Electric field measurements under DC corona discharges in ambient air by electric field induced second harmonic generation

Electric field distribution is critically important for quantitative insights into the physics of non-equilibrium plasma like corona. To analyze the electric field as well as the ion flow (space charge) distribution under DC corona discharges, the ion flow model has been widely adopted; Kaptzov's assumption, which states the {steady state} electric field at the conductor surface remains at the corona onset value, serves as a boundary condition. In this letter, we investigate the electric field distribution under DC corona discharges between coaxial cylindrical electrodes in ambient air by electric field induced second harmonic generation with nano-second pulse laser beams. The electric field distribution (with or without corona discharge) is obtained. By comparing the measurements with the results predicted by the ion flow model for negative corona discharge, it is found that the electric field at the conductor surface is proportional to the current density of the corona discharge with a negative constant of proportionality. Therefore, for negative corona discharges, Kaptzov's assumption is valid only when the discharge current approaches zero or is small.