A Numerical Scheme for the Integration of the Vlasov–Maxwell System of Equations

We present a discussion of some numerical algorithms for the solution of the Vlasov–Maxwell system of equations in the magnetized, nonrelativistic case. We show that a splitting scheme combined with a Van Leer type of discretization provides an efficient and accurate scheme for integrating the motion of charged particles in their self-consistent electromagnetic field. The problem of open boundary conditions is also considered. We then discuss the parallelization strategy as used on large parallel computers. Finally, we present an example of the evolution of an electromagnetic beam plasma instability as a typical problem of interest in plasma physics research which can be studied with the Vlasov code.