Kinetic and collisional effects on the linear evolution of fast ignition relevant beam instabilities

The fast ignition scheme will involve the generation and transport of a relativistic electron beam, which may be subject to a number of instabilities that act to inhibit energy transport. This study will address the effects of collisions and the initial electron beam distribution on the linear evolution of these instabilities for theoretical distributions including the relativistic waterbag, the relativistic Maxwellian (Jüttner), and the saddle point (low temperature) approximation of the relativistic Maxwellian. It will then be shown that a more physical distribution obtained from a 2D explicit particle-in-cell simulation of the laser-plasma interaction can be best modeled with a Jüttner distribution, but well-approximated with a relativistic waterbag distribution. In sum, for all distributions of interest, collisions were found to have the ability to both suppress and enhance growth for the filamentary instability, while they only suppress growth for the two-stream instability.