SELF-GRAVITATING INSTABILITY OF AN ANNULAR FLUID JET SURROUNDING A MANTLE TAR COLUMN UPON OSCILLATING PERIODICAL ELECTRIC-FIELDS

The self-gravitating instability of an annular fluid jet surrounding a very dense mantle tar cylinder under oscillating periodical oblique e lectric fields has been developed. The potential and kinetic energies of the system are computed and the characteristic integral differentia l Mathieu equation is derived by utilizing the Lagrangian energy princ iple. Some reported works could be recovered as limiting cases. The mo del is self-gravitationally unstable in axisymmetric mode while it is stable otherwise giving easier experimental observation relative to fl uid jets without a mantle. The electrodynamic force has a strong stabi lizing influence. Resonance domains appear due to the field periodicit y and in some regions the stability conditions depend only on the fiel d frequency. Thence the time-dependent oscillating electric field impr oves the electrogravitational instability and reduces it to a minimum. However, whatever is the largest electrodynamic stabilizing influence , the self-gravitational instability will never be suppressed because the gravitational instability of sufficiently long waves will persist and this is physically interpreted.