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.

翻译：在高温等离子体物理中，通常使用强磁场约束带电粒子。因此，研究此类物理问题的经典数学模型时需考虑外部磁场的影响。等离子体中的重要模型方程之一是含外部磁场的Vlasov-Poisson方程。本文研究了这类系统的哈密顿粒子方法的误差分析。我们分别证明了Vlasov方程的粒子方法收敛性和粒子方程的哈密顿方法收敛性。通过结合两者，可得出数值解收敛至精确粒子轨迹的结论。