On the numerical solution of relativistic Vlasov–Ampere equations

For the kinetic plasma model based on the relativistic Vlasov-Ampère equations, the implicit McCormack-type scheme is constructed. Compared to the explicit scheme, it has the weaker stability constraint, but retains the same computational efficiency, i.e., it does not use internal iterations. In this case, the error in the total energy corresponds to the second order of accuracy of the algorithm, and the total charge (number of particles) is preserved at the grid level. The formation of plasma waves excited by a short powerful laser pulse is considered as the simulated physical process. For the weakly relativistic initial distribution function, the scaling of the problem is proposed, which allows numerical analysis of the perturbation parameters in a wide range.