Saturation of a floating potential of an electron emitting electrode with increased electron emission: A one-dimensional kinetic model and particle-in-cell simulation

Abstract

A bounded plasma system is studied by a one-dimensional kinetic model and particle-in-cell computer simulation using the XPDP1 code. Three particle species are injected into the system from a planar source, which are the singly charged positive ions and the cool and the hot electrons. All the particle species are injected with half-Maxwellian velocity distributions with different temperatures. From the collector, the emitted electrons are injected, also with a half-Maxwellian velocity distribution, but with a much lower temperature than the cool electrons. As electron emission from the collector is increased, the floating potential of the collector increases also until the boundary of space charge limited emission is achieved. In the simulation, the emission can be increased further and it turns out that the floating potential of the collector remains constant in spite of the increased electron emission. The model on the other hand is valid only up to the boundary of space charge limited emission. The predictions of that limit and of the respective floating potential of the collector by the model are in very good agreement with the simulation. As the criterion for comparison of the model and the simulations propose the matching of the potential, electric field, and density profiles obtained from the simulation and from the numerical solution of the Poisson equation. The matching of potential and electric field profiles is usually almost perfect. On the other hand, the numerical solutions of the Poisson equation give larger ion density at the source and emitted electron density at the collector than obtained from the simulation, but the matching of the particle densities around the inflection point of the potential between the model and the simulation is excellent for all 4 particle species. The same is valid also for the hot electron density at the source. If the potentials and the electric fields are read from the simulation and inserted into the model equations, one obtains an over-determined system of 4 equations for 3 unknown parameters: the ion and the hot electron density at the source and the emitted electron density at the collector. A solution of such a system with the method of least squares is presented. The errors obtained by such a solution can be considered as a measure of how well does the model describe the simulated system.