Rucklidge (Leeds)