Abstract
The electrodynamic instability of a self-gravitating gas cylinder dispersed in a self-gravitating ideal fluid pervaded by a longitudinal periodic field has been developed on utilizing the Lagrangian energy principle. The basic equations are formulated, solved and the total changes in electric, kinetic and gravitational energies are identified, and on using the Lagrangian second-order differential equation, the perturbed system is governed by the integro-differential Mathieu equation. Under appropriate choices we could recover some reported works as limiting cases. The self-gravitating gas-core fluid jet is purely (infinite) unstable as long as the fluid is denser than the gas. If the gas and the fluid have equidensities we have neutral stability while there are stable and unstable domains if the gas is denser than the fluid matter and this has a correlation with the destroying of the spiral arms of galaxies and also with the appearance of condensation within celestial bodies. The stabilizing influence of the modulating electrodynamic force improves the gravitational stability of the present model. Resonance domains appear due to the field periodicity and in some regions the stability conditions depend only on the field frequency. Above the appropriate values of the electric-field strength and frequency, the self-gravitating instability could be reduced to a minimum and stability arises. The dielectric gravitational gas-core fluid cylinder is stable as the frequency of the periodic electric field is greater than a certain critical value omega(c). The time-dependent electric field is destabilizing or not under some restrictions of the densities ratio rho(e)/rho(i) as well as that of dielectric constants of the two media with rho(i) gas density and rho(e) fluid density. As rho(e) less than or equal to rho(i) the frequency omega(c) is stabilizing while it is destabilizing as rho(e) > rho(i) for all short and long wavelengths in non-axisymmetric perturbation modes. In axisymmetric mode, omega(c) is destabilizing as rho(e) > rho(i) while it is stabilizing or not as rho(e) less than or equal to rho(i) according to restrictions.