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

This test case corresponds to a simple 1D model of a Hall thruster. Although 1D (axial) and 2D (axial-radial) models based on fluid, hybrid or Particle-In-Cell simulations have been developed for a long time, there has not been systematic comparisons of results. Hall thrusters are very non-linear devices and small changes in the model assumptions can lead to drastic quantitative and even qualitative (eg presence or not of low frequency oscillations) changes in the model predictions. In order to make progress in the description, physical understanding, and predictions of  Hall thruster operations, it is necessary that the scientific community set up some standards in the modeling and show that models developed by different group can lead to identical results when the same assumptions are made. We propose to start with a 1D model with simple assumptions concerning anomalous electron transport. As progress are made with this simple benchmark, we will define more complex anomalous transport assumptions and propose 2D model benchmarks. The hybrid model included in the HALLIS software will be available for this benchmark.

Conditions of the benchmark

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SUMMARY

• 1D fluid, hybrid, or PIC simulation in the axial direction (x)

• Given profile of the radial magnetic field  B(x)

• Self-consistent axial electric field E(x)

• Describe atom, ion and electron transport in the axial direction, with self-consistent ionization, and obtain axial electric field from current equation in the case of a quasi-neutral model (non-quasineutral models are also possible; in that case the axial electric field is obtained from Poisson's equation) 

• Use a simple model (see below) to describe anomalous cross-field electron transport.

• Neutral atoms can be treated as a fluid with constant velocity or with a more sophisticated fluid model representing scattering by the walls (see Ref. 8). Alternatively, in a hybrid model, neutral atoms can be represented by particles and, although the model is 1D, atom trajectories can be described in 2D to take into account the effect of walls (with specular or diffuse scattering).

• In a purely fluid model neutral atoms and ions are described as fluids. Numerical problems may appear in the case of purely fluid ions without energy equation (an "artificial viscosity" may be added in the ion transport equation, see the model description).

• A number of papers based on hybrid models with particle representation of atom and ion transport (Refs.  1-4, 7-9) or with direct kinetic (DK) simulation (Refs. 5,6) have been published. These models use more or less complicated assumptions on different aspects of the problem, eg anomalous transport, wall sheaths, secondary electron emission, isotropy or not of the electron temperature etc... Because of this diversity in the model assumptions it is practically impossible to compare the results and to really understand what assumption is responsible for such or such property or performance of the thruster. Some of the benchmark results have been obtained with the hybrid model included in the HALLIS software which will be freely available in its 1D version at https://www.hallis-model.com/

• For this first 1D benchmark we consider a very simple model based on the following assumptions:

  • the anode or wall sheaths are not described​

  • electron temperature is isotropic

  • anomalous electron transport is described by using prescribed "effective" collision frequencies to represent wall collisions or turbulence. The corresponding coefficients can be different inside and outside the channel. An effective energy loss frequency is also used to describe electron energy losses due to electron-wall interaction.