The Role of the Collisions on the Weibel Instability Growth Rate in the Fast Ignition Scenario

Abstract

In this paper, the effects of Coulomb elctron-ion collisions and plasma density gradient, $\eta$, on the Weibel instability in inertial confinement fusion are investigated. The results are indicative that the corrected collision of Weibel instability growth rate of the relativistic region near the corona, $\eta >0.3$, increases with increasing relativistic parameter, $\upgamma$. Also, near the fuel core as $\eta$ goes down, the corrected collisional growth rate decreases with increasing $\upgamma$ for $\mathrm{{\upgamma }}<6$ and and increases with increasing $\upgamma$ for $\upgamma >6$. Therefore, for $\upgamma <6$, the effect of collision and fuel density gradient tend to stabilize the Weibel instability in fuel core, with the Weibel growth rate below the collisionless value. Also deposition condition of relativistic electron beam energy can be shifted to the fuel core for the suitable ignition.