Derivation of a 4-moment model for electron transport in Hall-effect thrusters from a gyrokinetic model
Résumé
We model the motion of a population of electrons in a strong electromagnetic field undergoing elastic electron/electron collisions. This regime is derived from a dimensional analysis of the electron confinement in Hall-effect thrusters. The electrons exhibit a very high cyclotron frequency and a E × B-drift, modelled by stiff PDEs at the mesoscopic scale. We obtain a gyrokinetic model in which the fastest oscillations of the system are filtered out by averaging the rotation of the electrons around the magnetic field lines. The model is derived in the strong electromagnetic field limit. Based on this gyrokinetic model, we then develop a 10-moment model. The averaging operation performed at the kinetic scale leads to symmetry properties that allow to reduce the 10-moment model to a 4-moment model.
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