Emitting Wall Boundary Conditions in Continuum Kinetic Simulations: Unlocking the Effects of Energy-Dependent Material Emission on the Plasma Sheath

Abstract

In a wide variety of applications such as the Hall thruster and the tokamak, understanding the plasma-material interactions which take place at the wall is important for improving performance and preventing failure due to material degradation. In the region near a surface, the plasma sheath forms and regulates the electron and ion fluxes into the material. Emission from the material has the potential to change sheath structure drastically, and must be modeled rigorously to produce accurate predictions of the fluxes into the wall. Continuum kinetic codes offer significant advantages for the modeling of sheath physics, but the complexity of emission physics makes it difficult to implement accurately. This difficulty results in major simplifications which often neglect important energy-dependent physics. A focus of the work is on proper simulation of the sheath. The implementation of source and collision terms is discussed, alongside a brief study of the Weibel instability in the sheath demonstrating the necessity of proper collision implementation to avoid missing relevant physics. A novel implementation of semi-empirical models for electron-impact secondary electron emission into the boundary conditions of a continuum kinetic code is presented here. The features of both high and low energy regimes of emission are represented self-consistently, and the underlying algorithms are flexible and can be easily extended to other emission mechanisms, such as ion-impact secondary electron emission. The models are applied to simulations of oxidized and clean lithium for fusion-relevant plasma regimes. Oxidized lithium has a high emission coefficent and the sheath transitions into space-charge limited and inverse modes for different parameters. The breakdown of the classical sheath results in an increase of energy fluxes to the surface, with potential ramification for applications.