Collisional effect on the Weibel instability with the bi-Maxwellian distribution function

In this paper, the Coulomb collision effect of electron-ion is investigated based on the equilibrium bi-Maxwellian anisotropic distribution function in dense and unmagnetized plasma. An analytical expression is derived for the real frequency and the growth rate of the Weibel instability for two limiting cases |ξ=(ω′/k||θ||)|≫1 and |ξ|≪1. In the limit |ξ|≪1, the quantity η that is due to a collisional term will appear in the growth and condition of the rate of the Weibel instability, which leads to a constraining condition of the growth rate. When η increases, the growth rate will increase and the wave instability will be distant from its own damping mode