Influence of the electrodynamic stability of streaming fluid cylinders surrounded by dielectric gravitational fluid under a radial-varying electric field

We study the relation between the electrodynamic stabilization of self-gravitating dielectric fluid cylinders with varying densities subjected to radially varying electric fields. We derive the perturbations for all models studied. The electric fields inside and outside the fluid cylinder stabilize the system across different densities and wavelengths. Additionally, the use of a magnetic field is identified as a potentially effective method to inhibit the onset of unstable motion. Gravitational marginal stability occurs when the two densities are equal. Stable and unstable regions are determined for two densities at each wavelength in all symmetric and nonsymmetric axial perturbations. The effect of streaming is significant and destabilizing: it reduces the stable regions and enlarges the capillary axisymmetric unstable domain. Furthermore, we identify the necessary conditions to contain gravitational instability. The results are interpreted physically and analytically, and are confirmed numerically.