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Abstract

In recent years, the artificial intelligence computing paradigm represented by physics-informed neural networks (PINNs) has received great attention in the field of plasma numerical simulation. However, the plasma chemical system considered in related research is relatively simplified, and the research on solving the more complex multi-particle low-temperature fluid model based on PINNs is still blank. In more complex chemical systems, the coupling relationship between particle densities and between particle densities and mean electron energy become more intricate. Therefore, the applicability of PINNs in dealing with sophisticated reaction systems needs further exploring and improving. In this work, we propose a general PINN framework (source term decoupled PINNs, Std-PINNs) for solving multi-particle low-temperature plasma fluid model. By introducing equivalent positive ions and replacing each particle transport equation with the current continuity equation as a physical constraint, Std-PINN splits the entire solution process into the training processes of two neural networks, realizing the decoupling of the source term of the heavy particle transport equation from the electron density and mean electron energy, which greatly reduces the complexity of neural network training. In this work, the application of Std-PINNs to solving multi-particle low-temperature plasma fluid models is demonstrated through two classic discharge cases with different complexity of reaction systems (low-pressure argon glow discharge and atmospheric-pressure helium glow discharge) and the performance of Std-PINN is compared with that of conventional PINN and finite element method (FEM). The results show that the training results output from the traditional PINN are completely incorrect due to the strong coupling correlation of each physical variable through the source terms of each particle transport equation, while the L ₂relative error between Std-PINN and FEM results can reach up to ~10 ^–2, thus verifying the feasibility of Std-PINN in simulating multi-particle plasma fluid model. Std-PINN expands the application of deep learning method to modeling complex physical systems and provides new ideas for conducting low-temperature plasma simulations. In addition, this study provides novel insights into the field of artificial intelligence scientific computing: the mathematical form that describes the state of a physical system is not unique. By introducing equivalent physical variables, equations suitable for neural network solutions can be derived and combined with observable data to simplify problems.

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Authors and contacts

Corresponding author:Dai Dong,ddai@scut.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 52377145).

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Cited By

DownLoad: Full-Size Img PowerPoint

案例	${n_0}$/m^–3	${\phi _0}$/V	${\bar \varepsilon _0}$/eV	${L_0}$/m
1	1×10¹³	1×10³	1	1×10^–2
2	5×10¹⁷	1×10³	1	1×10^–4

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序号	反应方程	速率常数	焓/eV	参考文献
1	e + Ar $\Rightarrow $ e + Ar	f($ \overline{\boldsymbol{\varepsilon}} $)	—	[48]
2	e + Ar $\Rightarrow $ e + Ar^*	f($ \overline{\boldsymbol{\varepsilon}} $)	11.5	[48]
3	e + Ar $\Rightarrow $ 2e + Ar⁺	f($ \overline{\boldsymbol{\varepsilon}} $)	15.8	[48]
4	e + Ar^*$\Rightarrow $ 2e + Ar⁺	f($ \overline{\boldsymbol{\varepsilon}} $)	4.43	[48]
5	Ar^+ Ar^$\Rightarrow $ e + Ar+ Ar⁺	6.2×10^–16	—	[40]
6	Ar^*+ Ar $\Rightarrow $ Ar+ Ar	3×10^–21	—	[40]
注: 表中f($ \overline{\boldsymbol{\varepsilon}} $)代表电子碰撞反应的速率常数, 为平均电子能的函数, 通过向Bolsig⁺导入电子碰撞反应截面数据计算得到; 双体反应的速率常数单位为m³/s.

DownLoad: CSV

序号	反应方程	速率常数	焓/eV	参考文献
1	e + He $\Rightarrow $ e + He	f($ \overline{\boldsymbol{\varepsilon}} $)	—	[48]
2	e + He $\Rightarrow $ e + He^*	f($ \overline{\boldsymbol{\varepsilon}} $)	19.8	[48]
3	e + He $\Rightarrow $ 2e + He⁺	f($ \overline{\boldsymbol{\varepsilon}} $)	24.6	[48]
4	e + He^*$\Rightarrow $ 2e + He⁺	$1.28 \times 10^{-13}\times T_{\rm e}^{0.6}\times \exp(-4.78/T_{\rm e}) $	4.8	[41]
5	e + He^*$\Rightarrow $ e + He	2.9 × 10^–15	–19.8	[41]
6	e + ${\mathrm{He}}_2^* $ $\Rightarrow $ e + 2He	3.8 × 10^–15	–17.9	[39]
7	2e + He⁺$\Rightarrow $ e + He^*	6.0 × 10^–32× (T_e/0.026)^–4.4	–4.8	[4]
8	2e + ${\mathrm{He}}_2^+ $ $\Rightarrow $ e + He + He^*	4.0 × 10^–32× (T_e/0.026)^–1	—	[39]
9	e + He+ ${\mathrm{He}}_2^+ $ $\Rightarrow $2He + He^*	5 × 10^–39× (T_e/0.026)^–1	—	[39]
10	2e + ${\mathrm{He}}_2^+ $ $\Rightarrow $ e + ${\mathrm{He}}_2^* $	4.0 × 10^–32× (T_e/0.026)^–1	—	[39]
11	e + He+ He⁺$\Rightarrow $ He + He^*	5.0 × 10^–39× (T_e/0.026)^–1	—	[39]
12	e + He+ ${\mathrm{He}}_2^+ $ $\Rightarrow $ He + ${\mathrm{He}}_2^* $	1.0 × 10^–38× (T_e/0.026)^–2	—	[39]
13	e + ${\mathrm{He}}_2^* $ $\Rightarrow $ 2e + ${\mathrm{He}}_2^+ $	5.0 × 10^–15× (T_e/0.026)^–1	3.4	[39]
14	He^*+ 2He $\Rightarrow $ 3He	2.0 × 10^–46	—	[39]
15	2He^*$\Rightarrow $ e + ${\mathrm{He}}_2^+ $	2.9 × 10^–15	—	[39]
16	2He + He⁺$\Rightarrow $ He + ${\mathrm{He}}_2^+ $	1.4 × 10^–43	—	[4]
17	2He + He^$\Rightarrow $ ${\mathrm{He}}_2^ $ + He	2 × 10^–46	—	[4]
18	He^+ ${\mathrm{He}}_2^ $ $\Rightarrow $ e + ${\mathrm{He}}_2^+ $ + He	5 × 10^–16	—	[4]
19	${\mathrm{He}}_2^* $ + ${\mathrm{He}}_2^* $ $\Rightarrow $ e + ${\mathrm{He}}_2^+ $ + 2He	1.2 × 10^–15	—	[4]
20	${\mathrm{He}}_2^* $ + He $\Rightarrow $ 3He	1.5 × 10^–21	—	[4]
注: 表中He^代表He(2³S)及He(2¹S), He₂^则代表He₂(${\rm a}{}^3\Sigma_{\rm u}^+ $) .

DownLoad: CSV

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Vol. 73, Issue 14 - 2024-07-20

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