The hydromagnetic instability of an infinitely long self-gravitating incompressible plasma cylinder

Abstract

An infinitely long self-gravitating incompressible plasma cylinder is considered. Inside the cylinder there is a uniform magnetic fieldBi parallel to its axis and outside there are magnetic fieldsBe parallel to the axis andB0r0r in the azimuthal direction. The surface currents arising due to the discontinuity in the magnetic fields across the surface are incorporated into the boundary conditions to derive a dispersion relation. The conclusions are: (a) The magnetic field configuration (Bi =Be =B0) has got a stabilizing effect for modesm = 0, 1 and 2, for modesm = 1 and 2 it keeps the cylinder always stable. (b) TheBi field is more effective than theBe field in stabilizing the cylinder for modem = 0 andm = 1. For modem = 2,Be becomes more effective thanBi. (c) The effect ofB0 field is to destabilize shortwave perturbations form = 0, to destabilize any given perturbation form = 1 whenB02 > 8π2ρ2r02G; but for modem = 2 it stabilizes very large waves as well as shortwave perturbations, while it destabilizes very short wave perturbations.