Instability of a compressible annular magnetized fluid

The instability of a compressible annular cylindrical fluid jet coaxial with a very dense fluid cylinder of negligible inertia endowed with surface tension and acting upon the electromagnetic force has been developed. A general eigenvalue relation is derived and discussed for all disturbances. The capillary force is destabilizing only for small symmetric perturbations and stabilizing for the rest. The axial fields internal and external to annular jet have stabilizing influences for all wavelengths in all possible perturbation modes. The azimuthal tenuous varying field is purely destabilizing in the symmetric mode but it is stabilizing or destabilizing in the asymmetric modes according to restrictions. The compressibility has a stabilizing tendency for all wavelengths. The capillary instability of the compressible fluid may be completely suppressed above a certain value of the basic magnetic field provided that the tenuous azimuthal field is very low and then the MHD stability arises. Some reported works are deduced as limiting cases.