A non-axisymmetric magnetorotational instability of a purely toroidal   magnetic field
  We consider the flow of an electrically conducting fluid between differentially rotating cylinders, in the presence of an externally imposed toroidal field B_0 (r_i/r) e_phi. It is known that the classical, axisymmetric magnetorotational instability does not exist for such a purely toroidal imposed field. We show here that a non-axisymmetric magnetorotational instability does exist, having properties very similar to the axisymmetric magnetorotational instability in the presence of an axial field. 
R. Hollerbach, G. Rudiger, M. Schultz, D. Elstner