AI 中文总结
该研究将时域谐波平衡方法扩展用于射频电容耦合等离子体模拟，采用时空算子分裂策略避免全局雅可比矩阵内存密集组装，经基准验证，其结果准确，能绕过物理瞬态，相比传统方法有显著加速，确立了高效模拟范例。
AI 中文摘要
快速准确地对射频电容耦合等离子体（RF CCPs）进行流体模拟，对于现代等离子体反应器的迭代设计和参数优化至关重要。本研究首次成功将时域谐波平衡（HB）方法扩展到用于RF等离子体模拟的具有完整电子能量传输的全耦合漂移 - 扩散 - 泊松系统。为解决高度非线性能量相关动力学和密集相耦合产生的严重数值刚度，采用了高效的时空算子分裂策略。该策略通过依次执行空间隐式松弛和单元局部时间反转，避免了全局雅可比矩阵的内存密集组装，同时保持了强大的数值稳定性。所提出的方法针对标准平行板氩CCP基准进行了严格验证。在所有离散时间配置点上评估，HB解表明保留八个谐波能完美解析准稳态体等离子体和高度非线性瞬态鞘层动力学，与传统双时间步长（DTS）解相比，宏观相对误差严格低于0.3%。时域HB方法不仅具有高物理保真度，还完全绕过了传统时间推进方法所需的昂贵物理瞬态。在纯顺序单核执行上评估，HB方法比完全收敛的DTS基线加速超过10倍，比最粗糙的时间推进配置快5倍以上。这些结果确立了时域HB框架作为实际RF等离子体模拟的物理严格、内存高效且高度加速的范例。
英文摘要
Fast and accurate fluid simulation of radio-frequency capacitively coupled plasmas (RF CCPs) is of great importance for the iterative design and parameter optimization of modern plasma reactors. This study presents the first successful extension of the time-domain harmonic balance (HB) method to a fully coupled drift-diffusion-Poisson system with complete electron-energy transport for RF plasma simulations. To resolve the severe numerical stiffness arising from highly nonlinear energy-dependent kinetics and dense phase-coupling, a highly efficient spatiotemporal operator-splitting strategy is employed. By sequentially executing a spatial implicit relaxation and a cell-local temporal inversion, this strategy entirely avoids the memory-intensive assembly of global Jacobians while preserving robust numerical stability. The proposed method is rigorously validated against a standard parallel-plate argon CCP benchmark. Evaluated across all discrete temporal collocation points, the HB solution demonstrates that retaining eight harmonics perfectly resolves both the quasi-steady bulk plasma and the highly nonlinear transient sheath dynamics, yielding macroscopic relative errors strictly below 0.3% compared to conventional dual-time stepping (DTS) solutions. Beyond its high physical fidelity, the time-domain HB method completely bypasses the prohibitive physical transients required by conventional time-marching methods. Evaluated on a purely sequential single-core execution, the HB method delivers a greater than 10-fold speedup over fully converged DTS baselines and remains over 5 times faster than the coarsest time-marching configurations. These results establish the time-domain HB framework as a physically rigorous, memory-efficient, and highly accelerated paradigm for practical RF plasma simulations.
Comments41 pages, 23 figures, research article
