Non--local macroscopic models based on Gaussian closures for the Spizer-Härm regime

Thierry Goudon; Martin Parisot

doi:10.3934/krm.2011.4.735

Article Contents

2011, Volume 4, Issue 3: 735-766. Doi: 10.3934/krm.2011.4.735

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Non--local macroscopic models based on Gaussian closures for the Spizer-Härm regime

Thierry Goudon^1, and
Martin Parisot^1,

1.
Project-Team SIMPAF–INRIA Lille Nord Europe, Park Plazza, 40 avenue Halley, F-59650 Villeneuve d’Ascq cedex

Received: February 28, 2011

Revised: May 31, 2011

Published: August 2011

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Abstract

The Spitzer-Härm regime arising in plasma physics leads asymptotically to a nonlinear diffusion equation for the electron temperature. In this work we propose a hierarchy of models intended to retain more features of the underlying modeling based on kinetic equations. These models are of non--local type. Nevertheless, owing to energy discretization they can lead to coupled systems of diffusion equations. We make the connection between the different models precise and bring out some mathematical properties of the models. A numerical scheme is designed for the approximate models, and simulations validate the proposed approach.

Keywords:

Plasma physics,
hydrodynamic limits.

Mathematics Subject Classification: 35Q99, 35B25, 82C70.

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