Monte-Carlo treatment of nonlinear collisional effects in charged particle transport

The Vlasov equation for charger-particle transport is often solved by codes that follow the particle motion.(1) The solution is nonlinear in the sense that the electromagnetic fields that influence the particle orbits are entirely or partly determined by the positions and velocities of the particles themselves. The effects of teo-body coulomb collisions of the simultation paticles against a background material are often treated by a Monte-Carlo collisional process in which the collision probability is determined by Fokker-Plank treatment.(2) This procedure is nonlinear if the properties of the background material are allowed to change as a result of the scattering of the simultation particles. A more completely nonlinear problem is obtained if the simultation particles themselves form all or part of the background distribution distribution. A new method is presented here for doing this, and examples will be discussed that illustrate the power of the technique.