Relativistic Nonlinear Waves in Plasmas

  • Andrea Macchi
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)


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.


Dispersion Relation Plasma Wave Nonlinear Refractive Index Ponderomotive Force Electrostatic Wave 
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Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.National Research CouncilNational Institute of Optics (CNR/INO)PisaItaly
  2. 2.Department of Physics “Enrico Fermi”University of PisaPisaItaly

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