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Selfgravitating electrodynamic stability of a fluid-tar annular jet pervaded by periodic time dependet electric field

Radwan Ahmed E.

Journal of Applied Analysis

1998

Vol. 4, nr 1

89-109

The self-gravitating electrodynamic stability of an annular fluid jet (a fluid jet having a tar cylinder as a mantle) pervaded and surrounded by periodic time dependent electric field has been developed. The perturbed system equations describing the model motion is turned to a second integro-differential Mathieu equation. The self-gravitational force is destabilizing only for small axisymmetric perturbation modes. The radii tar-fluid cylinders ratio plays an important role in stabilizing the model. The periodic longitudinal electric field is strongly destabilizing for all perturbation modes. However under some restrictions (independent of the electric field amplitude), it is found that the electric field frequency has a stabilizing influence and that influence suppresses almost the instability character of the annular jet. In contrast to the same model pervaded by classical (constant) electric field, the self-gravitational instability will never be suppressed whatever is the strength of the pervaded electric field. The present analyses have been performed on the basis of the Lagrangian energy principle which it was not an easy job.