AI 中文总结
本研究从非线性动力学视角，通过李雅普诺夫指数分析揭示稳态CCP放电中电子运动的混沌行为，确立其为无碰撞CCP有效随机散射的定量度量，为理解低压射频等离子体随机电子加热提供统一框架。
AI 中文摘要
尽管经过数十年研究，宽工作条件下电容耦合等离子体（CCP）放电的电子加热机制仍未完全明晰。随机加热虽被普遍视为低压下主导的无碰撞加热机制，但该过程背后固有的非线性电子动力学尚未得到充分量化。这些非线性相互作用驱动着随机加热——一种被认为对CCP中能量转移至关重要的机制，但其对等离子体参数的定量影响仍未得到充分探究。本研究调查稳态CCP放电中的电子动力学，证明等离子体体区的电子运动呈现固有的混沌行为；通过庞加莱截面识别混沌的出现，并通过李雅普诺夫指数分析进行量化。为进一步量化该行为，针对不同压力和射频电压，绘制等离子体体区中经电子-中性粒子碰撞频率归一化后的李雅普诺夫指数的空间分布。归一化李雅普诺夫指数随压力降低和射频电压升高而系统性增大，表明随机性增强，电子轨迹对初始条件的敏感性更强。这些结果确立李雅普诺夫指数为无碰撞CCP中有效随机散射的定量度量，并与Popov和Godyak提出的经典随机碰撞频率（《应用物理杂志》57卷，53-58页，1985年）进行直接对比。本分析为理解低压射频等离子体中的随机电子加热提供了统一的非线性动力学框架。
英文摘要
Despite decades of research, the electron heating mechanisms in capacitively coupled plasma (CCP) discharges over a wide range of operating conditions is not fully understood. Although stochastic heating is generally regarded as the dominant collisionless heating mechanism at low pressures, the inherently nonlinear electron dynamics responsible for this process have not been fully quantified. These nonlinear interactions drive stochastic heating, a mechanism considered crucial for energy transfer in CCPs, yet its quantitative impact on plasma parameters remains insufficiently explored. In this work, we investigate electron dynamics in steady-state CCP discharges and demonstrate that electron motion in the plasma bulk exhibits intrinsically chaotic behavior. The onset of chaos is identified using Poincare sections and quantified through Lyapunov exponent analysis. To further quantify this behavior, we map the spatial distribution of the Lyapunov exponent-normalized by the electron-neutral collision frequency-across the plasma bulk for different pressures and RF voltages. The normalized Lyapunov exponent increases systematically with decreasing pressure and increasing RF voltage, indicating enhanced stochasticity and a stronger sensitivity of electron trajectories to initial conditions. These results establish the Lyapunov exponent as a quantitative measure of effective stochastic scattering in collisionless CCPs and provide a direct comparison with the classical stochastic collision frequency proposed by Popov and Godyak [Journal of Applied Physics 57, 53-58 (1985)]. The present analysis offers a unified nonlinear dynamical framework for understanding stochastic electron heating in low-pressure RF plasmas.
