论文标题
渐近地保存粒子在圆环中强磁的粒子方法
Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus
论文作者
论文摘要
我们提出和分析一类粒子方法，用于vlasov方程，在圆环构型中具有强大的外部磁场。在此制度中，时间步长可以受到与Larmor半径较小有关的稳定性约束。为了避免这种限制，我们的方法基于已经在耗散系统上验证的高阶半密码数值方案[3]和指向固定方向的磁场[9，10，12]。它取决于[11]在连续水平上获得的渐近见解。因此，当外部磁场的大小较大时，该方案在考虑到曲率和磁场的变化方面提供了指导中心系统的一致近似。最后，我们执行一致性的理论证明，并执行几个数值实验，以对该方法及其基本概念建立可靠的验证。
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.
