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Published in:
Introduction: Some Plasma Characteristic Quantities Read chapter Read first chapter

2014 | OriginalPaper | Chapter

3. Laser Propagation: Coupling with Ion Acoustic Waves

Author : Rémi Sentis

Published in: Mathematical Models and Methods for Plasma Physics, Volume 1

Publisher: Springer International Publishing

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Abstract

This chapter contains most of fundamental concepts for the laser–plasma interaction. We first derive the paraxial approximation for the laser propagation from the full Maxwell equations. This is done by using a time envelope model and performing the Wenzel–Kramer–Brillouin (WKB) expansion. By the way, we compare the geometrical optics approximation and the paraxial approximation. In the second part of this chapter, we focus on the modelling of the Brillouin instability which corresponds to a coupling of the laser waves and an ion acoustic wave. This leads to the so-called three-wave coupling system which was introduced 40 years ago by Kadomstev. We give some crucial mathematical properties of this system, which are new according to our knowledge and which enable a better understanding of the structure of the three-wave coupling system.

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previous chapter Quasi-Neutrality and Magneto-Hydrodynamics
next chapter Langmuir Waves and Zakharov Equations
Footnotes
1
When one performs the geometrical optics approximation, a caustic phenomenon occurs if a family of optical rays have a envelope surface (which is called the caustic surface).
 
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Metadata
Title
Laser Propagation: Coupling with Ion Acoustic Waves
Author
Rémi Sentis
Copyright Year
2014
Book
Mathematical Models and Methods for Plasma Physics, Volume 1

Print ISBN: 978-3-319-03803-2

Electronic ISBN: 978-3-319-03804-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-03804-9_3