Theory of Electron Collection of Spherical Probes

Abstract

The theory of spherical probes based on the impact parameter of the carriers is given. Fields outside the sheath are neglected, which is justified for electron collection. The results are obtained more directly than by Mott‐Smith and Langmuir. General results such as the transition from impact parameter limitation to sheath limitation for the spherical case, not previously treated in the literature, are derived. The case of a uniformly accelerated half‐Maxwellian (as opposed to a Maxwellian with drift) is treated in detail; the case of a pure Maxwellian superimposed on the accelerated half‐Maxwellian and the superposition of two different accelerated half‐Maxwellians is discussed briefly.