Numerical Simulation of Probe Measurements in a Non-equilibrium Plasma

Abstract

This study investigates the axisymmetric plasma flow field near a fixed-potential surface, representing the conditions near a Faraday cup. A hybrid computational code simulates electrons with a fluid model using the Boltzmann relation, and heavy particles with a Particle In Cell method. The planar Bohm sheath solution is recovered accurately for plasma conditions n i = 1.1×10 14 m-3 , T i = 300 K, T e = 1eV. Conditions representative of a lowpower Hall thruster plume (n i = 1.1×10 14 m-3 , v i = 2,380 m/s, T i = 1 eV, T e = 1eV) also show good agreement with Bohm sheath theory. Simulated measurements of ion current on a 2D probe geometry are 10-20% higher than expected from elementary theory, suggesting a focusing effect of electric fields in the sheath.

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

“…Plasma potential and densities are averaged over the first 100 cells (4 mm) from the centerline at each fixed axial position to yield radial-average profiles in the sheath. Previous simulations using the Boltzmann model [6][7] have been in very close agreement with the Bohm sheath solutions.…”

“…(3). If the electron temperature is used to normalize the potential, the Debye length L D and Bohm velocity v B appear as appropriate length and velocity scales, and the sole remaining parameter is the Mach number based on Bohm velocity M. 6 The coordinate system begins with x = 0 at the sheath edge, where the boundary conditions are:…”

“…The derivation for both models begins by assuming a steady state and neglecting inertial terms, and expressing the electron pressure P e in terms of density and temperature using the ideal gas law. The continuity equation can then be written as a Poisson equation by introducing a streamfunction Ψ Ψ Ψ Ψ defined as ∇Ψ Ψ Ψ Ψ = n e v e so that continuity reduces to 0 2 = ∇ (6) At this point, several simplifying assumptions can be made about the electron fluid, eventually leading to the Boltzmann model. Alternatively, the governing equations can be manipulated mathematically to obtain the detailed model.…”

“…Previous numerical simulation studies suggest that the 1D Bohm sheath solution is a reliable predictor for instrument performance over a range of ambient plasma conditions. [6][7] However, these studies are limited by use of the Boltzmann relation in the electron fluid model. The Boltzmann model requires electrons to be unmagnetized, isothermal, currentless, and collisionless.…”

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

“…Previous numerical simulation studies suggest that the 1D Bohm sheath solution is reliable over a range of ambient plasma conditions, and that experimental techniques accurately deduce undisturbed plasma properties. [6][7] These simulations are limited by use of the Boltzmann model for the electron fluid, since typical EP thruster plumes do not satisfy the assumptions that electrons are isothermal, currentless, collisionless, and unmagnetized. 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.…”