We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius. To avoid this limitation, our approach is based on higher-order semi-implicit numerical schemes already validated on dissipative systems [3] and for magnetic fields pointing in a fixed direction [9, 10, 12]. It hinges on asymptotic insights gained in [11] at the continuous level. Thus, when the magnitude of the external magnetic field is large, this scheme provides a consistent approximation of the guiding-center system taking into account curvature and variation of the magnetic field. Finally, we carry out a theoretical proof of consistency and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

翻译：我们提出并分析了一类用于环面构型中强外磁场下Vlasov方程的粒子方法。在该机制下，时间步长可能受到与Larmor半径小量相关的稳定性约束。为避免这一限制，我们的方法基于已在耗散系统[3]以及固定方向磁场[9,10,12]中验证的高阶半隐式数值格式。该方法依赖于文献[11]在连续层面获得的渐近洞察。因此，当外磁场强度较大时，该格式能够对考虑磁场曲率及变化的引导中心系统提供一致近似。最后，我们进行了理论一致性证明，并开展了多项数值实验，从而对方法及其核心概念建立了可靠的验证。