Scaling of the beam-plasma discharge

A theoretical analysis is presented of the scaling of the critical beam current required for ignition and the narrow band emissions observed for beam currents less than critical in a beam plasma discharge experiment. The theory of the two-stream interaction between a nonrelativistic cold electron beam and a plasma in the presence of a magnetic field is developed, and conditions for the two-stream instability and the resulting amplification are derived. It is shown that the experimentally observed scaling is consistent with the assumption that the ignition triggering occurs when an instability near the electron plasma frequency is excited. Finally, it is shown that the wave emissions observed in the subthreshold range can be explained by the excitation of the kinetic instability of the upper branch and convective saturation.