Electrodynamic Stability of a Self-Gravitating Cylinder

Abstract

The electrodynamic (in-) stability of a self-gravitating dielectric fluid cylinder ambient with dielectric medium is discussed. A general dispersion relation valid to all (axisymmetric and non-axisymmetric) modes of disturbance is derived. The model is gravitationally stable to all non-axisymmetric disturbance modes while to axisymmetric mode it is so if the longitudinal wavenumber normalized with respect to the radius of the fluid cylinder is equal to or greater than 1.0668 and vice versa. The electrodynamic force has always stabilizing effects to all modes of disturbance for all wavelengths whatever the electric field intensity strength. As the latter is increasing the gravitational instability is decreasing and above a certain value of the electric field intensity the gravitational instability is completely suppressed and stability sets in. These analytical results are confirmed numerically.