Macroscopic plasma analysis from 1D-radial kinetic results of a Hall thruster discharge

Abstract

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.

Coupling plasma physics and chemistry in the PIC model of electric propulsion: Application to an air-breathing, low-power Hall thruster

“…where the fitting coefficient k is set to 0.2 by matching the results of experimental measurements obtained using Xe as a propellant [24]. The anomalous collision output velocity is computed as for an elastic isotropic one, although a recent study demonstrated how the isotropic and anisotropic characters of anomalous scattering can lead to different discharge characteristics [25].…”

Using electron fluid models to analyze plasma thruster discharges

“…A 1D radial (1Dr) fully kinetic model of the radial plasma response in a cross-section of an annular HET with a radial magnetic field and dielectric walls has been developed in [53][54][55][56]. Ions and electrons are treated as PIC macroparticles while (very-slow) neutrals constitute just a background population, with the neutral density adjusted to maintain a stationary discharge.…”

“…4 1D radial results for a cross-section of a HET, based on the kinetic model of Ref. [56]. a Normalized electron VDF along v z and v r at mid channel M:…”

“…The first one is that the radially-undulating gyroviscous term in Eq. ( 44) becomes marginal when integrated radially [56]. The second one is that the parallel and perpendicular temperatures isotropize quite fast when the magnetic field is curved with respect to the wall normal [60,61].…”

“…4(b) for φ(r) , where points Q1 and Q2 are the transition points between the plasma bulk and the sheaths, which here are set where the relative electric charge, defined as 1 − n e /n i , is a 2%, which coincides very well with a radial ion Mach number close to 1, as prescribed by the sonic Bohm criterion at a Debye sheath entrance. Finally, the kinetic computation of the electron fluxes towards each wall allowed us [55,56] to determine the values of parameters σ rp and a in Eqs. ( 73) and (77), which measure, for electron fluxes, the deviation of the electron VDF from a Maxwellian one.…”