Electrodynamic Instability of a Self-Gravitating Fluid Cylinder under General Varying Electric Field

The electrodynamic instability of a self-gravitating dielectric fluid penetrated by a uniform axial electric field surrounded by a self-gravitating vacuum pervaded by general varying electric field is investigated. A general eigenvalue relation valid to all possible (symmetric and asymmetric) modes of perturbation for all (short and long) wavelengths is derived and discussed in detail. The model is gravitationally stable to the pure asymmetric disturbances modes while to symmetric modes it is so if the longitudinal wave number normalized with respect to the jet radius is equal to or greater than 1.0668 and vice versa. The axial electric fields pervaded interior and exterior to the cylinder are stabilizing or destabilizing for all disturbance modes according to some restrictions. The transverse varying electric field is purely stabilizing in the symmetric disturbances for all wavelengths, while it is stabilizing in the asymmetric disturbance under some restrictions. The electrodynamic force has a strong stabilizing influence in the symmetric mode and can suppress the gravitational instability above a certain value of the basic electric field