中文摘要：

流注放电通常由流体模型描述，它由玻尔兹曼方程的矩量耦合泊松方程组成。光电离作为源项加在玻尔兹曼方程的一阶矩量即带电粒子连续性方程上。由于计算某一点的光电离需要对整个放电空间进行积分，且需要在每一仿真步长对其进行求解，导致流注仿真的计算量非常大。为提高光电离的计算速度，采用简化球谐法计算流注放电过程光电离。分析了光子在各向同性散射媒质中的辐射输运特性，推导出满足光学厚的辐射输运方程，得到了1阶简化球谐近似（SP1）和3阶简化球谐近似（SP3）的控制方程和边界条件。采用简化球谐法对高斯辐射源和双向流注放电过程光电离进行了仿真，结果表明：3组SP1方法计算效率远远高于Zheleznyak积分方法，计算精度高于3组Helmtoltz方法；采用3组SP1方法计算大气压下流注放电过程光电离足够准确。

英文摘要：

ABSTRACT：Streamer discharges are usually modeled by the fluid approach which consists of moments of the Boltzmann equation coupled with Poisson’s equation. Photoionization is added to the first order moment of the Boltzmann equation which is the continuity equations for the charged particles. As the calculation of the photoionization rate at a given point requires a quadrature over the complete volume, and it should be done at every time step, the computational cost of streamer discharges becomes very large. In order to improve the efficiency, photoionization in streamer discharges was calculated based on simplified spherical harmonics method. The radiative transfer characteristic of the photos in the isotropic scattering media was analyzed, and the radiative transfer equation which satisfies the optically thick condition was derived, then the governing equations and the boundary conditions of 1 order simplified spherical harmonics approximation （SP1） and 3 order simplified spherical harmonics approximations （SP3） were obtained. Specific validation comparisons are presented for computation of photoionization of Gaussian emission source and double-headed streamer. It is shown that the efficiency of 3 group SP1 is far higher than the integral method of Zheleznyak, and the accuracy of 3 group SP1 is higher than that of 3 group Helmtoltz models;it is sufficient to use 3 group SP1 method to calculate the photoionization of the streamer discharges at atmospheric pressure.