Investigation of the Effect of Density Gradients in Fuel Pellets on Filamentation Electromagnetic Instability during Beam-Plasma Interactions in Inertial Confinement Fusion

The transfer of a beam of high-energy particles, such as electrons, to the center of a fuel pellet is a significant aspect of plasma fusion processes. When the beam is directed toward the center of the fuel pellet, a counter-current is generated by the plasma electrons surrounding the pellet. This current leads to the production of an electromagnetic field. The growth of this electromagnetic field results in the appearance of instabilities, including filamentation instability within the plasma medium. Furthermore, the gradual growth of these instabilities disrupts energy transfer to the fuel pellet, hindering the achievement of ideal ignition conditions. The present study investigated the effects of parameters such as the density gradient of the fuel pellet, thermal anisotropy and the relativistic mass factor on filamentation instability in a beam-plasma system that includes non-relativistic background electrons and a relativistic mono-energetic electron beam. By linearizing Maxwell-Vlasov equations, the dispersion relation for filamentation instability was derived. While solving the dispersion equation and calculating the instability growth rate, it was observed that with increasing the scale length of the density gradient, due to the higher collision rate and the increase in energy transfer to the plasma particles, the growth rate of filamentation instability decreased. Additionally, it was found that increasing the relativistic mass factor and thermal anisotropy fraction leads to an increase in the instability growth rate due to increased internal energy dissipation.