The Space-Charge Limited Flow of Charged Particles in Planar, Cylindrical and Spherical Diodes at Relativistic Velocities†

Abstract

ABSTRACT This paper is devoted to the theoretical determinations of collector currents in diodes having planar, cylindrical and spherical electrode systems operating under conditions of space-charge limitation. The Langmuir (1913) and Child (1911) equations are extended to the case of relativistic velocities and the solutions are valid for any value of accelerating voltage. In the planar case a general power series solution is obtained by direct integration ; in the cylindrical and spherical cases, three ranges of accelerating voltage are considered and solutions obtained.