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Didier Benisti - One of the best experts on this subject based on the ideXlab platform.
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Envelope Equation for the linear and nonlinear propagation of an electron plasma wave including the effects of landau damping trapping plasma inhomogeneity and the change in the state of wave
2016Co-Authors: Didier BenistiAbstract:This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic, and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature, etc.) is supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential Equation. This Equation explicitly accounts for three-dimensional effects, plasma inhomogeneity, Landau damping, and the collisionless dissipation and electron acceleration due to trapping. It is derived by mixing results obtained from a direct resolution of the Vlasov-Poisson system and from a variational formalism involving a nonlocal Lagrangian density. In a one-dimensional situation, abrupt transitions are predicted in the coefficients of the wave Equation. They occur when the state of the electron pl...
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Envelope Equation for the linear and nonlinear propagation of an electron plasma wave including the effects of landau damping trapping plasma inhomogeneity and the change in the state of wave
2016Co-Authors: Didier BenistiAbstract:This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature,...) are supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential Equation. This Equation explicitly accounts for three-dimensional effects, plasma inhomogeneity, Landau damping, and the collisionless dissipation and electron acceleration due to trapping. It is derived by mixing results obtained from a direct resolution of the Vlasov-Poisson system and from a variational formalism involving a nonlocal Lagrangian density. In a one-dimensional situation, abrupt transitions are predicted in the coefficients of the wave Equation. They occur when the state of the electron plasma wave changes, from a linear wave to a wave with trapped electrons. In a three dimensional geometry, the transitions are smoother, especially as regards the nonlinear Landau damping rate, for which a very simple effective and accurate analytic expression is provided.
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nonlinear Envelope Equation and nonlinear landau damping rate for a driven electron plasma wave
2009Co-Authors: Didier Benisti, Olivier Morice, Laurent Gremillet, D J StrozziAbstract:In this article, we provide a theoretical description and calculate the nonlinear frequency shift, group velocity, and collionless damping rate, ν, of a driven electron plasma wave (EPW). All these quantities, whose physical content will be discussed, are identified as terms of an Envelope Equation allowing one to predict how efficiently an EPW may be externally driven. This Envelope Equation is derived directly from Gauss’ law and from the investigation of the nonlinear electron motion, provided that the time and space rates of variation of the EPW amplitude, , are small compared to the plasma frequency or the inverse of the Debye length. ν arises within the EPW Envelope Equation as a more complicated operator than a plain damping rate and may only be viewed as such because [] remains nearly constant before abruptly dropping to zero. We provide a practical analytic formula for ν and show, without resorting to complex contour deformation, that in the limit 0, ν is nothing but the Landau damping rate. We t...
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nonlinear Envelope Equation and nonlinear landau damping rate for a driven electron plasma wave
2009Co-Authors: Didier Benisti, Olivier Morice, Laurent Gremillet, D J StrozziAbstract:In this paper, we provide a theoretical description, and calculate, the nonlinear frequency shift, group velocity and collionless damping rate, $\nu$, of a driven electron plasma wave (EPW). All these quantities, whose physical content will be discussed, are identified as terms of an Envelope Equation allowing one to predict how efficiently an EPW may be externally driven. This Envelope Equation is derived directly from Gauss law and from the investigation of the nonlinear electron motion, provided that the time and space rates of variation of the EPW amplitude, $E_p$, are small compared to the plasma frequency or the inverse of the Debye length. $\nu$ arises within the EPW Envelope Equation as more complicated an operator than a plain damping rate, and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant before abruptly dropping to zero. We provide a practical analytic formula for $\nu$ and show, without resorting to complex contour deformation, that in the limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term $\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the nonlinear frequency shift of the EPW, it is also derived theoretically and found to assume values significantly different from previously published ones, assuming that the wave is freely propagating. Moreover, we find no limitation in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye length, for a solution to the dispertion relation to exist, and want to stress here the importance of specifying how an EPW is generated to discuss its properties. Our theoretical predictions are in excellent agreement with results inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an application of our theory to the study of SRS is presented.
Scott A Diddams - One of the best experts on this subject based on the ideXlab platform.
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mid infrared frequency comb generation via cascaded quadratic nonlinearities in quasi phase matched waveguides
2018Co-Authors: Abijith S Kowligy, Alex Lind, Daniel D Hickstein, David R Carlson, Henry Timmers, Nima Nader, Flavio C Cruz, Gabriel Ycas, Scott B Papp, Scott A DiddamsAbstract:We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-χ(2) nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive wave generation in the 2.5–3 μm region and intrapulse difference frequency generation in the 4–5 μm region. By engineering the quasi-phase-matched grating profiles, tunable, narrowband MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear Envelope Equation, which shows good quantitative agreement with the experiment—and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.
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mid infrared frequency comb generation via cascaded quadratic nonlinearities in quasi phase matched waveguides
2018Co-Authors: Abijith S Kowligy, Alex Lind, Daniel D Hickstein, David R Carlson, Henry Timmers, Nima Nader, Flavio C Cruz, Gabriel Ycas, Scott B Papp, Scott A DiddamsAbstract:We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$\chi^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\text{\mu}$m region and intra-pulse difference-frequency generation in the 4--5 $\text{\mu}$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear Envelope Equation, which shows good quantitative agreement with the experiment---and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.
Nam C. Lee - One of the best experts on this subject based on the ideXlab platform.
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Envelope Equation of electrostatic nonlinear waves in relativistic two fluid plasmas
2010Co-Authors: Nam C. LeeAbstract:The reductive perturbation method is used to derive the nonlinear Schrodinger (NLS) Equation describing the evolution of electrostatic waves in fully relativistic two-fluid plasmas with arbitrarily large streaming velocity and temperature. As an application of the general result, a pair plasma with relativistically hot temperature is considered. From the derived NLS Equation, it can be predicted that the width of the wave packet is independent of the temperature T if kλD⪡1, while it scales as ∼1/T if kλD⪢1, where k is the wave number of the carrier wave and λD is the Debye length of the plasma.
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the Envelope Equation of oblique alfven waves
2003Co-Authors: Nam C. Lee, G K ParksAbstract:An Equation is derived to describe the evolution of Envelope of electromagnetic waves having arbitrary propagation directions and modulation in cold plasma. The ambient magnetic field is assumed constant and uniform. The derived Equation is applied to Alfven waves propagating obliquely with respect to the ambient magnetic field and it is shown that it can have both a kink-type solitary wave as well as a bump-type solitary wave solution.
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Envelope Equation for nonlinear transverse waves in a warm two-fluid plasma
1998Co-Authors: Nam C. Lee, George K. ParksAbstract:An Equation describing the nonlinear development of an Envelope of weakly dispersive transverse waves propagating along the ambient magnetic field in a warm two-fluid plasma is derived by using the Fourier transformation method. This Equation contains three nonlinear terms, a cubic, a derivative of cubic, and a quadratic multiplied by a derivative term. For the case of small wave amplitude, the Equation is of non-Schrodinger type that includes a linear term involved with mixed second-order derivatives (space and time), in addition to the usual two terms of the Schrodinger-type Equation. This mixed derivative term arises from the inclusion of the displacement current in the formulation. The nonlinear terms in the derived Equation explicitly contain a smallness parameter which vanishes in the limit of zero dispersion. The low frequency limit of the Equation is compared with the standard derivative nonlinear Schrodinger Equation (DNLS), and differences are discussed. The new Equation predicts that the condit...
Ronald C Davidson - One of the best experts on this subject based on the ideXlab platform.
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generalized kapchinskij vladimirskij distribution and Envelope Equation for high intensity beams in a coupled transverse focusing lattice
2009Co-Authors: Hong Qin, Moses Chung, Ronald C DavidsonAbstract:In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell Equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix Envelope Equation.
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symmetries and invariants of the time dependent oscillator Equation and the Envelope Equation
2005Co-Authors: Hong Qin, Ronald C DavidsonAbstract:The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant is fundamentally a result of the corresponding symmetry admitted by the oscillator Equation with time-dependent frequency. A careful analysis of the admitted symmetries reveals a deeper connection between the non-linear Envelope Equation and the oscillator Equation. A general theorem regarding the symmetries and invariants of the Envelope Equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the Envelope Equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.
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nonlinear properties of the kapchinskij vladimirskij equilibrium and Envelope Equation for an intense charged particle beam in a periodic focusing field
1994Co-Authors: Chiping Chen, Ronald C DavidsonAbstract:The nonlinear properties of the Kapchinskij-Vladimirskij (KV) equilibrium and Envelope Equation are examined for an intense charged-particle beam propagating through an applied periodic solenoidal focusing magnetic field, including the effects of the self-electric and self-magnetic fields associated with the beam space charge and current. It is found that the beam emittance is proportional to the maximum canonical angular momentum achieved by the particles within the KV distribution. The Poincare mapping technique is used to determine systematically the axial dependence of the radius of the matched (equilibrium) beam and to study nonlinear behavior in the nonequilibrium beam Envelope oscillations. It is shown that the nonequilibrium beam Envelope oscillations exhibit nonlinear resonances and chaotic behavior for periodic focusing magnetic fields and sufficiently high beam densities. Certain correlations are found between the nonlinear resonances and well-known instabilities for the KV equilibrium. It is also shown, in agreement with previous studies, that there exists a uniquely matched beam in the parameter regime of practical interest, i.e., [sigma][sub 0][lt]90[degree], where [sigma][sub 0] is the vacuum phase advance over one axial period of the focusing field. The nonlinear resonances and chaotic behavior in the nonequilibrium beam Envelope oscillations may play an important role in mismatched ormore » multiple beam transport, including emittance growth and beam halo formation and evolution.« less
Abijith S Kowligy - One of the best experts on this subject based on the ideXlab platform.
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mid infrared frequency comb generation via cascaded quadratic nonlinearities in quasi phase matched waveguides
2018Co-Authors: Abijith S Kowligy, Alex Lind, Daniel D Hickstein, David R Carlson, Henry Timmers, Nima Nader, Flavio C Cruz, Gabriel Ycas, Scott B Papp, Scott A DiddamsAbstract:We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-χ(2) nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive wave generation in the 2.5–3 μm region and intrapulse difference frequency generation in the 4–5 μm region. By engineering the quasi-phase-matched grating profiles, tunable, narrowband MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear Envelope Equation, which shows good quantitative agreement with the experiment—and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.
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mid infrared frequency comb generation via cascaded quadratic nonlinearities in quasi phase matched waveguides
2018Co-Authors: Abijith S Kowligy, Alex Lind, Daniel D Hickstein, David R Carlson, Henry Timmers, Nima Nader, Flavio C Cruz, Gabriel Ycas, Scott B Papp, Scott A DiddamsAbstract:We experimentally demonstrate a simple configuration for mid-infrared (MIR) frequency comb generation in quasi-phase-matched lithium niobate waveguides using the cascaded-$\chi^{(2)}$ nonlinearity. With nanojoule-scale pulses from an Er:fiber laser, we observe octave-spanning supercontinuum in the near-infrared with dispersive-wave generation in the 2.5--3 $\text{\mu}$m region and intra-pulse difference-frequency generation in the 4--5 $\text{\mu}$m region. By engineering the quasi-phase-matched grating profiles, tunable, narrow-band MIR and broadband MIR spectra are both observed in this geometry. Finally, we perform numerical modeling using a nonlinear Envelope Equation, which shows good quantitative agreement with the experiment---and can be used to inform waveguide designs to tailor the MIR frequency combs. Our results identify a path to a simple single-branch approach to mid-infrared frequency comb generation in a compact platform using commercial Er:fiber technology.