Numerical Simulation of Probe Measurements in a Non-equilibrium Plasma, Using a Detailed Model Electron Fluid

Abstract

This study investigates the axisymmetric plasma flow field near a Faraday probe. A hybrid fluid PIC computational code simulates heavy particles with a Particle In Cell (PIC) model, and electrons with a detailed model derived from conservation of mass, momentum, and energy. These simulations show significant departures from the planar Bohm sheath solution and from previous simulations using the Boltzmann model electron fluid. In the current work, the sheaths extend three to six Debye lengths from the probe depending on the properties of the ion distribution. This is significantly more compact than seen in the Bohm sheath solution and previous simulations, which show sheaths that extend twice as far from the probe. Simulated measurements of ion current at the probe surface do not change as much, only increasing by 1% over Bohm sheath solution values. Variation in the conductivity of the plasma is believed to be the main source of the discrepancies.

pdFOAM: A PIC-DSMC code for near-Earth plasma-body interactions

“…Under these assumptions, magnetohydrodynamic equations of continuity, momentum, and energy reduce to [11],…”

“…The approach taken here is to assume that the electron distribution function can be described by an isothermal, currentless (electrostatic), unmagnetized (B = 0), inertia-less (m e /m i → 0) electron fluid (EF); this approach has been used successfully for the study of plasma-body interaction from a charging/arcing context [54] and in the analysis of plasma thrusters [11]. Under these assumptions, magnetohydrodynamic equations of continuity, momentum, and energy reduce to [11],…”

Comparison of Detailed Electron Fluid Model Formulations for Non-equilibrium Plasma Simulations

“…Previous simulations using this formulation demonstrated the same departures from the Bohm sheath behavior that are observed here. 8 Mainly, the detailed formulation produces sheath profiles that do not extend as far from the probe as the Bohm sheath solution suggests. A contour plot of electron density for the cold CEX case using the Poisson-consistent formulation is shown in Fig.…”

“…This expression can also be treated as a constantcoefficient Poisson equation during iteration. (8) The electron density, electron temperature, and plasma potential are all coupled, so Eqs. 3, 7, and 8 must be solved iteratively.…”

“…Further studies using a detailed model electron fluid indicate that the Bohm sheath solution may over-estimate the size of the sheath, but measurements at the probe surface would still be consistent with the undisturbed plasma properties. 8 This paper continues the development of the detailed model by describing an alternative approach to solving the system of equations. The original formulation and new Poisson-consistent formulation are described first, with emphasis on the differences in the solution process and the required boundary conditions.…”