On Variational Methods In the Physics of Plasma Waves

Nonlinear interactions of waves via instantaneous cross-phase modulation can be cast in the same way as ponderomotive wave-particle interactions in high-frequency electromagnetic field. The ponderomotive effect arises when rays of a probe wave scatter off perturbations of the underlying medium produced by a second, modulation wave, much like charged particles scatter off a quasiperiodic field. Parallels with the point-particle dynamics, which itself is generalized by this theory, lead to new methods of wave manipulation, including asymmetric barriers for light.

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“…One can check then that Eq. (17) reproduces the OC Hamiltonians derived earlier, and Φ . = H − H 0 is the well-known ponderomotive potential [1].…”

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confidence: 74%

“…= I , where the angular brackets denote local averaging over Θ. As usual [15,17], the Lagrangian density of slow, adiabatic dynamics can then be calculated as L = L . After neglecting terms of order |ω c | r with r > 2, one gets…”

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confidence: 99%

Ponderomotive ForcesonWaves in Modulated Media

Dodin

Fisch

2014

Phys. Rev. Lett.

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“…The force density η produced by broad-band radiation can be written as η = η k d 3 k, where I is replaced with the phase-space action density F . [One can also understand F/ as the phase-space photon probability distribution (Dodin 2014a). ] This gives…”

Section: Pde-based Approachmentioning

confidence: 99%

Photon polarizability and its effect on the dispersion of plasma waves

Dodin

Ruiz

2017

J. Plasma Phys.

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High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

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“…Then, the adiabatic or neo-adiabatic theories described in Refs [13][14][15][16][17][18][19] apply, which allows to precisely derive the electron distribution function in the so-called action variable, defined by Eq. (42). Now, in Refs.…”

Section: Introductionmentioning

confidence: 98%

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

Bénisti

2017

Plasma Phys. Control. Fusion

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In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling. * Electronic address: didier.benisti@cea.fr

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On Variational Methods In the Physics of Plasma Waves

Cited by 28 publications

References 85 publications

Ponderomotive ForcesonWaves in Modulated Media

Ponderomotive ForcesonWaves in Modulated Media

Photon polarizability and its effect on the dispersion of plasma waves

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

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