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

 

This test case is aimed at studying the Electron Cyclotron Drift Instability when the particle motion and electric development is allowed along the magnetic field (radial direction of the Hall thruster) and in the azimuthal direction (EXB drift) . Periodic boundary conditions are used in the azimuthal direction. The constant electric field is applied along the axial direction (not resolved in the simulation, but the positions of the particles in this direction can be tracked to study the effect of a finite channel length/acceleration region). ​

The objective of the benchmark is to study the EXB EDI under 2D conditions (constant E and B, and description of the EXB and radial directions) and the conditions of the possible transition to an ion acoustic instability. The effects of 1) numerical noise and accuracy of the simulations, 2), of the imposed spatial period in the azimuthal direction, and 3) of the re-injection of particles (i.e. finite length of the acceleration region) must also be evaluated.

Conditions of the benchmark

  • 2D-3V model periodic in the azimuthal direction y (EXB direction) and finite length along z-direction (B direction)

  • given electric field Ex in the direction x (axial direction) perpendicular to y, typically Ex=200 V/cm

  • given magnetic field Bz in the direction z perpendicular to x and y, typically Bz=200 Gauss

  • no collisions

  • 2D PIC model coupling electron and ion transport + Poisson in the y and z direction

  • electrons and ions are subject to the self-consistent Ey and Ez fields and to the imposed constant Ex and Bz electric and magnetic fields.

  • Plasma has a finite length along z-direction and terminated by the dielectric walls. The dielectric boundary conditions are used as in Ref 1

  • initial conditions with equal and uniform electron and ion densities, on the order of 10^(17) m^-3, Maxwellian initial velocity distributions with temperature respectively on the order of a few eV and fraction of one eV

  • the conditions of Ref. 1 are used for the benchmark

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What do we need to study ? - Questions 

  • continuous heating and plasma decay: electrons and ions are not removed from the simulation domain, gain energy continuously in the x, y and z directions​ - use the conditions of Ref 1. Plasma decays with time due to sheath losses.

  • Quasistationary plasma with a source: a more realistic situation corresponding to quasistationary conditions can be simulated by trying to add plasma source which would balance the sheath losses. The source is uniform in y direction and localized in z.  

  • The questions are:

What are the effects of the finite length and finite kz (along B) on the ECDI? What is the mode structure along magnetic field and how it is affected by dielectric boundary conditions? At what point the ECDI transits to the ion sound mode? How it is affected by boundary conditions and SEE?  What is the role of the modified two-stream instability (MDTS) which occurs with finite kz and is typically a long wavelength mode? How does MDTS affects plasma heating along the magnetic field? What are the amplitude of the fluctuations, spectra and the ​measured anomalous transport?

​

References​

Organized by Willca Villafana and published  in 2021

Reference: W 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)

Other references ​

  1. Janhunen, S., A. Smolyakov, D. Sydorenko, M. Jimenez, I. Kaganovich and Y. Raitses (2018). "Evolution of the electron cyclotron drift instability in two-dimensions." Physics of Plasmas 25(8): 082308.  Download

  2. Croes, V., T. Lafleur, Z. Bonaventura, A. Bourdon and P. Chabert (2017). "2D particle-in-cell simulations of the electron drift instability and associated anomalous electron transport in Hall-effect thrusters." Plasma Sources Science \& Technology 26(3): 034001

  3. Heron, A. and J. C. Adam (2013). "Anomalous conductivity in Hall thrusters: Effects of the non-linear coupling of the electron-cyclotron drift instability with secondary electron emission of the walls." Physics of Plasmas 20(8): 082313.

  4. Hara K and Cho S 2017 35th International Electric Propulsion Conference (The Electric Rocket Propulsion Society, Atlanta, GE, 2017), paper IEPC-2017-495

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