The WASP Model: A Micro-Macro System of Wave-Schrodinger-Plasma Equations for Filamentation
E. Lorin 1*, S. Chelkowski 2, A. D. Bandrauk 21 School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada.
2 Laboratoire de Chimie Theorique, Faculte des Sciences, Universite de Sherbrooke, Sherbrooke, J1K 2R1, Canada.
Received 7 October 2009; Accepted (in revised version) 30 April 2010
Available online 27 August 2010
In this paper, we model laser-gas interactions and propagation in some extreme regimes. After a mathematical study of a micro-macro Maxwell-Schrodinger model  for short, high-frequency and intense laser-gas interactions, we propose to improve this model by adding a plasma equation in order to precisely take into account free electron effects. We examine if such a model can predict and explain complex structures such as filaments, on a physical and numerical basis. In particular, we present in this paper a first numerical observation of nonlinear focusing effects using an ab-initio gas representation and linking our results with existing nonlinear models.AMS subject classifications: 35M10, 78A60, 65Z05
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Key words: Maxwell equations, Schrodinger equation, laser-gas interaction, filamentation, quantum nonlinear optics.
Email: firstname.lastname@example.org (E. Lorin), stephane.chelkowski@USherbrooke.ca (S. Chelkowski), Andre.Bandrauk@USherbrooke.ca (A. D. Bandrauk)