A spectral algorithm for solving the relativistic Vlasov–Maxwell equations Original Research Article

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov–Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.