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 vertical bar xi = omega'/k(parallel to)theta(parallel to)vertical bar >> 1 and vertical bar xi vertical bar << 1. In the limit vertical bar xi vertical bar << 1, the quantity eta 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 g increases, the growth rate will increase and the wave instability will be distant from its own damping mode. (C) 2013 AIP Publishing LLC.