By Andrea Macchi
The continual development in the direction of larger and better laser intensities has opened the best way to new actual regimes and complex functions of laser-plasma interactions, hence stimulating novel connections with ultrafast optics, astrophysics, particle physics, and biomedical purposes. This publication is basically orientated in the direction of scholars and younger researchers who have to collect swiftly a simple wisdom of this energetic and swiftly altering study box. To this target, the presentation is concentrated on a range of uncomplicated types and encouraging examples, and contains themes which emerged lately reminiscent of ion acceleration, "relativistic engineering" and radiation friction. The contents are offered in a self-contained means assuming just a easy wisdom of classical electrodynamics, mechanics and relativistic dynamics on the undergraduate (Bachelor) point, with out requiring any past wisdom of plasma physics. for this reason, the booklet may well serve in numerous methods: as a compact textbook for lecture classes, as a brief and available creation for the newcomer, as a short reference for the skilled researcher, and likewise as an creation to a few nonlinear mathematical equipment via examples in their program to laser-plasma modeling.
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Extra info for A Superintense Laser-Plasma Interaction Theory Primer
High Power Laser-Matter Interaction. : Phys. Rev. Lett. : Phys. : Surprises in Theoretical Physics. : Numerical Recipes Third Edition: The Art of Scientific Computing, 3rd edn. : New J. Phys. : Phys. Rev. : Phys. Rev. Lett. : Opt. : IEEE Trans. Antennas Propag. 14, 302 (1966) Chapter 3 Relativistic Nonlinear Waves in Plasmas Abstract In this chapter we focus on waves in a relativistic plasma. 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.
1963, Sect. 4). 73) and Eqs. 71) for ions yield a consistent model which, when the equations are linearized, provides the dispersion relation for ion-acoustic waves. The model, keeping the nonlinear terms, will be used to describe the expansion of a warm plasma (Sect. 3) and the formation of collisionless shock waves (Sect. 5), both phenomena being of current interest for laser-plasma acceleration of ions. 2 Macroscopic Description 25 The other choice for the EoS which will be considered in the following is indeed υa : the a trivial one, Pa = 0.
First we review linear waves in a homogeneous plasma with uniform and constant electron density n e , neglecting all nonlinear and “relativistic” terms. Thus we linearize Eq. 71) obtaining ∂t J −(e/m e )n e E. For monochromatic fields, using the same notation as in Eq. 38) we obtain i ω2p ˜ n 0 e2 ˜ E=− E, J˜ = −i meω 4π ω A. 2) 37 38 3 Relativistic Nonlinear Waves in Plasmas with the plasma frequency ωp ≡ 4π e2 n e me 1/2 . 4) E˜ − ∇(∇ · E) where we introduced the well-known expressions for the dielectric function ε(ω) and the refraction index n(ω) of a cold plasma ε(ω) = n2 (ω) = 1 − ω2p ω2 .