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## A three-dimensional simplified simulation model based on charge conservation law for internal charging in spacecraft

Yuan Qing-Yun, Sun Yong-Wei, Zhang Xi-Jun
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• #### 摘要

仿真模拟是开展航天器内带电风险评估的重要方法之一. 基于电荷守恒定律, 建立了内带电电位和电场三维计算模型, 给出了模型的一维稳态和瞬态求解算法及二维和三维求解方案, 设计了迭代算法来解耦电导率与电场强度, 并分析了该迭代算法的收敛性; 运用有限元算法和局部网格细化, 该模型具有方便考察关键点处电场畸变的优势; 与现有的辐射诱导电导率模型对比分析, 新模型更适合内带电三维数值计算; 与实验数据对比, 验证了内带电三维计算模型的正确性. 为解决航天器内介质带电评估问题提供了手段.

#### Abstract

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.

#### 作者及机构信息

###### 通信作者: 原青云, qingyuny@163.com
• 基金项目: 国家自然科学基金(批准号: 51577190)和电磁环境效应国家级重点实验室基金(批准号: 614220501020117)资助的课题

#### Authors and contacts

###### Corresponding author: Yuan Qing-Yun, qingyuny@163.com
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51577190) and the National Key Laboratory of Electromagnetic Environment Effect Foundation of China (Grant No. 614220501020117)

#### 施引文献

• 图 1  内带电三维仿真方案

Fig. 1.  3-D simulation scheme for internal charging.

图 2  背面接地的平板内带电模型

Fig. 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

Fig. 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)

Fig. 4.  Schema of conductivity enhance due to intense electric field (T = 293 K).

图 5  迭代算法流程图

Fig. 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

Fig. 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

Fig. 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

Fig. 8.  Importing Qj of Geant4 into computation by interpolation function in Comsol.

图 9  内带电数值计算设置

Fig. 9.  Configurations of internal charging numerical simulation.

图 10  时域充电电位对比(背面接地)

Fig. 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

Fig. 11.  Comparisons in cases of front &both surfaces grounding.

图 12  电路板试样与外壳结构示意图

Fig. 12.  Structure diagram of PCB sample and its crust.

图 13  电路板内带电实验系统示意图

Fig. 13.  Diagram of the experiment system for PCB internal charging.

图 14  实验与仿真结果的对比

Fig. 14.  Comparison of charging results from experiment and numerical simulation.