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Gas breakdown is one of the key factors restricting the increase of power capacity around the outer surface of high-power microwave dielectric window. It is of great significance to conduct corresponding simulation studies. Compared with the fluid model, the particle-in-cell-Monte Carlo collision model has two advantages: firstly, the influence of numerical dispersion and instability problems is insignificant; secondly, it can accurately describe microphysical processes. Therefore, the breakdown characteristics on gas side of dielectric window are simulated by the particle-in-cell-Monte Carlo collision model. The two-in-one macro-particle merging method is introduced into the model, which greatly reduces the number of macro-particles tracked, so that the whole breakdown process can be simulated and analyzed. The results show that the spatial and temporal evolution of breakdown under the variable macro-particle weight is in good agreement with that under the constant macro-particle weight. This suggests that the two-in-one macro-particle merging method is applicable under the simulation conditions of interest in this paper, i.e., when the ratio of the effective electric field of microwaves to the pressure is between $1.76\times10^3$ and $1.41\times10^4$ V/(m$\cdot$Torr). Since the yield of secondary electron emission is much less than 1, gas ionization is the dominant mechanism of breakdown on gas side of dielectric window. Electron ionization and diffusion lead to a significant increase in the density and thickness of the plasma over time. The peak of electron density does not appear at the dielectric surface, but at a position 100–150 μm away from the dielectric surface. This is because a large number of electrons are deposited on the dielectric surface, and the accompanying self-organized normal electric field drives the electrons away from the dielectric surface. Since the background gas pressure of interest in this paper is higher than the critical pressure corresponding to the maximum ionization rate (about 10~Torr), the ionization rate decreases monotonically with increasing pressure and leads to a slower development of breakdown. The accuracy of the particle-in-cell-Monte Carlo collision model is confirmed by comparing the simulated values of breakdown time with experimental data. This work provides an important theoretical basis for understanding and controlling the breakdown on gas side of dielectric window. The following figure (a) shows that the mean electron energy under the variable macro-particle weight agrees well with that under the constant macro-particle weight at 100~Torr. The following figure (b) shows that using the particle-in-cell-Monte Carlo collision model with a two-in-one macro-particle merging method allows the breakdown process to be considered when the plasma density increases by a factor of $10^8$.
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Keywords:
- Gas breakdown /
- dielectric surface /
- high-power microwave /
- particle-in-cell-Monte Carlo collision model /
- macro-particle merging method
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图 1 高功率微波作用下介质窗气体侧击穿的示意图
Figure 1. Schematic diagram of breakdown on gas side of dielectric window of high power microwave.
图 2 在背景气体压强为100 Torr和宏粒子权重分别为变量与常数下, (a)平均电子能量, 微波电场以及(b)电子数量随时间的变化
Figure 2. The change of (a) mean electron energy, microwave electric field, and (b) number of electrons over time with the macro-particle weights as variables and constant, respectively. The background gas pressure is 100 Torr in this figure.
图 3 在背景气体压强为100 Torr和宏粒子权重分别为变量与常数下, $ t=2.5\; $ns时的电子数密度随坐标z的变化
Figure 3. The variation of electron number density with coordinate z at time $ t=2.5 $ ns when the weights of macro–particles are variables and a constant, respectively. The background gas pressure is 100 Torr in this figure.
图 4 在背景气体压强为100 Torr和宏粒子权重分别为变量与常数下, 代表电子的宏粒子数量随时间的变化
Figure 4. The variation of the number of macro–particles representing electrons over time when the weights of macro–particles are variables and a constant, respectively. The background gas pressure is 100 Torr in this figure.
图 5 背景气体压强为100 Torr下电子密度$ n_\mathrm{d} $随时间和空间的变化
Figure 5. The variation of electron density $ n_\mathrm{d} $ with time and space under background gas pressure of 100 Torr.
图 6 背景气体压强为100 Torr下带电粒子密度和自组织法向电场$ E_\mathrm{n} $在$ t=7 $ ns时的空间分布
Figure 6. Spatial profiles of charged particle density and self-organizing normal electric field $ E_\mathrm{n} $ at time $ t=7 $ ns under background gas pressure of 100 Torr.
图 7 背景气体压强分别为50, 100和200 Torr下电子数量随时间的变化
Figure 7. Change in the number of electrons over time under background gas pressures of 50, 100 and 200 Torr.
图 8 电离率与 次级电子发射产额关于时间的平均值$ \nu_{\mathrm{av}} $和$ \delta_{\mathrm{av}} $随背景气体压强的变化
Figure 8. The average values $ \nu_{\mathrm{av}} $ and $ \delta_{\mathrm{av}} $ of ionization rate and secondary electron emission yield with respect to time as a function of background gas pressure.
类型 碰撞表达式 反应阈值/eV 弹性散射 e+Ar$ \rightarrow $e+Ar 激发 e+Ar$ \rightarrow $e+Ar$ ^* $ 11.5 电离 e+Ar$ \rightarrow $e+Ar$ ^+ $+e 15.6 电荷交换 Ar+Ar$ ^+\rightarrow $Ar$ ^+ $+Ar 弹性散射 Ar+Ar$ ^+\rightarrow $Ar+Ar$ ^+ $ 
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