Article

# Interaction of a weakly nonlinear laser pulse with a plasma

University of Southern California

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (Impact Factor: 2.81). 03/1993; 47(2):1249-1261. DOI: 10.1103/PhysRevE.47.1249 Source: PubMed

**ABSTRACT**

Based on a one-dimensional model, a perturbation expansion is carried out to solve the equations describing a weakly nonlinear laser pulse in a plasma in which the electrons are treated relativistically and the plasma frequency is much less than the laser frequency. To lowest order, the expansion yields two coupled equations for the vector and scalar potentials. For a pulse which is long compared with a plasma wavelength, the coupled equations reduce to the nonlinear Schrödinger equation with well-known soliton solutions. An initial pulse of hyperbolic-secant shape which is short compared with a plasma wavelength broadens and acquires a characteristic asymmetric shape with a steep trailing edge and a much broader, gently sloping front portion, and has a frequency and wave-number shift which vary from a positive value at the front to a negative value at the rear of the pulse. The peak and rear part of a short pulse are strongly influenced by nonlinear effects, whereas the front is governed primarily by linear dispersion. The average pulse frequency continually decreases as energy is lost to the plasma wake. The wake-field phase velocity is shown to be approximately equal to the velocity of the pulse peak.

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**ABSTRACT:**The relativistic harmonic content of large-amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady-state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense ( w <sub>p</sub>/ w <sub>0</sub>)≪1 and critical density ( w <sub>p</sub>/ w <sub>0</sub>)≃1 limits. For weak nonlinearities, eE <sub>0</sub>/ mc ω<sub>0</sub><1, the nonlinear source term for the third harmonic is derived for arbitrary w <sub>p</sub>/ w <sub>0</sub>. Arguments are given for extending these results for arbitrary wave amplitudes. It is also shown that the use of the variable x - ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady-state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third-harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results - [Show abstract] [Hide abstract]

**ABSTRACT:**The laser wake-field acceleration concept is studied using a general axisymmetric formulation based on relativistic fluid equations. This formalism is valid for arbitrary laser intensities and allows the laser–plasma interaction to be simulated over long propagation distances (many Rayleigh lengths). Several methods for optically guiding the laser pulse are examined, including relativistic guiding, preformed plasma density channels and tailored pulse profiles. Self-modulation of the laser, which occurs when the pulse length is long compared to the plasma wavelength and the power exceeds the critical power, is also examined. Simulations of three possible laser wake-field accelerator (LWFA) configurations are performed and discussed: (i) a channel-guided LWFA, (ii) a tailored-pulse LWFA, and (iii) a self-modulated LWFA. - [Show abstract] [Hide abstract]

**ABSTRACT:**The properties of one-dimensional, weakly nonlinear electromagnetic solitary waves in a plasma are investigated. The solution of the resulting eigenvalue problem shows that the solitary waves have amplitudes which are allowed discrete values only and their vector and scalar potentials are proportional to ωp/ω0 and (ωp/ω0)2, respectively, where ωp and ω0 are the plasma and electromagnetic wave frequencies, respectively. Their widths are comparable to the plasma wavelength λp=2πc/ωp (where c is the velocity of light), except for the lowest-order solitary wave, whose width is large compared with λp, which is a true wakeless solitary wave only in the limit of vanishing amplitude. Simple analytical solutions are derived for higher-order solitary waves, whose vector-potential envelope is highly oscillatory, and are shown to consist, in the group-velocity frame, of two trapped, oppositely traveling waves.

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