Space Charge and Transit Time Considerations in Planar Diodes for Relativistic Velocities

Abstract

The usual Child-Langmuir equation is extended to the case of relativistic velocities for a diode with parallel plane electrodes. The solutions obtained are valid for any value of the accelerating voltage. As the variation of mass with velocity becomes important, the exponent giving the dependence of current density on anode voltage becomes less than three-halves, and for very large values of accelerating potential approaches unity. The variation with anode voltage of the transit time, both for the space-charge-free case and for the space-charge-limited case, has been calculated. The potential distribution across the diode is also discussed.