Linear theory of a cold relativistic beam propagating along an external magnetic field

The linear theory of a cold relativistic electron beam propagating parallel to an external magnetic field and through a cold, homogeneous plasma is investigated. The electromagnetic dispersion relation is solved numerically and compared with analytical predictions based on the electrostatic approximation. It is found that electromagnetic effects are important for determining the entire unstable spectrum. However, except for the strong magnetic field regime, the maximum growth rates and corresponding frequencies are in agreement with those predicted by the electrostatic approximation. In the strong magnetic field regime the two−stream spectrum is found to be much narrower in angle than predicted by the electrostatic approximation. In the moderate and strong magnetic field regime the growth rate of waves propagating at large angles with respect to the beam are independent of beam energy.