Numerical studies of the ExB electron drift instability in Hall thrusters

Abstract

The properties of the ExB drift mode in Hall thrusters were investigated through particle-based simulations. Two different two-dimensional models coupling the ExB drift azimuthal direction with the axial accelerating field and radial magnetic field directions, respectively, were implemented assuming Cartesian slab geometry. While the azimuthal-axial model is selfsustaining through the closure of the anode-cathode circuit, the radial-azimuthal one is equipped with an injection system that preserves the number of ions and with a secondary electron emission module for electron-wall interaction. Results identify the linear growth and nonlinear saturation mechanisms consisting of electron heating along azimuthal and radial directions and of ion wave trapping. The latter leads to the ion rotation along the azimuthal direction giving the ion distribution a long tail. The discrete band structure of ExB electron drift instability evolves by an inverse cascade process toward small wavenumbers characterized by broader resonances giving to the spectrum an ion-acoustic-like nature. The larger lobes are due to electron heating and to the presence of a radial component by a modified two-stream instability. Important correlations at macroscopic level between the azimuthal modulation of the azimuthal electric field and the axial modulation of the accelerating field are proof of the complexity of the electron transport in Hall thrusters.

2D radial-azimuthal particle-in-cell benchmark for E × B discharges

“…This code has been benchmarked with other codes through the 2D axial-azimuthal benchmark by Charoy et al [33] and tested for other instability cases [36,61] 4.1.5. ISTP The 2D PIC code [18] developed at ISTP is a combination of previous 1D-radial [62,63,64] and 1D-azimuthal [30] PIC codes. The code is written in Fortran90 and it uses a structured, uniform, rectangular grid.…”

Latest progress in Hall thrusters plasma modelling

“…Secondly, short wavelength instabilities with a significantly large component along the magnetic field reduce to the unmagnetized (ion-sound) form as seen from the analytical solution of the dispersion relation. Recent models (Héron-Adam 2013, Hara-Cho 2017, Croes et al 2017, Jahnunen et al 2018b, Tavant et al 2018, Taccogna et al 2019 have added the radial coordinate resolving the direction along the magnetic field and accounting for the sheath boundary conditions. They have shown that the full ion sound regime is not realized, but a more effective regime of discrete cyclotron resonance instabilities (again inverse cascade towards low wavenumbers) occur.…”

“…Another important aspect that these models can handle is the coupling between SEE and ExB EDI assessing the relative importance of these two phenomena on the electron anomalous transport. It has been recently shown (Tavant et al 2018, Taccogna et al 2019) that the electron radial heating due to ExB EDI can induce a larger SEE, but this, in turn, can help the ExB EDI saturation by cooling the electrons. As a result, it was observed that the anomalous electron cross-field mobility in the bulk plasma (induced by ExB EDI) decreases by 20% as the effective SEE coefficient increases.…”

“…As seen before, missing the axial coordinate is a possible candidate of discrepancies and inconsistencies among the different results obtained. 2D(q,z) models (Adam et al 2004, Coche and Garrigues 2014, Boeuf and Garrigues 2018, Katz et al 2018, Taccogna et al 2019, in the two possible versions (prescribed neutral or ionization source term profiles), take naturally into account the finite axial length and the wave convection, density/temperature axial gradients and axial magnetic field profile. Differently from the results obtained with some 1D(azimuthal) and 2D(azimuthal-radial) models, the scaling of wavelength ( ∼ ô@ ), frequency ( ∼ ƒS ) and amplitude of the azimuthal field…”

Electron loss mechanisms in a miniature microwave discharge water neutralizer

“…We assumed that neutral particles are spatially and temporally uniform with a Maxwellian velocity distribution at the gas temperature of 300 K, which is the common assumption for low-pressure plasma sources. [23][24][25] For the water neutralizer, H2O + , OH + , H + , H − , O − , OH − , and electrons were taken into account, whereas only Xe + and electrons were considered for the xenon neutralizer. The collision reactions and their cross sections for each neutralizer were the same as those employed in our previous papers (see Ref.…”