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.
陈慎, 贺恒鑫, 陈盈, 刘畅, 陈维江. 沿激光正交方向多点测量场致二次谐波的轴对称电场空间分布重构方法[J]. 电工技术学报, 2025, 40(21): 6844-6855.
Chen Shen, He Hengxin, Chen Ying, Liu Chang, Chen Weijiang. Reconstructing the Axisymmetric Inhomogeneous Electric Field Spatial Distribution by Multiple Electric Field-Induced Second Harmonic Signals Measured Perpendicular to the Laser. Transactions of China Electrotechnical Society, 2025, 40(21): 6844-6855.
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