Collisional Effect on Weibel Instability with Semi-Relativistic Maxwellian Distribution Function

In this paper, the Coulomb collisional effect of electron-ion on the growth rate of Weibel instability is investigated based on the semi-relativistic Maxwellian distribution function in dense and unmagnetized plasma. An analytical expression was derived for the dispersion relation of Weibel instability for two limit cases vertical bar xi = omega'/k(parallel to)T parallel to vertical bar >> 1 and vertical bar xi vertical bar <1. In limit vertical bar xi vertical bar >> 1 the dispersion relation only includes a real part and in limit vertical bar xi vertical bar<<1 the imaginary part of the frequency of waves' instability plays a role in the dispersion relation. In limit vertical bar xi vertical bar <<1, the two quantities mu and eta, that are due to the relativistic and collisional effects, will appear in the growth rate of Weibel instability. The growth rate of Weible istability will be increased through decreasing the Coulomb collisional frequency and also increasing the temperature anisotropic parameter in strong relativistic limit.