# Boundary Conditions for Continuum Simulations of Wall-bounded Kinetic Plasmas

## TL;DR

This paper introduces a novel continuum kinetic boundary condition framework for wall-bounded plasmas, enabling detailed modeling of secondary electron emission effects with high fidelity and computational efficiency.

## Contribution

It presents the first continuum kinetic boundary conditions using the distribution function, applicable to complex wall interactions including quantum-mechanical models.

## Key findings

- Secondary electron emission significantly affects plasma sheath behavior.
- Discontinuous Galerkin implementation effectively models boundary phenomena.
- Boundary conditions improve the accuracy of plasma simulations.

## Abstract

Continuum kinetic simulations of plasmas, where the distribution function of the species is directly discretized in phase-space, permits fully kinetic simulations without the statistical noise of particle-in-cell methods. Recent advances in numerical algorithms have made continuum kinetic simulations computationally competitive. This work presents the first continuum kinetic description of high-fidelity wall boundary conditions that utilize the readily available particle distribution function. The boundary condition is realized through a reflection function that can capture a wide range of cases from simple specular reflection to more involved first principles models. Examples with detailed discontinuous Galerkin implementation are provided for secondary electron emission using phenomenological and first-principles quantum-mechanical models. Results presented in this work demonstrate the effect of secondary electron emission on a classical plasma sheath.