In this paper, the role of degeneracy parameter, in both directions parallel and perpendicular with propagation direction of the laser beam in plasma, on the growth rate of Weibel instability, is studied. Calculations show that with the temperature anisotropy, b ¼ Tk/T? ¼ 0.2 and a 0.75 times reduction of the degeneracy parameter, the increased rate of the the Weibel instability growth rate is 72%. The degeneracy required for minimal growth rate in interaction laser plasma with a density of 1.2 1032m3, is larger than 3. The reduction of temperature and the degeneracy parameter of plasma in parallel direction will also increase growth rate about 30% more than incrossing degeneracy parameter in transverse direction. With the minimum pressure costs of cold compression, subsequent degeneracy parameters, and the minimum value of electron quiver energy, we can expect growth rate of Weibel instability order 0.01.
