A unified treatment of the Langmuir probe and diode equations

An argument is presented which justifies the simultaneous use of both the Langmuir Mott‐Smith orbit‐limited, and the diode space‐charge‐limited equations for current collection by electrostatic probes. From these two equations the sheath size can be eliminated and the current to a probe obtained for a large range of values of probe potential and Debye length. Numerical solutions are presented for both the spherical and cylindrical cases. Asymptotic properties are considered. Comparison with results of previous probe theoretical treatments are made.