Absence of saturation for finite injected currents in axially symmetric cavity diode

The Child-Langmuir law is investigated numerically using a fully electromagnetic particle-in-cell code for a closed axially symmetric diode. It is found that the average current transmitted to the anode (J(TR)) increases with the injected current (J(IN)) even after the formation of virtual cathode in both the nonrelativistic and relativistic cases. The increase is found to be a power law, J(TR)similar toJ(IN)(1-beta). In other words, the time averaged fraction f of electrons reaching the anode varies with the input current as, fsimilar toJ(IN)(-beta), where beta<1. In contrast, for an infinite parallel plate diode, fsimilar toJ(IN)(-1). The possibility of asymptotic saturation is also discussed. (C) 2003 American Institute of Physics.