In this work, we develop and rigorously analyze a new class of particle methods for the magnetized Vlasov--Poisson--Fokker--Planck system. The proposed approach addresses two fundamental challenges: (1) the curse of dimensionality, which we mitigate through particle methods while preserving the system's asymptotic properties, and (2) the temporal step size limitation imposed by the small Larmor radius in strong magnetic fields, which we overcome through semi-implicit discretization schemes. We establish the theoretical foundations of our method, proving its asymptotic-preserving characteristics and uniform convergence through rigorous mathematical analysis. These theoretical results are complemented by extensive numerical experiments that validate the method's effectiveness in long-term simulations. Our findings demonstrate that the proposed numerical framework accurately captures key physical phenomena, particularly the magnetic confinement effects on plasma behavior, while maintaining computational efficiency.

翻译：本文发展并严格分析了一类用于磁化Vlasov--Poisson--Fokker--Planck体系的新型粒子方法。所提出的方法解决了两个基本挑战：(1) 维度灾难问题——我们通过粒子方法在保持系统渐近特性的同时缓解该问题；(2) 强磁场中微小拉莫尔半径导致的时步长限制——我们通过半隐式离散格式克服该限制。我们建立了该方法的理论基础，通过严格的数学分析证明了其保渐近特性与一致收敛性。这些理论结果得到了大量数值实验的补充，验证了该方法在长期模拟中的有效性。我们的研究结果表明，所提出的数值框架在保持计算效率的同时，能够准确捕捉关键物理现象，特别是磁场约束对等离子体行为的影响。