The electric field in the cathode fall region of an Ar hollow cathode discharge has been measured by the use of optogalvanic spectroscopy in a gas pressure range from 1 to 6 Torr and at a discharge current from 12 to 20 mA. The radial variation of the field strength follows the mathematical expression derived from the space charge distribution function of ρ(r) = −Ar + B, where r is the radial distance from the cathode axis. In this equation the parameters A and B have been found by curve fitting to follow the formula B = aA + b, in which a is constant at −2.57 ± 0.1 mm when A and B are expressed in units of C/m4 and C/m3, respectively, while b is directly related to the gas pressure. In addition, the current- and pressure-dependent behavior of the cathode fall voltage and the electric field at the cathode surface have been examined.
Takashi Masaki, Akihide Wada, Yukio Adachi, and Chiaki Hirose, "Pressure Dependence of Space Charge Distribution in the Cathode Fall Region of Ar Hollow Cathode Discharges," Appl. Spectrosc. 42, 51-54 (1988)