Abstract
In this chapter we focus on waves in a relativistic plasma. For electromagnetic waves, we introduce the nonlinear refractive index and the two most prominent phenomena of “relativistic optics”, i.e. self-focusing and transparency. For both phenomena, an account of a more complete theoretical description is presented along with an introduction to some methods of nonlinear physics, such as the multiple scale expansion, the nonlinear Schrödinger equation, and the Lagrangian approach. A brief description of standing nonlinear solutions, i.e. cavitons or (post-)solitons, is also given. For electrostatic waves we discuss the wave-breaking limit and focus on properties relevant to electron accelerators and field amplification schemes that will be described in the following chapters.
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Notes
- 1.
Actually a depletion region appears only if \(n_0\ge 1.5\) (in units of \(n_c\)) (Cattani et al. 2000). For the sake of brevity we restrict ourselves to the \(n_0>1.5\) case; a more complete discussion can be found in the references.
- 2.
In Goloviznin and Schep (2000) it was also shown that in some range of parameters evanescent and propagating solutions may coexist, allowing in principle for instability and hysteresis effects, although only the evanescent solution is observed in simulations.
- 3.
The second definition is by far the most used, although the present author is not fully satisfied with that as he believes the term “soliton” to identify a more specific nonlinear structure.
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Macchi, A. (2013). Relativistic Nonlinear Waves in Plasmas. In: A Superintense Laser-Plasma Interaction Theory Primer. SpringerBriefs in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6125-4_3
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