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The simulation is one of the important methods to evaluate the internal charging risk in spacecraft. In this paper, based on the charge conservation law, a three-dimensional calculation model of the potential and electric field of internal charging is established, and the one-dimensional steady state and transient solution algorithm and the two-dimensional and three-dimensional solution scheme of the model are given. An interative algorithm is designed to solve the required conductivity and the electric field intensity, and the convergence of the interative algorithm is analyzed. Using the finite element algorithm and the local mesh refinement, the model has the advantage of easily investigating the electric field distortion at key points. Comparing with the existing radiation-induced conductivity (RIC) model, due to the fact that the internal charging time constant is much higher than the charge capture time and the trap density in the dielectric is much higher than the charge density after the charge balance, the free charge will be rapidly converted into the captured charge. Therefore, it is unnecessary to consider the charge capture mechanism in the RIC model. The CCL model can be used to evaluate the internal charging and has higher computational efficiency. Comparing with the experimental data, the correctness of the three-dimensional calculation model is verified. It provides a means to evaluate the dielectric internal charging in spacecraft.
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Keywords:
- internal charging /
- spacecraft /
- electric field distortion /
- radiation induced conductivity (RIC) model
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图 1 内带电三维仿真方案
Figure 1. 3-D simulation scheme for internal charging.
图 2 背面接地的平板内带电模型
Figure 2. Internal charging model of back grounded planar board.
图 3 时域有限差分计算过程的空间与时间离散
Figure 3. Mesh on space and time domain in the finite difference time domain method.
图 4 电导率的强电场效应图示(T = 293 K)
Figure 4. Schema of conductivity enhance due to intense electric field (T = 293 K).
图 5 迭代算法流程图
Figure 5. Flowchart for the iterative algorithm.
图 6 关键点处的网格加密和对应的电场分布
Figure 6. Mesh refinement and the corresponding enlarged electric field.
图 7 基于Comsol平台的内带电三维求解图示
Figure 7. 3-D computation of internal charging on the Comsol platform.
图 8 利用插值函数导入Geant4的计算结果Qj
Figure 8. Importing Qj of Geant4 into computation by interpolation function in Comsol.
图 9 内带电数值计算设置
Figure 9. Configurations of internal charging numerical simulation.
图 10 时域充电电位对比(背面接地)
Figure 10. Comparison of the charging potential in time domain.
图 11 正面与双面接地情况下的电位对比
Figure 11. Comparisons in cases of front &both surfaces grounding.
图 12 电路板试样与外壳结构示意图
Figure 12. Structure diagram of PCB sample and its crust.
图 13 电路板内带电实验系统示意图
Figure 13. Diagram of the experiment system for PCB internal charging.
图 14 实验与仿真结果的对比
Figure 14. Comparison of charging results from experiment and numerical simulation.
表 1 CCL模型与RIC模型对比分析
Table 1. Comparison of CCL model and RIC model.
类别 充电机理 数学表达式 边界条件 是否便于三维计算 内带电计算效果 CCL 电荷守恒 一元偏微分方程 清晰 是 一定条件下充电结果相同 RIC 电荷守恒与电荷俘获机制 三元偏微分方程组 较难设定 否 
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[1] Wrenn G L 1995 J. Spacecraft Rockets 32 514
Google Scholar
[2] Fredrickson A R 1996 IEEE Trans. Nucl. Sci. 43 426
Google Scholar
[3] Frederickson A R, Dennison J R 2003 IEEE Trans. Nucl. Sci. 50 2284
Google Scholar
[4] Han J, Huang J, Liu Z, Wang S 2005 J. Spacecraft Rockets 42 1061
Google Scholar
[5] Jun I, Garrett H B, Kim W 2008 IEEE Trans. Plasma Sci. 36 2467
Google Scholar
[6] Sorensen J D, Rodgers J 2000 IEEE Trans. Plasma Sci. 47 491
[7] Weber K H 1964 Nucl. Instrum. Methods 25 261
[8] Tabata T, Andreo P, Shinoda K 1998 Radiat. Phys. Chem. 53 205
Google Scholar
[9] Tabataa T, Andreob P, Shinodac K 1999 Radia. Phys. Chem. 54 11
Google Scholar
[10] 焦维新, 濮祖荫 2000 中国科学(A辑) 30 136
Jiao W X, Pu Z Y 2000 Science in China (Series A)
30 136 [11] 全荣辉, 张振龙, 韩建伟, 黄建国, 闫小娟 2013 62 059401
Google Scholar
Quan R H, Zhang Z L, Han J W, Huang J G, Yan X J 2013 Acta Phys. Sin. 62 059401
Google Scholar
[12] 孙建军, 张振龙, 梁伟, 岳赟, 杨涛, 韩建伟 2014 航天器环境工程 31 173
Google Scholar
Sun J J, Zhang Z L, Liang W, Yue Y, Yang T, Han J W 2014 Spacecraft Environment Engineering 31 173
Google Scholar
[13] 全荣辉, 韩建伟, 黄建国, 张振龙 2007 56 6642
Google Scholar
Quan R H, Han J W, Huang J G, Zhang Z L 2007 Acta Phys. Sin. 56 6642
Google Scholar
[14] 黄建国, 陈东 2004 53 961
Google Scholar
Huang J G, Chen D 2004 Acta Phys. Sin. 53 961
Google Scholar
[15] 黄建国, 陈东 2004 地球 47 442
Huang J G, Chen D 2004 Chin. J. Geophys. 47 442
[16] 乌江, 白婧婧, 沈宾, 郑晓泉 2010 中国空间科学技术 49
Wu J, Bai J J, Shen B, Zheng X Q 2010 Chinese Space Science and Technology 49
[17] 秦晓刚, 贺德衍, 王骥 2009 58 684
Google Scholar
Qing X G, He D Y, Wang J 2009 Acta Phys. Sin. 58 684
Google Scholar
[18] 易忠, 王松, 唐小金, 武占成, 张超 2015 64 125201
Google Scholar
Yi Z, Wang S, Tang X J, Wu Z C, Zhang C 2015 Acta Phys. Sin. 64 125201
Google Scholar
[19] 王松, 易忠, 唐小金, 武占成, 孙永卫 2015 高电压技术 41 687
Wang S, Yi Z, Tang X J, Wu Z C, Sun Y W 2015 High Voltage Engineering 41 687
[20] 秦晓刚 2010 博士学位论文(兰州: 兰州大学)
Qing X G 2010 Ph. D. Dissertation (Lanzhou: Lanzhou University) (in Chinese)
[21] 张振龙, 全荣辉, 韩建伟, 黄建国 2010 原子能科学技术 44 538
Zhang Z L, Quan R H, Han J W, Huang J G 2010 Atomatic Energy Science and Technology 44 538
[22] 王松, 唐小金, 易忠, 武占成, 孙永卫 2016 原子能科学技术 50 1537
Google Scholar
Wang S, Tang X J, Yi Z, Wu Z C, Sun Y W 2016 Atomatic Energy Science and Technology 50 1537
Google Scholar
[23] 周庆2013 硕士学位论文(长春: 吉林大学)
Zhou Q 2013 M.S. Dissertation [Changchun: Jilin University) (in Chinese)
[24] Adamec V, Calderwood J H 1975 J. Phys. D: Appl. Phys. 8 551
Google Scholar
[25] 原青云, 王松 2018 67 195201
Google Scholar
Yuan Q Y, Wang S 2018 Acta Phys. Sin. 67 195201
Google Scholar
[26] Sessler G M, Figueiredo M T, Leal Ferreira G F 2004 IEEE Trans. Dielectr. Electr. Insul. 11 192
[27] 苏京, 张丽新, 刘刚, 周博, 潘阳阳, 曹康丽 2018 上海航天 35 74
Su J, Zhang L X, Liu G, Zhou B, Pan Y Y, Cao K L 2018 Aero-space Shanghai 35 74
[28] Sessler G M 1992 IEEE Trans. Dielectr. Electr. Insul. 27 961
Google Scholar
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