While boundary plasmas in present-day tokamaks generally fall in a fluid regime, neutral species near the boundary often require kinetic models due to long mean-free-paths compared to characteristic spatial scales in the region. Monte-Carlo (MC) methods provide a complete, high-fidelity approach to solving kinetic models, and must be coupled to fluid plasma models to simulate the full plasma-neutrals system. The statistical nature of MC methods, however, prevents the convergence of coupled fluid-kinetic simulations to an exact self-consistent steady-state. Moreover, this forces the use of explicit methods that can suffer from numerical errors and require huge computational resources. Correlated Monte-Carlo (CMC) methods are expected to alleviate these issues but have historically enjoyed only mixed success. Here, a fully implicit method for coupled plasma-neutral systems is demonstrated in 1D using the UEDGE plasma code and a homemade CMC code. In particular, it is shown that ensuring the CMC method is a differentiable function of the background plasma is sufficient to employ a Jacobian-Free Newton-Krylov solver for implicit time steps. The convergence of the implicit coupling method is explored and compared with explicit coupling and uncorrelated methods. It is shown that ensuring differentiability by controlling random seeds in the MC is sufficient to achieve convergence, and that the use of implicit time-stepping methods has the potential for improved stability and runtimes over explicit coupling methods.

翻译：当前托卡马克装置中的边界等离子体通常处于流体状态，但边界区域的中性粒子由于平均自由程远大于该区域的特征空间尺度，往往需要采用动理学模型进行描述。蒙特卡洛（MC）方法为求解动理学模型提供了一种完整且高保真的途径，且必须与流体等离子体模型耦合才能模拟完整的等离子体-中性粒子系统。然而，MC方法的统计特性阻碍了耦合流体-动理学模拟收敛至精确的自洽稳态。此外，这迫使采用显式方法，而显式方法可能受数值误差影响且需要巨大的计算资源。相关蒙特卡洛（CMC）方法有望缓解这些问题，但历史上仅取得了有限的成功。本文利用UEDGE等离子体代码和自研的CMC代码，在一维情况下演示了一种适用于耦合等离子体-中性粒子系统的全隐式方法。特别地，研究表明，确保CMC方法是背景等离子体的可微函数，便足以采用无雅可比牛顿-克雷洛夫求解器进行隐式时间步进。本文探讨了隐式耦合方法的收敛性，并与显式耦合及非相关方法进行了比较。结果表明，通过控制MC中的随机种子来确保可微性足以实现收敛，并且使用隐式时间步进方法相较于显式耦合方法，在稳定性和运行时间方面具有提升潜力。