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.A corona is a cold plasma that results from a locally enhanced electric field near an energized conductor or a metal tip, and has broad applications, such as the electrostatic precipitators 1 , polyester fabric 2 , polyaniline doping 3 and high voltage transmission line designs 4 . Therefore, regulating the corona discharge is greatly desired, especially for many engineering purposes. To better regulate the corona (as well as other non-equilibrium plasmas), the electric field distribution is critically important for quantitative insights because it is strongly correlated with the microphysical processes of discharges that involve electron transport, kinetics of ionization, electron energy partition, and generation of excited species and atoms 5,6 .However, when a self-sustained corona discharge emerges in a system, we are unable to calculate the electric field distribution by simply solving a Laplace equation. To analyze the spatial electric field distribution under corona discharges, the ion flow model, which accounts for most key features such as ion drift and recombination, has been widely adopted 7-9 . The model includes the transport equations and a Poisson equation.To make the model complete, the value of the electric field at the surface of the electrode, which serves as the boundary condition of the model 7-10 , is assumed to remain constant. The solution to the electric field and charge distributions under a corona discharge is sensitive to this value. Townsend first attempted to estimate this value and suggested that the electric field at the surface of the conductor remains at its onset value 11 . The basis of this assumption is that a reduction in value below the onset value results in the extinction of the discharge. Cobine suggested that a highly ionized region near a line conductor may require for a field greater than the onset field 12 . Nowadays, ...