A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

Abstract

A 14-moment maximum-entropy system of equations is applied to the description of non-equilibrium electrons in crossed electric and magnetic fields and in the presence of low collisionality, a characteristic of low-temperature plasma devices. The flexibility of this formulation is analyzed through comparison with analytical results for steady-state non-equilibrium velocity distribution functions and against particle-based solutions of the time-dependent kinetic equation. Electric and magnetic source terms are derived for the 14-moment equations, starting from kinetic theory. A simplified collision term based on the Bhatnagar–Gross–Krook operator is formulated to describe the collision of electrons with background neutrals, accounting for the large mass disparity and energy exchange. An approximated expression is proposed for the collision frequency, to include the effect of the electrons' drift velocity, showing good accuracy in the considered conditions. The capabilities of the proposed 14-moment closure to accurately capture the non-equilibrium behavior of electrons for space homogeneous problems under conditions representative of those found in Hall thrusters are demonstrated.

14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

“…This expression is the simplest among a set of possibilities for a fourth-order maximum-entropy distribution, and can be shown to maximise the statistical entropy for a given set of known moments [23]. As also discussed in [31], this choice can represent anisotropic and asymmetric VDFs, with non-Maxwellian kurthosis, and recovers, as a limiting case, the Maxwellian and the Druyvestein's distributions. The coefficients, α ••• , can be formally obtained by solving the entropy maximisation problem [36].…”

“…For this 14-moment system, the formulation of approximated interpolative solutions to the entropy-maximisation problem has solved the long lasting problem of a high computational cost, and made a class of such methods computationally affordable [25,26]. To date, maximum-entropy methods have been applied to a number of single and multi-fluid problems [27,28], microfluidics [29], radiation transport [30] and were recently applied to the study of electrons in E × B fields [31,32].…”

Numerical Investigation of Reversed Gas-Feed Configurations for Hall Thrusters

“…Then, we repeat the simulations for a selected number of configurations by introducing the background gas, obtained from additional DSMC simulations. The "residence time" variable attached to each simulated particle is updated only when the particle is inside the ionization region ∈ [13,18] mm, and does not account for the time spent by the particle either before (closer to the anode) or after it. the ionization region and the anode does not bring substantial improvements.…”

“…where 𝜈 iz is the electron-neutral ionization frequency, that depends on the local electron density, temperature and in general on their distribution function [18]. For the goals of this work, it is not necessary to specify 𝜈 iz further.…”

“…Then, we repeat the simulations for a selected number of configurations by introducing the background gas, obtained from additional DSMC simulations. The "residence time" variable attached to each simulated particle is updated only when the particle is inside the ionization region 𝑧 ∈ [13,18] the ionization region and the anode does not bring substantial improvements. In the limit of 𝑧 𝑠 → 0, the residence time curve flattens and reaches the value obtained by direct injection.…”