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Abstract

In order to investigate the radiative properties of plasma in non local thermodynamic equilibrium (NLTE), it is of great importance to determine energy level populations, which are often obtained by the so-called collisional-radiative (CR) model. As is well known, the CR model is accurate but computationally costly, and thus it is difficult to be applied to engineering calculations for such as complex three-dimensional plasmas. In this work, a bound-state characteristic temperature (BCT) method is proposed, which can be used to calculate quickly the energy level populations in non-equilibrium plasmas. In this method, we assume that for each kind of ionization stage, the bound-state population is Boltzmannian at a certain characteristic temperature. The assumed characteristic temperature is related to the degree of none-equilibrium and may be different from the electronic temperature of the plasma. Based on a modified Saha equation, the assumed characteristic temperature can be calculated easily, and then the energy level populations are obtained conveniently. Five cases of non-equilibrium neon plasma at variable electronic temperatures and densities are investigated and compared with the results from a CR model. Good agreement is found between them if the degree of non-equilibrium is not very large. It shows that the present method is effective and at least 3000 times faster in computation time than the CR model. The method is very useful in engineering applications.

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Authors and contacts

Corresponding author:Gao Cheng,gaocheng@nudt.edu.cn

Funds:Project supported by the National Numerical Windtunnel of China (Grant No. NNW2019ZT3-B07) and the National Natural Science Foundation of China (Grant No. 12074430)

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	算例1	算例2	算例3	算例4	算例5
$k{T_{\rm{e}}}$/eV	5	15	40	15	40
Ne核总数密度/${\rm{c}}{{\rm{m}}^{ - 3}}$	10¹⁸	10¹⁸	10¹⁸	10²⁰	10²⁰
${\rm{Ne}}$粒子数含量/%	0.0258
${\rm{N}}{{\rm{e}}^ + }$粒子数含量/%	5.2017
${\rm{N}}{{\rm{e}}^{2 + }}$粒子数含量/%	88.6853	0.0015		5.0406
${\rm{N}}{{\rm{e}}^{3 + }}$粒子数含量/%	6.0863	0.4202		38.9713	0.0002
${\rm{N}}{{\rm{e}}^{4 + }}$粒子数含量/%	0.0008	19.4618		48.9205	0.0299
${\rm{N}}{{\rm{e}}^{5 + }}$粒子数含量/%		67.8883	0.0037	6.9899	1.0996
${\rm{N}}{{\rm{e}}^{6 + }}$粒子数含量/%		12.1407	0.6767	0.0777	15.7779
${\rm{N}}{{\rm{e}}^{7 + }}$粒子数含量/%		0.0874	20.1261		48.7610
${\rm{N}}{{\rm{e}}^{8 + }}$粒子数含量/%			79.1935		34.3313
${\rm{N}}{{\rm{e}}^{9 + }}$粒子数含量/%
${\rm{N}}{{\rm{e}}^{10 + }}$粒子数含量/%
e^–数含量/(10¹⁸cm^–3)	2.01	4.92	7.79	351.00	712.00

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原子(离子)	电离能/eV
${\rm{Ne}}$	19.441
${\rm{N}}{{\rm{e}}^ + }$	40.565
${\rm{N}}{{\rm{e}}^{2 + }}$	63.007
${\rm{N}}{{\rm{e}}^{3 + }}$	93.588
${\rm{N} }{ {\rm{e} }^{4 + } }$	123.924
${\rm{N}}{{\rm{e}}^{5 + }}$	157.561
${\rm{N}}{{\rm{e}}^{6 + }}$	201.788
${\rm{N}}{{\rm{e}}^{7 + }}$	230.156
${\rm{N}}{{\rm{e}}^{8 + }}$	1183.642
${\rm{N}}{{\rm{e}}^{9 + }}$	1345.217

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	程序语言	计算平台	CPU	总耗时
CR模型	Fortran	IBM服务器	Intel Xeon E5649: 6核2.53 GHz	约24 h
本文方法	Matlab	Thinkpad笔记本电脑	Intel Core i5-3320 M: 2核2.60 GHz	约28 s

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Vol. 70, Issue 14 - 2021-07-20

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