Potential formation in a one-dimensional bounded plasma system containing a two-electron temperature plasma: Kinetic model and PIC simulation

Abstract

Potential formation in a bounded plasma system that contains electrons with a two-temperature velocity distribution and is terminated by a floating, electron emitting electrode (collector) is studied by a one-dimensional kinetic model. A method on how to determine the boundary conditions at the collector for the numerical solution of the Poisson equation is presented. The difference between the regular and the irregular numerical solutions of the Poisson equation is explained. The regular numerical solution of the Poisson equation fulfills the boundary conditions at the source and can be computed for any distance from the collector. The irregular solution does not fulfill the source boundary conditions and the computation breaks down at some distance from the collector. An excellent agreement of the values of the potential at the inflection point found from the numerical solution of the Poisson equation with the values predicted by the analytical model is obtained. Potential, electric field, and particle density profiles found by the numerical solution of the Poisson equation are compared to the profiles obtained with the particle in cell computer simulation. A very good quantitative agreement of the potential and electric field profiles is obtained. For certain values of the parameters the analytical model predicts three possible values of the potential at the inflection point. In such cases always only one of the corresponding numerical solutions of the Poisson equation is regular, while the other two are irregular. The regular numerical solution of the Poisson equation always corresponds to the solution of the model that predicts the largest ion flux to the collector.

Floating Potentials in Two‐Electron Temperature Plasma with Two Species of Positive Ions: Kinetic Model and PIC Simulation

“…According to the absolute value of the respective Ψ P we call them the low, the middle and the high solution. The middle solution is not physical because (i) Ψ C has to be a continuous function of β, and (ii) Ψ P can not increase with the increasing ratio β (see discussion in [11] and references therein). The low solution is valid, when the source potential drop is determined mainly by the cool electrons and the high solution means that the source potential drop is determined mostly by the hot electrons.…”

“…For a more extensive discussion of this problem see e.g. [11,12]. Because the length of the system is much larger than the Debye length sheath L λ D the plasma must be quasi-neutral at some z = z 0 between the source and the collector.…”

A Fluid Model of the Sheath Formation in Front of an Electron Emitting Electrode with Space Charge Limited Emission Immersed in a Plasma that Contains a One‐Dimensional Mono‐Energetic Electron Beam

“…Also possible dependence of the secondary emission coefficients on the energy of the impacting particles plays no role. Similar effects on space charge limitation of the electron emission can be caused not only by an electron beam, but also by the high temperature electron component, when the electron velocity distribution function is Maxwellian with two electron temperatures [37].…”

Floating Potential of an Electron Emitting Collector that Terminates a Bounded Plasma System

“…This electric field is also normalized by (20). But it must be emphasized that the model can be solved also for any negative η S that still allows sufficient penetration of the electrons from the source into the system for the plasma to be created [30]. The system of 4 equations (21), (22), (24) and (25) forms the basis of the model.…”

“…Already Schwager herself [24] has expanded her original model to include electron emission from the collector. Jolivet and Roussel [28] and Taccogna et al [29] have developed their own PIC codes also based on [24] and applied these codes to study secondary electron emission, while Gyergyek et al [30,31] have studied potential formation in a bounded plasma system in the presence of both -emitted and hot electrons. Next Stephens II and Ordonez went further and simulated the emission by the surface of secondary electrons consecutively to the impact of electrons from the plasma [26,27].…”