Instability and dynamics of two nonlinearly coupled laser beams in a plasma

Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for Stimulated Raman Scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width σ of the radiation field, scaling with 1/σ for backscattering (three-wave process), and with 1/σ 1/2 for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.Parametric instabilities are pervasive in many fields of science, associated with the onset of nonlinear and collective effects such as solitons, vortices, self-organization, and spontaneous ordering. Recent developments in light sources and laser technology continue to reveal novel features of the parametric instabilities, for instance in nonlinear optics, with the recent experimental discovery of white light solitons [1], or in plasma physics, in the realm of relativistic nonlinear optics [2]. The standard theoretical approach to study parametric instabilities is based on a coherent wave description which is clearly limited because, in most systems, waves are only partially coherent, with incoherence either inherently induced by fluctuations, or induced by external passive systems (e.g. random phase plates in inertial confinement fusion (ICF)). Recent theoretical work in nonlinear optics, triggered by the work of Segev and co-workers [1], led to the development of techniques capable of describing the propagation and the modulation instability of partially coherent/incoherent "white" light in nonlinear media [3]. The critical underlying assumption of all these models is the paraxial wave approximation, valid in transparent media for radiation beams not tightly focused, which reduces the problem of electromagnetic wave propagation in dispersive (and diffractive) nonlinear media to the search of a forward propagating solution, formally described by the nonlinear Schrödinger equation. While in nonlinear optics, and for the conditions studied so far, such approximation is clearly valid, in plasma physics it is not. The instabilities associated with the partially reflected backscattered radiation [4] are critical in many laser-plasma and astrophysical scenarios [5], and the paraxial approximation has limited applicability even in the description of forward scattering instabilities driven by ultra intense lasers in underdense/transparent plasmas [6].Inclusion of bandwidth/incoherence effects in laser driven parametric instabilities in plasmas and in three-wave processes is a long-standing problem [7,8], because incoherent pumps can decrease the growth of the laser driven instabilities in ICF, Fast Ignition, or novel laser amplification schemes [9]. The difficulty resides in the lack of an appropriate theoretical framework...

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“…[15]. Recently, a dispersion relation with two pump waves was also obtained [16], which also can be derived from Eq. (10) for two photon beams…”

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confidence: 99%

White-Light Parametric Instabilities in Plasmas

Santos¹,

Silva²,

Bingham

2007

Phys. Rev. Lett.

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“…For large wavenumbers, we recover almost identically the stimulated Raman and Brillouin cases treated in Ref. [31]. Thus, we shall here concentrate on the regimes of smaller wavenumbers in which the two-plasmon decay and ion parametric decay instabilities become important, and where it is crucial to have a fully multi-dimensional treatment.…”

Section: Resultsmentioning

confidence: 98%

“…Our previous treatment of the instability of two coupled laser beams in an electron-ion plasma [31] and a two-temperature electron plasma [32] were limited to the investigation of the relativistic Raman and Brillouin scattering instabilities in one dimension, and twodimensional effects were only partly included. The purpose of the present paper is to include the multi-dimensional effects, which are particularly important for the cases where an electromagnetic wave decays into one low-frequency wave and one high-frequency electrostatic wave that are propagating obliquely to the pump wave.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional instability of two nonlinearly coupled electromagnetic waves in a plasma

Stenflo¹,

Eliasson²,

Marklund³

2008

J. Plasma Phys.

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The three-dimensional instability of two coupled electromagnetic waves in an unmagnetized plasma is investigated theoretically and numerically. In the regime of two-plasmon decay, where one pump wave frequency is approximately twice the electron plasma frequency, we find that the coupled pump waves give rise to enhanced instability with wave vectors between those of the two beams. In the case of ion parametric decay instability, where the pump wave decays into one Langmuir wave and one ion acoustic wave, the instability regions are added with no distinct amplification. Our investigation can be useful in interpreting laser-plasma as well as ionospheric heating experiments.

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“…The detailed results of this transient analysis based on the quadratic nonlinearity and simulation can hardly be compared with the steady-state analysis incorporating saturating nonlinearity (Sodha et al, 2006a(Sodha et al, , 2007a; however, both the theories lead to situations for attraction and repulsion of the beams. Shukla et al (2006) have recently investigated the nonlinear interaction between two weakly relativistic crossing laser beams in plasmas. A set of nonlinear mode coupled equations and nonlinear dispersion relations have been derived and analyzed for Raman (backward and forward) scattering instabilities as well as Brillouin and modulation self-focusing instabilities.…”

Section: Introductionmentioning

confidence: 99%

Interaction between parallel Gaussian electromagnetic beams in the ionosphere

Agarwal

Sharma

2008

Journal of Atmospheric and Solar-Terrestrial Physics

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. AbstractIn this paper, the propagation of two initially (z ¼ 0) parallel Gaussian electromagnetic beams, propagating in the z-direction in ionosphere, has been investigated. The nonlinearity in the dielectric function, responsible for the interaction between the beams arises from the redistribution of the electron density, caused by the nonuniform distribution of electron temperature determined by the Ohmic heating of the electrons and the energy loss of electrons on account of collisions. The wave frequencies have been assumed to be much larger than the electron collision frequency and gyrofrequency. A selfconsistent solution of the electromagnetic wave equation and energy balance equation (considering the solar radiation) has been obtained in the paraxial approximation. Second-order coupled ordinary differential equations have been obtained for the distance between the centers of the beams and the beam widths in the x and y directions as a function of the distance of propagation along the z-axis. Using the available database for the mid-latitude daytime ionosphere, the equations have been solved numerically for a range of parameters and a discussion of the results has been presented. The physical basis for the fact that the beams move towards each other, when the resulting irradiance distribution of the two beams has a maximum in the space between the two beams, has been highlighted. r

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Instability and dynamics of two nonlinearly coupled laser beams in a plasma

Cited by 20 publications

References 24 publications

White-Light Parametric Instabilities in Plasmas

White-Light Parametric Instabilities in Plasmas

Three-dimensional instability of two nonlinearly coupled electromagnetic waves in a plasma

Interaction between parallel Gaussian electromagnetic beams in the ionosphere

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