Continuum Kinetic Simulations of Plasma Sheaths and Instabilities

Abstract

A careful study of plasma-material interactions is essential to understand and improve the operation of devices where plasma contacts a wall such as plasma thrusters, fusion devices, spacecraft-environment interactions, to name a few. This work aims to advance our understanding of fundamental plasma processes pertaining to plasma-material interactions, sheath physics, and kinetic instabilities through theory and novel numerical simulations. Key contributions of this work include (i) novel continuum kinetic algorithms with novel boundary conditions that directly discretize the Vlasov/Boltzmann equation using the discontinuous Galerkin method, (ii) fundamental studies of plasma sheath physics with collisions, ionization, and physics-based wall emission, and (iii) theoretical and numerical studies of the linear growth and nonlinear saturation of the kinetic Weibel instability, including its role in plasma sheaths.The continuum kinetic algorithm has been shown to compare well with theoretical predictions of Landau damping of Langmuir waves and the two-stream instability. Benchmarks are also performed using the electromagnetic Weibel instability and excellent agreement is found between theory and simulation. The role of the electric field is significant during nonlinear saturation of the Weibel instability, something that was not noted in previous studies of the Weibel instability. For some plasma parameters, the electric field energy can approach magnitudes of the magnetic field energy during the nonlinear phase of the Weibel instability.A significant focus is put on understanding plasma sheath physics which is essential for studying plasma-material interactions. Initial simulations are performed using a baseline collisionless kinetic model to match classical sheath theory and the Bohm criterion. Following this, a collision operator and volumetric physics-based source terms are introduced and effects of heat flux are briefly discussed. Novel boundary conditions are developed and included in a general manner with the continuum kinetic algorithm for bounded plasma simulations. A physics-based wall emission model based on first principles from quantum mechanics is selfconsistently implemented and demonstrated to significantly impact sheath physics. These are the first continuum kinetic simulations using self-consistent, wall emission boundary conditions with broad applicability across a variety of regimes.

Current-driven Langmuir Oscillations and Streaming Instabilities

“…1, in order to see how the instabilities are modified by current-driven Langmuir oscillations. To this end, we use the openly available stateof-the-art code Gkeyll 2.0, which is developed at PPPL (see for instance The Gkeyll team [8], Cagas [10], Hakim and Juno [17], Juno et al [18]). Of utmost importance to us is the fact that Gkeyll solves the full set of Vlasov-Maxwell's equations, instead of relying upon the Poisson equation, since, as we have seen in the preceeding section, current-driven Langmuir oscillations can hardly be predicted from the Poisson equation.…”

“…Inspired by the thesis of Cagas [10], we use contour plots to identify solutions of the dispersion relations, but for a range of different electron drift velocities u ∈ [0, u 0 ]. u 0 is the inital drift velocity in accordance with table I.…”

Energy-dependent implementation of secondary electron emission models in continuum kinetic sheath simulations

“…This allow simulations to capture small-scale kinetic physics which is often lost by fluid models, while avoiding the statistical noise that poses problems for particle-in-cell (PIC) methods [11]. When applied to the situation of the classical plasma sheath which forms at the boundary of a plasma and a material surface, continuum kinetic models allow for accurate simulation of the sheath region and instabilities [7,12]. However, the addition of secondary electron emission (SEE) physics poses several unique challenges to these models.…”