The Weibel instability plays an important role in stopping the hot electrons and energy deposition mechanism in the fast ignition of inertial fusion process. In this paper, the effects of the density gradient and degeneracy on Weibel instability growth rate are investigated. Calculations show that decreasing the density degenerate in the plasma corona, near the relativistic electron beam emitting region by 8.5% leads to a 92% reduction in the degeneracy parameter and about 90% reduction in Weibel instability growth rate. Also, decreasing the degenerate density near the fuel core by 8.5% leads to 1% reduction in the degeneracy parameter and about 8.5% reduction in Weibel instability growth rate. The Weibel instability growth rate shrinks to zero and the deposition condition of relativistic electron beam energy can be shifted to the fuel core for a suitable ignition by increasing the degeneracy parameter in the first layer of plasma corona.
