Collisional effect on the Weibel instability in the limit of high plasma temperature

The Weibel instability (WI) of relativistic electron beam (REB) penetrating an infinite collisional plasma was studied in the following models: i) REB model, where the total equilibrium distribution function f0(p→) is approximated by nonrelativistic background electron and REB distribution functions and ii) relativistic monoenergetic beam (RMB) model, where f0(p→) is approximated by nonrelativistic background electrons and RMB distribution functions. The dispersion equation including the effect of collision for a purely transverse mode describing each model was derived and solved analytically to obtain growth rates and conditions of excitation of the WI in the limit of high plasma temperature. The purpose of this paper is to determine the effect of collision within the plasma on the growth rate of the WI for the two models. It was proved that the plasma collision frequency reduces the growth rate of WI at high plasma temperature. That is to say, collisions are inversely proportional to the growth rate. This leads to the important results: WI can be stabilized by increasing the plasma temperature. Comparing the growth rate of WI in the two models (RMB and REB models), we came to the conclusion that growth rate of WI is more in the second case (REB case). (author)