Relativistic Nonlinear Waves in Plasmas
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.
KeywordsDispersion Relation Plasma Wave Nonlinear Refractive Index Ponderomotive Force Electrostatic Wave
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