AI 中文总结
本文针对弱电离等离子体中非平衡离子输运问题，提出含真实碰撞的一维高阶矩模型，对比不同矩模型，推导解析碰撞源项，验证后发现六矩模型可高保真捕捉强非平衡离子动力学，计算成本低。
AI 中文摘要
离子-中性粒子碰撞是部分电离等离子体输运的基础。当碰撞尺度与系统尺度相当或电场较强时，离子会出现非平衡条件，由于大漂移、强热通量和温度各向异性，超出了经典输运模型的适用范围。本文提出了非线性高阶矩封闭的求解方法，用于模拟一维弱电离等离子体中的非平衡离子动力学。我们对比了四种模型：四矩各向异性麦克斯韦模型（质量、轴向动量、轴向和垂直能量）、五矩基于双曲求积的模型（前五个轴向矩），以及新的六矩基于双曲求积的模型（前五个轴向矩+垂直能量）。我们从玻尔兹曼算子中推导了离子-中性粒子散射的解析碰撞源项，适用于任意微分截面。该公式将查普曼-考林理论推广到任意漂移速度、温度各向异性和热通量的情况，确保分布严格可实现。这些模型通过非线性模拟进行验证，以具有真实截面（0.05-500 mTorr）的氩等离子体的动力学解为基准。我们测试了浮壁间的有界等离子体和直流放电场景。六矩模型能可靠捕捉离子动力学，尤其在强非平衡条件下，此时各向异性和热通量具有非局域性，它以高保真度重构分布函数，无噪声，且自洽计算成本与流体模型相当。
英文摘要
Ion-neutral collisions are fundamental in the transport of partially ionized plasmas. When collisional scales are comparable to the system scales or the electric field is strong, nonequilibrium conditions for the ions arise that are beyond classical transport models due to large drifts, strong heat flux, and temperature anisotropy. In this paper, we propose the resolution of non-linear high-order moment closures for simulating nonequilibrium ion dynamics in one-dimensional weakly ionized plasmas. We compare a four-moment anisotropic Maxwellian model (mass, axial momentum, and axial and perpendicular energies), a five-moment hyperbolic quadrature-based model (first five axial moments), and a novel six-moment hyperbolic quadrature-based model (first five axial moments + perpendicular energy). We derive analytical collision source terms from the Boltzmann operator for ion-neutral scattering with arbitrary differential cross sections. This formulation generalizes the Chapman-Cowling theory for arbitrary drift velocities, temperature anisotropies, and heat flux, ensuring strictly realizable distributions. The models are validated via non-linear simulations benchmarked against kinetic solutions for argon plasmas with realistic cross sections (0.05-500 mTorr). We test a bounded plasma between floating walls and a direct-current discharge. The six-moment model robustly captures ion dynamics, particularly under strong nonequilibrium, where anisotropy and heat flux are non-local. It reconstructs the distribution function with high fidelity, without noise, and at a cost comparable to fluid models in a self-consistent manner.
