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The electromagnetic instability of a relativistic electron beam penetrating an infinite plasma is analyzed. The purpose of this paper is to determine the effect of collisions within the plasma upon the growth rate of the Weibel-type electromagnetic instability. The dispersion relation including the effect of collisions is solved analytically and numerically. It is found that collisions can enhance the growth rate of the electromagnetic instability in the case of low plasma temperature.

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From a dispersion relation, linear growth rates of electromagnetic instabilities are obtained in an electron plasma whose velocity distribution function has a high-energy tail. Theory is developed to derive the reduction in the thermal flux caused by these electromagnetic instabilities. Nonlinear theory leads to the saturation level of instabilities. Numerical simulations are carried out using a particle-in-cell method. The reduction in thermal conduction predicted by the theory is found to be in good agreement with computer simulations.