The numerical solution of the Vlasov-Poisson-Fokker-Planck equation in the context of accelerator physics

Abstract

We discuss the numerical solution of the Vlasov-Poisson-Fokker-Planck (VPFP) equation in the context of accelerator physics. Our experiments focus on the single particle type case, which is useful in study- ing intrabeam scattering. The theory and algorithms, however, are derived for the more general case with multiple species of particles, so that applications in the simulation of electron cooling, for example, are also possible. We first review the derivation of the VPFP equation and the associated stochastic differential equations, after which we formulate a particle-in-cell algorithm to solve them. Our experiments are carried out with a one-dimensional restriction of the model, and their results are promissing enough to warrant implementation and investigation of a three dimensional version. We show that the choice of boundary conditions is of particular interest.