Non-axisymmetric magnetodynamic instability of a fluid cylinder subject to varying fields

Abstract

The magnetodynamic instability of a fluid cylinder subject to the inertia, capillary and electromagnetic (the fluid is pervaded by uniform field and surrounded by a field which is generally varying) forces is presented to all (axisymmetric and non-axisymmetric) modes of perturbation. A general dispersion relation is derived, studied analytically and the results are confirmed numerically for different values of the vacuum magnetic field. The surface tension has the same influence as in the absence of the magnetic fields; however, sometimes for certain values of the vacuum field parameters the capillary instability is completely suppressed. The axial magnetic fields inside and outside the cylinder always have stabilizing effects to all modes of perturbation, whatever the values of the problem parameters are, as is expected. The azimuthal vacuum varying magnetic field has a destabilizing or stabilizing effect according to certain restrictions. This is confirmed by studying the dispersion relation asymptotically and numerically. It is found that there are unstable states in the non-axisymmetric modes, this is due to the fact that the vacuum magnetic field is a varying field and not uniform. In contrast to the case in which just uniform fields are acting, the model is completely stable in all non-axisymmetric modes.