| 21. |
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| 22. |
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| 23. |
- Fedele, R., et al.
(författare)
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How the coherent instabilities of an intense high energy charged particle beam in the presence of nonlocal effects can be explained within the context of the Madelung fluid description
- 2006
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Ingår i: European Physical Journal B. - : Springer Science and Business Media LLC. - 1434-6028 .- 1434-6036. ; B49:3, s. 275-281
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Tidskriftsartikel (refereegranskat)abstract
- A hydrodynamical description of coherent instabilities that take place in the longitudinal dynamics of a charged-particle coasting beam in a high-energy accelerating machine is presented. This is done within the framework of the Madelung fluid picture provided by the Thermal Wave Model. The well known coherent instability charts in the complex plane of the longitudinal coupling impedance for monochromatic beams are recovered. The results are also interpreted in terms of the deterministic approach to modulational instability analysis usually given for monochromatic large amplitude wave propagation governed by the nonlinear Schrodinger equation. The instability analysis is then extended to a non-monochromatic coasting beam with a given thermal equilibrium distribution, thought of as a statistical ensemble of monochromatic incoherent coasting beams ("white" beam). In this hydrodynamical framework, the phenomenon of Landau damping is predicted without using any kinetic equation governing the phase space evolution of the system.
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| 28. |
- Galant, Grzegorz, 1985, et al.
(författare)
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Simplified models for the nonlinear evolution of two fast-particle-driven modes near the linear stability threshold
- 2011
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Ingår i: Physica Scripta. - : IOP Publishing. - 1402-4896 .- 0031-8949. ; 83:5, s. 055502-
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Tidskriftsartikel (refereegranskat)abstract
- An analytical model that is based on purely differential equations of the nonlinear dynamics of two plasma modes driven resonantly by high-energy ions near the instability threshold is presented here. The well-known integro-differential model of Berk and Breizman (BB) extended to the case of two plasma modes is simplified here to a system of two coupled nonlinear differential equations of fifth order. The effects of the Krook, diffusion and dynamical friction (drag) relaxation processes are considered, whereas shifts in frequency and wavenumber between the modes are neglected. In spite of these simplifications the main features of the dynamics of the two plasma modes are retained. The numerical solutions to the model equations show competition between the two modes for survival, oscillations, chaotic regimes and 'blow-up' behavior, similar to the BB model.
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| 29. |
- Garnier, J., et al.
(författare)
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Toward a wave turbulence formulation of statistical nonlinear optics
- 2012
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Ingår i: Journal of the Optical Society of America B: Optical Physics. - 1520-8540 .- 0740-3224. ; 29:8, s. 2229-2242
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Tidskriftsartikel (refereegranskat)abstract
- During this last decade, several remarkable phenomena inherent to the nonlinear propagation of incoherent optical waves have been reported in the literature. This article is aimed at providing a generalized wave turbulence kinetic formulation of random nonlinear waves governed by the nonlinear Schrodinger equation in the presence of a nonlocal or a noninstantaneous nonlinear response function. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are obtained. In the spatial domain, when the incoherent wave exhibits fluctuations that are statistically homogeneous in space, the relevant kinetic equation is the wave turbulence (Hasselmann) kinetic equation. It describes, in particular, the process of optical wave thermalization to thermodynamic equilibrium, which slows down significantly as the interaction becomes highly nonlocal. When the incoherent wave is characterized by inhomogeneous statistical fluctuations, different forms of the Vlasov equation are derived, which depend on the amount of nonlocality in the system. This Vlasov approach describes, in particular, the processes of incoherent modulational instability and the formation of localized incoherent soliton structures. In the temporal domain, the noninstantaneous nonlinear response function is constrained by the causality condition. It turns out that the relevant kinetic equation has a form analogous to the weak Langmuir turbulence equation, which describes, in particular, the formation of nonlocalized spectral incoherent solitons. In the regime of a highly noninstantaneous nonlinear response and a stationary statistics of the incoherent wave, the weak Langmuir turbulence equation reduces to the Korteweg-de Vries equation. Conversely, in the regime of a highly noninstantaneous response in the presence of a nonstationary statistics, we derive a long-range Vlasov-like kinetic equation in the temporal domain, whose self-consistent potential is constrained by the causality condition. From a broader perspective, this work indicates that the wave turbulence theory may constitute the appropriate theoretical framework to formulate statistical nonlinear optics.
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