Beam-Temperature Effects on the Electrostatic Instability for an Electron Beam Penetrating a Plasma

The electrostatic instability of an infinite electron beam penetrating an infinite plasma is analyzed. The objective is to determine the effect of beam temperature upon the growth rate of the electrostatic waves (a Gaussian velocity distribution is assumed). In addition, the role of collisions within the plasma is explored. A conclusion of this study is that a high-temperature limit for the beam can be defined in terms of the plasma frequencies of the beam and of the plasma. At the high-temperature limit, the plasma collisions can quench the electrostatic instability; at lower temperatures, collisions tend to enhance the growth rate. The results presented here are based upon a numerical analysis of the usual dispersion equation that is obtained for this beam-plasma system. In addition to the numerical results, approximate analytic expressions for the growth rate are derived for a number of cases of interest.