中文摘要：

流注放电过程通常用流体模型来描述，它由粒子连续性方程耦合泊松方程组成，光电离作为源项加在电子和正离子连续性方程上。目前光电离一般用精度较低的空间均匀背景预电离代替或者用计算效率低的 Zheleznyak 积分模型进行求解。针对上述两种方法的不足，有学者用多组Helmholtz方程代替积分方程计算光电离，但并没有揭示此方法的物理意义和得到有效的边界条件。结合Penney和Hummert用离子室测量光电离的实验，若把吸收函数表示成指数和形式，即可得到Helmholtz模型的控制方程；根据辐射物理特性，给出了Helmholtz方程Sommerfeld远场辐射边界条件。将该方法应用于高斯辐射源和大气压下双向流注传播过程计算，并与采用其它边界条件的Helmholtz方法和Zheleznyak积分方法进行对比实验。仿真结果表明：采用 Sommerfeld远场辐射边界的Helmholtz模型和采用Zheleznyak积分方法计算结果接近，但计算效率更高。

英文摘要：

Streamer discharges are usually modeled by the fluid approach which consistes of continuity equations for charged particle densities coupled with Poisson’s equation. Photoionization is taken into account through a source term which is added to the continuity equations for electron and positive ion densities. But photoionization was substituted by a spatially uniform background pre-ionization level which had low precision or derived by the integral model proposed by Zheleznyak et al which was very time consuming. In order to overcome the above deficiencies, multigroup Helmholtz method had been proposed to derive the photoionization instead of evaluating the integral, however, the intrinsic significance of this method wasn’t revealed and an efficient boundary condition wasn’t derived. Here it is investigated that if the absorption function is expressed as the exponential sum according to the photoionization measurement experiment of Penny and Hummert, the governing equation of the Helmholtz model can be obtained; and Sommerfeld far-field radiative boundary condition is proposed based on the properties of radiation. Then the method has been verified by the Gaussian radiative source and atmospheric double-headed streamer discharge simulation. The results show that the Helmholtz model with Sommerfeld boundary condition has the same precision as the Zheleznyak integral method, nevertheless it is more efficient.