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In high-temperature plasma physics, a strong magnetic field is usually usedto confine charged particles. Therefore, for studying the classicalmathematical models of the physical problems it is needed to consider theeffect of external magnetic fields. One of the important model equations inplasma is the Vlasov-Poisson equation with an external magnetic field. In thispaper, we study the error analysis of Hamiltonian particle methods for thiskind of system. The convergence of particle method for Vlasov equation and thatof Hamiltonian method for particle equation are provided independently. Bycombining them, it can be concluded that the numerical solutions converge tothe exact particle trajectories.

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