A Note on Schottky's Method of Determining the Distribution of Velocities Among Thermionic Electrons

Abstract

Limiting conditions for Schottky's formula for the thermionic current from a filament to a coaxial cylinder.—The formula must fail when, due to space charge, the potential at any distance $x(r<x<R)\mathrm{}$ from the axis is less than $V{r}^2\frac{(R^2-x^2)}{x^2(R^2-r^2)}$, $V$ being the potential of the filament with respect to the cylinder, and $r$ and $R$ the radii of filament and cylinder respectively. This is more restrictive than the condition for failure which has been previously assumed.