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

In this paper, we study the error analysis of Hamiltonian particle methods for the magnetized Vlasov{Poisson equation. The convergence of particle method for Vlasov equation and Hamiltonian method for particle equation is provided independently. By combining them, we can conclude that the numerical solution converges to the exact particle trajectories.