Child-Langmuir flow in a planar diode filled with charged dust impurities

The Child-Langmuir (CL) flow in a planar diode in the presence of stationary charged dust particles is studied. The limiting electron current density and other diode properties, such as the electrostatic potential, the electron flow speed, and the electron number density, are calculated analytically. A comparison of the results with the case without dust impurities reveals that the diode parameters mentioned above decrease with the increase of the dust charge density. Furthermore, it is found that the classical scaling of D-2 (the gap spacing D) for the CL current density remains exactly valid, while the scaling of V32 (the applied gap voltage V) can be a good approximation for low applied gap voltage and for low dust charge density.