White-Light Parametric Instabilities in Plasmas

Abstract

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...

Transition from one-dimensional antiferromagnetism to three-dimensional antiferromagnetic order in single-crystalline CuSb2O6

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Geometric view on noneikonal waves

“…(However, contrary to a common practice, identifying such distributions as "quasiprobabilities" is somewhat misleading, as will be discussed below.) This new, invariant representation readily leads also to the general quantitative correspondence between the classical WKT and the phase-space formulation of QM [22], so far explored mainly ad hoc [23,24,25].…”

“…which can be used as an invariant representation of the corresponding terms in the Lagrangian (25). Similarly, ψ|ψ = a * n a n , where the right-hand side is recognized as the total action I.…”

Structure formation in turbulence as an instability of effective quantum plasma

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