  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.
