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

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