Plasma-sheath transition in multi-fluid models with inertial terms under low pressure conditions: Comparison with the classical and kinetic theory

Abstract

We present high-order accuracy simulations of the plasma-sheath transition with an ion-electron multi-fluid model that considers the electron inertial terms and the ion pressure gradient. By means of a third-order accuracy time-dependent finite volume scheme, we solve the isothermal multi-fluid equations with realistic ion-to-electron mass ratios. We propose a numerical procedure and boundary conditions that retrieve a steady-state solution of a planar 1D floating sheath. The classical solution to this problem neglects the ion temperature since the model equations present a singularity for a finite ion temperature. The multi-fluid simulations provide a rigorous solution to the plasma-sheath transition without singularities. We compare our solution to the classical theory, finding perfect agreement when the ion-to-electron temperature tends to zero. We discuss the effect of the ion temperature, the electron inertia, and the elastic collisions with neutrals in low-pressure plasmas. Finally, relying on a kinetic approach, we derive analytical expressions for the electron macroscopic quantities inside a steady sheath that assumes a truncated Maxwellian electron velocity distribution function (EVDF) with a wall that collects the electron random flux. The derived analytical expressions are beyond the classical isothermal solution with Boltzmann electrons. The isothermal multi-fluid solution captures properly the first two moments of the EVDF inside the sheath. Our analytical expressions show the need for solving for higher-order moments to fully explain the electron physics inside the sheath, as opposite to the classical isothermal assumption. This work demonstrates that the multi-fluid simulations are able to capture the plasma-sheath transition under weakly collisional conditions with a solution that is consistent with the classical and the kinetic theory.

Introduction to Plasma Based Propulsion System: Hall Thrusters

“…Smolyakov et al reported that sheath instabilities has a vital role in anomalous transport phenomena in Hall plasma thruster [41]. Plasma sheath plays an important role to control the mobility of electrons inside a plasma channel [42][43][44].…”

Patterning and control of the nanostructure in plasma thin films with acoustic waves: mechanicalvs.electrical polarization effects

“…25 These interactions are modified when plasmas enter in contact with a solid surface and form a so called plasma-sheath. 26 Plasma sheaths are always present when a thin film is deposited via any plasma driven procedure. 25 Despite the growing emergence of AWs-plasma interactions studies with promising technological implications, 27,28 the involvement of these interactions in the deposition and nano-structuration of thin films has been largely overlooked by the scientific community (to our knowledge, except for an early work by Takahashi et al 29 that will be briefly discussed later, no other attempts have addressed this problem).…”

Second-order uniformly asymptotic-preserving space-time-ImEx schemes for hyperbolic balance laws with stiff relaxation

“…Such systems can result from relaxation approximations of conservation laws [18,33] as well as fluid limits of kinetic equations [4]. Our incentive originates in the field of plasma physics to perform high-fidelity simulations of sheaths through a new class of numerical methods [3,35] for fluid models [2]. However, we provide here the key ideas in a simpler context, where numerical analysis is attainable.…”