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Deux problemes en transport des particules chargees intervenant dans la modelisation d'un propulseur ionique

Abstract : The modelling of the ionic thruster belonging to the SPT class
raises many problems of plasma physics. We studied two of them, namely the
electron transport and the computation of the electric potential.
The electron transport is subject to the influence of the fields (magnetic
and electric) set in the channel of the thruster on the one hand, and to
the collisions of electrons with heavy species and at the walls on the other
hand. We participated to the development of a SHE model (Spherical Harmonics
Expansion), which is derived by performing an asymptotic analysis of the
Boltzmann equation with a condition that models the reflection at the walls.
This model allows to approximate the Electron Energy Distribution Function
by solving a diffusion equation in the \{position, energy\} space,
whose scales are macroscopic. More precisely, we extended an existing
approach to the case where scattering against atoms are taken into account,
as well as inelastic collisions at the walls. Eventually, we compared the
implementation of this model to the results of a Monte Carlo simulation.
We obtain similar results at a very reduced computational cost. This work
lead to three publications, which are incorporated to the thesis.

\vspace*{1mm}
In a second stage, we studied the computation of the electric field in two
dimensions. Due to the presence of a magnetic field, this problem gives
rise to an anisotropic elliptic problem. Furthermore, the conductivities
along the magnetic field and across the magnetic field lines can differ
by several orders of magnitude, thus leading to ill conditioned discretization
matrices. We implemented a finite volume scheme and we showed these numerical
difficulties. Hence, we improved this method by developing a parametrization
allowing us to relate the solution of a highly anisotropic problem to a
sequence of isotropic problems. This method proved to behave well and we
should be able to treat realistic cases shortly.
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Contributor : Vladimir Latocha <>
Submitted on : Tuesday, December 24, 2002 - 3:23:57 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:43:15 PM

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  • HAL Id : tel-00002194, version 1

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Vladimir Latocha. Deux problemes en transport des particules chargees intervenant dans la modelisation d'un propulseur ionique. Mathématiques [math]. INSA de Toulouse, 2001. Français. ⟨tel-00002194⟩

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