|
|
|
| Reconstructing the Axisymmetric Inhomogeneous Electric Field Spatial Distribution by Multiple Electric Field-Induced Second Harmonic Signals Measured Perpendicular to the Laser |
| Chen Shen1, He Hengxin1, Chen Ying1, Liu Chang1, Chen Weijiang2 |
1. State Key Laboratory of Strong Electromagnetic Technology School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan 430074 China;
2. State Grid Corporation of China Beijing 100031 China |
|
|
|
Abstract The electric field measurement method based on the electric field-induced second harmonic (E-FISH) effect has the advantage of high spatiotemporal resolution. However, when it is applied to the measurement of non-uniform electric field, it needs to rely on the equivalent gap or prior calculation to determine the calibration relationship between the measured electric field and the second harmonic intensity, which restricts its application in gas discharge plasma diagnosis.
A method for reconstructing the axisymmetric inhomogeneous electric field spatial distribution by multiple E-FISH signals measured perpendicular to the laser is presented. The proposed approach is built upon an electric field inversion model derived from the linear discretization of the measured electric field combined with E-FISH tomography techniques. By constructing a set of linear equations for the electric field inversion, where the elements of the coefficient matrix are real numbers, the method ensures that the solution is unique and free from multiple solutions that typically arise in non-linear inversion models. This guarantees that the reconstructed electric field distribution is accurate and reliable. The impact of Rayleigh distance and measuring point configuration on the condition number of the coefficient matrix used in the inversion process was further analyzed. A quantitative study was conducted to determine how these factors influence the accuracy and stability of the inversion model. The results demonstrate that the proposed method performs optimally when a specific Rayleigh range-to-range ratio configuration is adopted for different node arrangements. This configuration maximizes the robustness of the electric field inversion model, thereby enhancing its resistance to measurement errors and noise. Additionally, when the ratio of Rayleigh distance to field radius exceeds 0.1, the ability of this method to capture the electric field gradient is enhanced fivefold compared to traditional multi-point measurement methods, which typically rely on measurements along the laser direction. This improvement in gradient resolution is crucial for accurately mapping complex electric field distributions, especially in high- precision applications such as plasma diagnostics.
A non-uniform electric field measurement system with a spatial resolution of 300 μm was established. The Laplace electric field distribution of rod-rod and rod-plate gaps was measured when the electric field non-uniformity coefficient was 1.36~10.7. The experimental results showed that the maximum deviation between the measured axial field and the finite element method (FEM) results was less than 10%, confirming the accuracy of the proposed method. Furthermore, the Poisson field distribution of the positive glow corona discharge in a 2 cm rod-plate gap was studied at different applied voltages. The results revealed that as the applied voltage increased, the Poisson field strength 1 mm below the rod electrode decreased relative to its Laplacian electric field strength, while the Poisson field strength 1 mm above the plate increased. This trend was consistent with established engineering research findings, reinforcing the validity of the model.
The method is more suitable for stable electric fields such as electrostatic fields, positive glow corona, and transient electric fields with good discharge repeatability. For electric fields with significant randomness in discharge, due to the repetition frequency and power of the laser, it is currently difficult to achieve continuous measurement with high temporal resolution. For discharge phenomena such as arc that have a significant heating effect on the surrounding gas, the temperature rise of the gas will cause a change in the dielectric refractive index, which in turn affects the calibration coefficient and wave vector mismatch coefficient, resulting in the failure of the method. Therefore, it is necessary to identify the discharge object and assess the applicability of the method before conducting the measurement.
|
|
Received: 19 January 2025
|
|
|
|
|
|
[1] 李长云, 李岩青, 于永进. 大气条件下厘米级棒-板间隙负极性电晕放电中流注的产生与发展机制[J]. 电工技术学报, 2024, 39(3): 887-900.
Li Changyun, Li Yanqing, Yu Yongjin.The generation and development mechanism of streamers in centimeter- level rod-plate gap negative corona discharge under atmospheric conditions[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 887-900.
[2] 方雅琪, 毛苏涵, 杨炳森, 等. 高海拔正极性操作冲击下球-板间隙流注起始发展特性[J]. 电工技术学报, 2024, 39(19): 6175-6186.
Fang Yaqi, Mao Suhan, Yang Bingsen, et al.Initiation and development characteristics of streamer discharge of sphere-plane gaps under positive switching impulse in high altitude area[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 6175-6186.
[3] 程晨, 陈维江, 贺恒鑫, 等. 基于脉冲定量纹影系统的正先导放电起始阶段通道瞬态温度测量[J]. 电工技术学报, 2023, 38(23): 6483-6493.
Cheng Chen, Chen Weijiang, He Hengxin, et al.Experimental measurement on the transient tempera- ture evolution of positive initial leader channel based on pulse-driven quantitative schlieren system[J]. Transactions of China Electrotechnical Society, 2023, 38(23): 6483-6493.
[4] 彭长志, 董旭柱, 赵彦普, 等. 正极性先导起始与发展过程中的等离子体特征[J]. 电工技术学报, 2023, 38(2): 533-541.
Peng Changzhi, Dong Xuzhu, Zhao Yanpu, et al.Plasma characteristics of positive leader inception and development[J]. Transactions of China Electrotech- nical Society, 2023, 38(2): 533-541.
[5] Morrow R.The theory of positive glow corona[J]. Journal of Physics D: Applied Physics, 1997, 30(22): 3099.
[6] 饶宇飞, 魏诗超, 刘阳, 等. 基于电光聚合物薄膜的芯片式光学硅基电场传感器传感及温度特性研究[J]. 高压电器, 2024, 60(4): 65-71.
Rao Yufei, Wei Shichao, Liu Yang, et al.Research on sensing and temperature characteristics of chip type optical-silicon-based electric field sensor based on electro-optical polymer film[J]. High Voltage Apparatus, 2024, 60(4): 65-71.
[7] 蒋国雄, 杨建中. 工频电场测量和一种新型测量探头的研究[J]. 高电压技术, 1985, 11(4): 1-5.
Jiang Guoxiong, Yang Jianzhong.Power frequency electric field measurement and the study of a new type measuring probe[J]. High Voltage Engineering, 1985, 11(4): 1-5.
[8] 李成榕, 王文端, 林章岁, 等. 暂态电场球形测量探头的研究[J]. 华北电力学院学报, 1993, 20(增刊1): 21-28.
Li Chengrong, Wang Wenduan, Lin Zhangsui, et al.A study of potential: free spherical sensor for transient electric field measurment[J]. Journal of North China Electric Power University (Natural Science Edition), 1993, 20(S1): 21-28.
[9] 王泽忠, 李成榕, 李鹏, 等. 用球形三维电场探头测量变电站瞬态电场[J]. 华北电力大学学报, 2002, 29(3): 16-19.
Wang Zezhong, Li Chengrong, Li Peng, et al.Transient E-field measurement in substation using spherical sensor[J]. Journal of North China Electric Power University, 2002, 29(3): 16-19.
[10] 宋欣, 王克奇, 李迪飞. 场磨式电场仪在雷电预警中的研究与应用[J]. 自动化与仪表, 2011, 26(2): 8-11.
Song Xin, Wang Keqi, Li Difei.Research and application of field mill electric field meter in the lightning early warning[J]. Automation & Instrumenta- tion, 2011, 26(2): 8-11.
[11] Hidaka K.Progress in Japan of space charge field measurement in gaseous dielectrics using a Pockels sensor[J]. IEEE Electrical Insulation Magazine, 1996, 12(1): 17-28.
[12] Hidaka K, Fujita H.A new method of electric field measurements in corona discharge using Pockels device[J]. Journal of Applied Physics, 1982, 53(9): 5999-6003.
[13] Dogariu A, Goldberg B M, O'Byrne S, et al. Species- independent femtosecond localized electric field measurement[J]. Physical Review Applied, 2017, 7(2): 024024.
[14] Finn R S, Ward J F.DC-induced optical second- harmonic generation in the inert gases[J]. Physical Review Letters, 1971, 26(6): 285-289.
[15] Cui Yingzhe, Zhuang Chijie, Zeng Rong.Electric field measurements under DC corona discharges in ambient air by electric field induced second harmonic generation[J]. Applied Physics Letters, 2019, 115(24): 244101.
[16] 白晗, 黄邦斗, 邱锦涛, 等. 基于场致激光二次谐波产生原理的纳秒脉冲电场非介入测量方法研究[J]. 中国电机工程学报, 2020, 40(17): 5700-5707.
Bai Han, Huang Bangdou, Qiu Jintao, et al.Investiga- tion on non-intrusive measurement of nanosecond- pulsed electric field based on electric field induced second harmonic generation[J]. Proceedings of the CSEE, 2020, 40(17): 5700-5707.
[17] Limburg A A A. Electric field measurements on plasma bullets with electric field induced second- harmonic generation[D]. Eindhoven: Eindhoven Univer- sity of Technology, 2019.
[18] Keur T E W, Nijdam S, Limburg A A A, et al. Invasiveness of high power ns and ps pulsed laser beams on a ns pulsed N2 atmospheric pressure plasma jet in E-FISH[R]. Eindhoven: Eindhoven University of Technology, 2020.
[19] Li Xu, Jin Shaohui, Song Ke, et al.Temporal electric field of a helium plasma jet by electric field induced second harmonic (E-FISH) method[J]. Plasma Science and Technology, 2023, 25(1): 015402.
[20] Cui Yingzhe, Wang Hao, Zhuang Chijie, et al.Electric field measurement in dielectric barrier discharges using electric field induced second harmonic generation in ambient air[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2020, 27(6): 2071-2077.
[21] Broekman B E T. Electric field measurements on streamers using electric field induced second- harmonic generation[D]. Eindhoven: Eindhoven Univer- sity of Technology, 2021.
[22] Chng T L, Starikovskaia S M, Schanne-Klein M C. Electric field measurements in plasmas: how focusing strongly distorts the E-FISH signal[J]. Plasma Sources Science and Technology, 2020, 29(12): 125002.
[23] Chng T L, Brisset A, Jeanney P, et al. Electric field evolution in a diffuse ionization wave nanosecond pulse discharge in atmospheric pressure air[J]. Plasma Sources Science and Technology, 2019, 28(9): 09LT02.
[24] Chng T L, Pai D Z, Guaitella O, et al.Effect of the electric field profile on the accuracy of E-FISH measurements in ionization waves[J]. Plasma Sources Science and Technology, 2022, 31(1): 015010.
[25] 赵政, 郑昕雷, 黄宗泽, 等. 基于场致二次谐波的大气压脉冲流注放电时变非均匀电场测量研究[J]. 中国电机工程学报, 2024, 44(8): 3347-3359.
Zhao Zheng, Zheng Xinlei, Huang Zongze, et al.Time-varying non-uniform electric field measurement of atmospheric-pressure pulsed streamer discharge based on electric field induced secondary harmonic[J]. Proceedings of the CSEE, 2024, 44(8): 3347-3359.
[26] Nakamura S, Sato M, Fujii T, et al.Electric-field- profile measurement along a probing laser path based on electric-field-induced second-harmonic generation[J]. Physical Review A, 2021, 104(5): 053511.
[27] Nakamura S, Sogame M, Sato M, et al.Electric field measurement in DC corona discharge in atmospheric pressure air using E-FISHG and laser-triggering methods[J]. Plasma Sources Science and Technology, 2024, 33(5): 055010.
[28] Sogame M, Nakamura S, Sato M, et al.Adequate laser focusing and signal acquisition conditions for 3D measurement of electric-field distribution by the E-FISHG method[J]. Plasma Sources Science and Technology, 2024, 33(5): 055001.
[29] Chen Shen, He Hengxin, Chen Ying, et al.Measurement of inhomogeneous electric field based on electric field-induced second-harmonic generation[J]. Measurement, 2024, 231: 114576.
[30] Nazari A Z, Ishino Y, Ito F, et al.Quantitative schlieren image-noise reduction using inverse process and multi-path integration[J]. Journal of Flow Control, Measurement & Visualization, 2020, 8(2): 25-44.
[31] Agrawal A K, Albers B W, Griffin D W.Abel inversion of deflectometric measurements in dynamic flows[J]. Applied Optics, 1999, 38(15): 3394-3398. |
|
|
|
2025, Vol. 40 
