As the binary collision process requires much more computation time, a statistical electron-electron collision model based on modified Langevin equation is developed to reduce it. This collision model and a simple electron-ion scattering model are installed into one-dimensional PIC code, and collisional effects on fast electron generation and transport in fast ignition are investigated. In the collisional case, initially thermal electrons are heated up to a few hundred keV due to direct energy transfer by electron-electron collision, and they are also heated up to MeV by Joule heating induced by electron-ion scattering. Thus the number of low energy component of fast electrons increase than that in the collisionless case.

Envision a one-dimensional system of infinitely many identical particles, in which initial particle positions constitute a Poisson random measure and the initial velocity of a particle depends only on its initial position. Given its initial conditions the system evolves deterministically, by means of perfectly elastic collisions. In this note we derive conditions for continuity of the probability laws of the system and of the particle paths, as functions of the parameters of the initial conditions. These results have the physical interpretation of stability theorems.