Potential Formation in a Bounded Plasma System which is Terminated by an Electron Emitting Floating Collector Studied by a Particle‐in‐Cell Computer Simulation

Abstract

AbstractPotential formation in one‐dimensional bounded plasma system terminated by a floating, electron emitting collector is studied by particle‐in‐cell (PIC) computer simulation. Attention is focused to the case of rather strong space charge limited emission. Formation of a potential well (virtual cathode) in front of the collector is observed. As emission increases the floating potential of the electrode and the potential of the bottom of the potential well both increase. The floating potential increases faster than the virtual cathode potential and consequently the depth of the potential well in front of the collector increases also. As long as the emission is not to large (up to approximately 40 times the critical emission) the relation between the depth of the potential well and the normalized emission follows a simple logarithmic formula. For larger emissions the depth of the potential well is larger than predicted by the model. It seems that at very large emission the floating potential of the collector might even exceed the zero reference potential of the source electrode. Such phenomenon has been reported by [A. Marek et al. Contrib. Plasma Phys., 48, 491 (2008)], where it was observed that the floating potential of a strongly emissive probe exceeded the plasma potential determined from the knee of the current‐voltage characteristics when the same probe was used as a Langmuir probe. But before this actually happens the simulation breaks down. When positive ions start to be repelled by the positive collector back towards the source the system becomes unstable so that a steady state can not be reached and no results can be read from the output of the simulations. That electron emission may destabilize the sheath in front of it, was found also in Hall thrusters, see e.g. [Daren Yu et al. Phys. Plasmas, 15, 104501, 2008] and [F. Taccogna et al Appl. Phys. Lett., 94, 251502, 2009]. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)