Two-stream instability in a self-pinched relativistic electron beam

The two-stream stability properties are investigated for a self-pinched relativistic electron beam propagating through a weakly ionized plasma channel. The analysis is carried out within the framework of a macroscopic cold-fluid model, and electrostatic stability properties are investigated for the case of rectangular beam and channel density profiles. Depending upon the ionization condition of the channel, either the beam electron-ion two-stream or the beam electron-plasma electron two-stream instability is excited. In either case, the critical beam current for instability is obtained. In contrast with the one-dimensional analysis of the two-stream instability, the stabilizing influence of a self-pinched beam originates from the finite beam radius. From the critical current, it is shown that for an appropriate choice of physical parameters, the electron beam is free from the two-stream instability. Moreover, the growth rate of instability under unstable conditions can be drastically reduced for a small axial wave number