The Current-Voltage Relation in the Corona

Current-voltage relation for the corona discharge between a cylinder and a coaxial wire.—An equation is derived on the basis of a small region (of radius $a$) of intense ionization around the wire, outside of which the current is carried only by ions of one sign, whose space density $\rho$ is constant. At the boundary between the two regions the field is assumed to be the minimum field required to start the corona, and the field beyond is taken to be the sum of the electrostatic field and that due to the space charge. Putting in the experimental result that $a$ is a linear function of the applied voltage $V$, the equation for the current $i$ is put in the form $i=\frac{cV(V-V_0)}{(V_1-V)}$, when $c$ is a constant proportional to the mobility. Measurements with a brass tube 17.8 cm long and 4.75 cm inside diameter, through which a slow stream of dried or moist air was passed, show good agreement with the above equation as far as variation with $V$ is concerned, for voltages from 4.7 kv to 8.8 kv, for temperatures from 290°K to 417°K and for moisture content up to 44 percent. The theory is evidently imperfect, however, as the absolute values of the mobilities come out from 2 to 4 times the values obtained in small fields although the variation with absolute temperature is correct.