Test Case 1 -  1D azimuthal PIC simulation of the EXB EDI  

This test case is aimed at studying the possible development of microinstabilites induced by the large EXB electron drift in the magnetic barrier of a Hall thruster.  The Electron Cyclotron Drift Instability (which we call EXB Drift Instability, EXB EDI, in the present context) studied in the 1970's in space plasmas, has been evidenced in axial-azimuthal PIC simulations of Hall thrusters. The proposed benchmark is aimed at studying the EXB EDI under 1D conditions (constant E and B, and description of the EXB, azimuthal direction)  and the conditions of the possible transition to an ion acoustic instability. The effects of numerical noise, accuracy of the simulations, and spatial periodicity in the EXB direction must also be evaluated   

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Test Case 2a - 2D axial-azimuthal PIC simulation of the EXB EDI  

Here we study the EXB EDI under slightly more realistic conditions that can naturally take into account the finite transit time of electrons in the acceleration region, and the effects of density and magnetic field gradients. We simplify the problem by assuming a given ionization rate profile. This suppresses the non-linear coupling of the plasma density and atom density leading to the well know low frequency ("breathing") oscillations of Hall thrusters. The proposed benchmark allows to study the formation, convection and saturation of the EXB EDI. The issues are the transition to an ion acoustic instability, the effect of the instability on the anomalous electron cross-field mobility, the possible effect of numerical noise and of the finite period of the model in the azimuthal direction. 

benchmark organized by Thomas CHAROY and published in 2019 

Reference: T Charoy, JP Boeuf , A Bourdon , JA Carlsson, P Chabert, B Cuenot , D Eremin, L Garrigues , K Hara , ID Kaganovich, AT Powis, A Smolyakov , D Sydorenko, A Tavant ,O Vermorel and W Villafana, Plasma Source Sci. Technol. 28 105010 (2019)

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Test Case 2b - 2D radial-azimuthal PIC simulation of the EXB EDI  

In this case the  EXB EDI is studied in the radial and azimuthal directions. The electron and ion transport in the axial direction is described as in Test Case 1 (constant electric field in the axial direction, constant magnetic field in the radial direction).

Benchmark organized by Willca Villafana and published in 2021

Reference: TW Villafana, F Petronio, AC Denig, M J Jimenez, D Eremin, L Garrigues, F Taccogna, A Alvarez-Laguna, J P Boeuf, A Bourdon, Plasma Source Sci. Technol.  30 075002  (2021)

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Test Case 3 - 1D axial fluid, hybrid, or PIC simulation of a Hall thruster

This test case corresponds to the classical 1D axial description of a Hall thruster. The 1D models can predict low frequency current and plasma oscillations due to the non-linear coupling beteween plasma transport, ionization, and atom transport in the channel, but cannot self-consitently describe anomalous electron transport across the magnetic barrier. Empirical coefficients or coefficients based on simple electron-wall interaction theory have been used to represent anomalous electron transport in these models. Although this is a classical problem that has been addressed by different groups in the last 20 years, there has not been any systematic comparaison of the results. It turns out that the  well known low frequency oscillations of Hall thrusters ("breathing mode") are extremely dependent, in the models, on the assumptions made, eg, on atom transport, ion recombination at the walls (ion losses), etc... Different models for anomalous cross-field electron transport coefficients and electron-wall interaction have been used by different groups but there is no consensus on the most realistic way or most physical way of representing these phenomena. The objectives of this test case are to 1) to compare results from different groups for the same specified anomalous transport coefficients or model, 2) to understand possible discrepancies and converge toward identical results, 3), to clearly identify and understand (possibly with the help of analytical theory) the parameters controling low frequency oscillations, and, 4) to try to identify, by comparisons with experimental trends, the most realistic anomalous transport model

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Test Case 4 - Penning Spoke Benchmark

This test case corresponds to the radial-azimuthal simulation of the rotating spoke (macroscopic instability) in a collisionless Penning discharge with injection of electrons and ions from a central region.  The magnetic field is uniform and perpendicular to the simulation domain.

Organized by AT Powis, L Garrigues, G Fubiani, started August 2022

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