Stability of rolls in rotating magnetoconvection in a layer with no-slip electrically insulating horizontal boundaries.

We consider the onset of Boussinesq convection in a horizontal layer of electrically conducting fluid rotating about a vertical axis with an imposed vertical magnetic field. Rigid electrically insulating horizontal boundaries are assumed. Our goal is to identify the region of parameter values, for which rolls emerge at the onset of convection. The following conditions are necessary for convective fluid motion to set in as stable rolls: instability of the trivial steady state is monotonic; the rolls bifurcate supercritically; they are stable to perturbations of the form of rolls rotated by any angle (without an imposed magnetic field this is called the Küppers-Lortz instability). For each of the three conditions we derive equations for respective boundaries in the parameter space and determine the boundaries numerically.