Relativistic solutions for one- and two-dimensional space-charge limited current in coaxial diode

This paper reports the two-dimensional physics and space-charge limited current (SLC) of coaxial diodes with a finite-length emitter. A full-voltage and one-dimensional approximate solution is first obtained by matching the non-relativistic solution to the super-relativistic solution. Including the effects of fields induced by the anode current and the beam itself yields the pinch-limited current in the coaxial diode. The SLC of a practically applied coaxial diode with a finite length emitter is obtained by a semi-analytical method. The solutions well agree with numerical solutions and particle-in-cell simulations. (C) 2013 AIP Publishing LLC.