Stability of Compressible Hollow Jet Pervaded by a Transverse Varying Magnetic Field

The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by a transverse varying magnetic field, under the influence of capillary, inertia, and Lorentz force, has been developed. The problem is modelized. The basic equations formulated, solved, and, upon applying appropriate boundary conditions, the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the nonaxisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform field and varying transverse one. The axial field is stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here, the high compressibility increases rapidly the magnetodynamic stable domains and leads to shrinking those of instability.