一种用于ICP中双向电感-电容耦合的自洽相量PIC算法
Phasor-particle-in-cell algorithm for bidirectional external-circuit coupling of inductively coupled plasma
- State Key Laboratory of Advanced Electromagnetic Technology, International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology（华中科技大学电气与电子工程学院）
- School of Physics and Mechanics, Wuhan University of Technology（武汉理工大学物理与力学学院）
- School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种自洽相量PIC算法，实现ICP中匝分辨双向场-电路耦合，通过分布式网络和周期更新，在基准和GEC电池中验证了高精度及电容加热贡献。
AI中文摘要：
感应耦合等离子体（ICP）的自洽粒子-网格/蒙特卡罗碰撞（PIC/MCC）模拟要求线圈电流和每匝电势响应等离子体负载。预设电流或单一集总阻抗忽略了这种分布式反馈。我们开发了一种循环耦合的相量PIC算法，将二维轴对称PIC/MCC模型与具有2N+1个未知数的分布式复数网络相连接。预计算的单位电流亥姆霍兹解提供每匝真空阻抗矩阵，而仅等离子体场提供串联反电动势。基于电荷的静电耦合被扩展到单个匝：基于泊松面系数的离散高斯定律得出表面电荷，其基波谐波决定并联位移电流。两种响应均在闭合射频周期内测量，以每个周期更新一次松弛电路状态。真空电感差异对于单螺线管为-1.58%，对于互感为-4.38%。在具有两个通道激活的五节点制造基准中，无粒子场-电路计算相对于连续参考的缩放复态误差为1.90e-5，相对于使用提取矩阵的独立网络的误差为6.26e-12。空间细化确认了二阶收敛；有限网格互易性和无损耗功率缺陷被量化。在无屏蔽氩气GEC参考电池的统计平稳状态下，在线圈端口功率为60 W和100 W时，净电容性等离子体加热分别贡献了组合的电感性和电容性等离子体功率的29.35%和20.07%。独立累积的场侧和电路侧功率一致在约0.5%以内。该方法实现了轴对称、基频ICP模拟的匝分辨双向场-电路耦合。
英文摘要：
We develop a self-consistent phasor-particle-in-cell algorithm to capture bidirectional inductive and capacitive feedback between an inductively coupled plasma and a distributed radio-frequency coil circuit. The method couples a two-dimensional axisymmetric particle-in-cell model with Monte Carlo collisions to a network that resolves the current and potential of each coil turn. Precomputed unit-current Helmholtz solutions provide the vacuum impedance matrix, while projection of the plasma-only field supplies the series back electromotive force. An established charge-based electrostatic coupling is extended to individual turns: surface charges obtained from a discrete Gauss law consistent with the Poisson solver yield shunt displacement currents through their fundamental harmonics. Both responses are accumulated over a complete radio-frequency period to update the relaxed circuit state once per period. Vacuum tests showed differences of -1.58 percent in single-solenoid inductance and -4.38 percent in mutual inductance relative to analytical references. A particle-free five-node manufactured benchmark with both coupling channels active yielded a scaled complex-state error of 1.90 x 10^-5 against the continuous reference and approximately second-order spatial convergence. Application to an unshielded argon reference cell reached statistically stationary states at coil-port powers of 60 and 100 W. Net capacitive heating accounted for 29.35 percent and 20.07 percent, respectively, of the combined inductive and capacitive plasma power. Independently accumulated field-side and circuit-side powers, including conductor loss, agreed within approximately 0.5 percent. These results support turn-resolved bidirectional field-circuit coupling for axisymmetric plasma simulations using a fundamental-frequency circuit representation.
