A Gyromoment Approach for Electron Dynamics in Low-Temperature E × B Plasmas of Hall Thrusters

Le résumé fourni par la source

We study the electron dynamics in the acceleration region of a Hall thruster (HT). The strong crossed electric and magnetic fields induce both a fast electron cyclotron gyration around the magnetic field lines and a E × B drift. Starting from a Boltzmann-Poisson system, we perform a dimensional analysis to identify the dominant physical effects within this zone. This yields a non-dimensional kinetic equation tailored to the regime of interest, featuring multiple small parameters and a clear scale separation. The fast cyclotron gyration are filtered out through a Hilbert expansion combined with a gyroaveraging operator, yielding a reduced gyrokinetic model. Then a gyrofluid model is derived using a moment method with an entropy-based closure. Owing to the symmetries introduced by the gyroaveraging process, the number of required moments is reduced, and the closure corresponds to an anisotropic Gaussian requiring only four moments: the density, parallel momentum, and two directional temperatures. A numerical strategy using common tools from the literature is provided to handle the remaining small scales. Numerical experiments exhibit promising results for our applications.

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