Limiting stable currents in bounded electron and ion streams

The classical static analysis of the infinite planar diode has been extended to include the effects of finite transverse beam size. Simple expressions have been found for the increase in maximum stable current density over that of an infinite stream for finite cylindrical and strip streams flowing between plates of infinite diodes. The results are also given in terms of stream perveance. The effect of a nonuniform distribution of current across the stream is shown to be relatively small. Experimental values of maximum stable current agree with those obtained from the analysis. A further extension of the static analysis has been made to include the effects of additional conducting plane boundaries parallel to the stream motion. For length-to-width ratios L/D less than 0.25 the tube is adequately described by the results for the infinite planar diode and for L/D greater than 4, the infinitely-long drift tube theory suffices. At intermediate values of L/D, the maximum amount of current that can be stably passed through the tube is greater than that predicted by either asymptotic theory.