Stability properties of the electron return current for intense ion beam propagation through background plasma

When an intense ion beam propagates through a dense background plasma, its current is partially neutralized by the electron plasma return current. Due to the non-uniformity of the background plasma electrons longitudinal velocity profile (v) over bar (r), the flow can be unstable. The instability is similar to the Kelvin-Helmholz instability for the non-uniform flow of an incompressible neutral fluid, with the electrostatic potential playing the role of pressure. For the case of electron return current flow, the significant new feature is the presence of the partially self-neutralized magnetic field of the ion beam, which significantly affects the evolution of small-amplitude excitations. In this paper the stability properties of the flow of electrons making up the plasma return current is investigated using the macroscopic cold-fluid-Maxwell equations. It is shown that this flow may become unstable, but the instability growth rates are exponentially small. This unstable body mode is qualitatively different from previously studied surface-mode excitations of the electron plasma return current for an intense ion beam with a sharp radial boundary, which is found to be stable due to the stabilizing influence of the partially neutralized magnetic field of the ion beam.