Convergence of Hamiltonian Particle methods for Vlasov--Poisson equations with a nonhomogeneous magnetic field

In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it is needed to consider the effect of external magnetic fields. One of the important model equations in plasma is the Vlasov-Poisson equation with an external magnetic field. In this paper, we study the error analysis of Hamiltonian particle methods for this kind of system. The convergence of particle method for Vlasov equation and that of Hamiltonian method for particle equation are provided independently. By combining them, it can be concluded that the numerical solutions converge to the exact particle trajectories.