Measurement Method for Electric Field in Streamer Discharge Based on Electric-Field-Induced Second-Harmonic Generation

Abstract

Electric-field measurement based on the electric-field-induced second-harmonic generation (E-FISHG) method is a highly desirable tool for a noninvasive field measurement in plasmas and gases. Several papers, including ours, have pointed out and discussed the fact that the SHG signal is affected by the field length along a laser path [1] , [2] . Therefore, it is necessary to use an appropriate optical geometry depending on the target. In this paper, we examine an electric-field measurement method to a streamer discharge. We consider the case where one measures a field in the streamer discharge with a diameter of several hundred µm. We assume that the streamer discharge propagates along z axis with good reproducibility. We verify that if one acquires the signal profile along the x axis using cylindrical lenses, one can restore the field profile from the signal by performing the Abel transformation. Furthermore, we explore optical conditions under which one can obtain the maximum field value along the laser path; we elucidate the optimal Rayleigh length and calibration electrode shape and size. We also clarify how to measure the field profile in the streamer discharge using our proposed field restoration method.