Three dimensions varying MHD instability of an annular fluid cylinder

Abstract

The magnetohydrodynamic (MHD) (in-)stability of an annular jet having a solid rod as a mantle acted upon by the capillarity, inertia and electromagnetic (with general vacuum varying magnetic fields) forces, is presented. An eigenvalue relation, based on the linear perturbation technique, valid for all disturbances is derived. The characteristics of the model are identified analytically, confirmed numerically and interpreted physically for different forms of the vacuum varying magnetic field and for several values of the basic field. There were unstable domains not only to axisymmetric disturbance but also to non-axisymmetric disturbances due to the strong destabilizing influence of the azimuthal vacuum varying field. In the absence of the latter, the electromagnetic force has a strong stabilizing effect and above a certain value of the basic magnetic field, the capillarity instability is completely suppressed and stability sets in. The thicker the solid cylinder, the larger its stabilizing effect and the oscillations are slowed down, so more and easier observations are allowed than in the case of a full liquid jet whether the model is acting upon by the capillarity or electromagnetic force or even the combined effect of them.