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

As Test Case 1, Test Case 2a is aimed at studying the possible development of microinstabilites (EXB Drift Instability, EXB EDI) induced by the large EXB electron drift in the magnetic barrier of a Hall thruster.  The model of Test Case 2a is two-dimensional in the axial-azimuthal directions. The  external magnetic field is perpendicular to the simulation plane and has a given profile along the axial direction. The problem is collisionless, with a given ionization rate profile. Electrons are injected from the cathode side to ensure quasineutrality and current continuity.

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The objectives of the benchmark are similar to those of Test Case 1.  Study of the conditions of the transition to an ion acoustic instability, effects of numerical noise and accuracy of the simulation,  of the imposed spatial period in the azimuthal direction,  of the magnitude of the ionization rate and of its spatial profile, of the magnetif field intensity and profile 

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Conditions of the benchmark

  • 2D-3V model periodic in the axial-azimuthal (x,y) plane  perpendicular to the magnetic field

  • given magnetic profile Bz along the x direction (uniform in y) 

  • given ionization rate profile along the x direction (uniform along the azimuthal, y direction)

  • PIC model coupling electrons, ions, + Poisson in the (x,y) direction

  • electrons and ions are subject to the self-consistent (Ex,Ey) field  and to the imposed  Bz  magnetic field.

  • initial conditions with equal and uniform electron and ion densities, typically 10^(17)  /m3, Maxwellian velocity distributions with given temperatures

  • the conditions of Refs. 1,2 are used for the benchmark

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What do we need to study ? - Questions 

  • Do we (different groups) all agree with the results of Ref. 2

  • Is there any effect of numerical noise - What are the requirements in terms on number of particles per cell, grid size, time steps, to obtain reliable results

  • What is the physics of the instability in this 2D domain 

  • what is the effect of the azimuthal length of the simulation domain (i.e. formation of longer wavelength structures for longer azimuthal lengths, what is their effect on the measured anomalous transport coefficients or "effective" collision frequency.

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References

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)

The benchmark was based on:​

J.P. Boeuf and L. Garrigues, Phys. Plasmas 25 061204 (2019) 

See also J.P. Boeuf, New insights from PIC simulations on the EXB ElectronDrift Instability in Hall thrusters, IEPC-2017-216 - 

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