Child-Langmuir flow with periodically varying anode voltage

Using the Lagrangian technique, we study settled Child-Langmuir flows in a one dimensional planar diodes whose anode voltages periodically vary around given positive values. Our goal is to find analytically if the average currents in these systems can exceed the famous Child-Langmuir limit found for the stationary current a long time ago. The main result of our study is that in a periodic quasi-stationary regime the average current can be larger than the Child-Langmuir maximum even by 50% compared with its adiabatic average value. The cathode current in this case has the form of rectangular pulses which are formed by a very special triangular voltage modulation. This regime, i.e., periodicity, shape of pulses, and their amplitude, needs to be carefully chosen for the best performance. (C) 2015 AIP Publishing LLC.