Particle capture by a slowly varying periodic potential

Васильев, А. Н.; Гузев, М. А.

doi:10.1007/bf01019392

Cited by 13 publications

(18 citation statements)

References 2 publications

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“…In the homogeneous situation when the wave amplitude only depends on time, it has been proved in Ref. [14][15][16][17][18][19], that, indeed, I changes very little when the dynamics is slowly-varing, even after the electrons have crossed the frozen separatrix. Then, making the so-called adiabatic approximation amounts to neglecting the change in I and to assuming that the distribution in the angle, θ, canonically conjugated to I, is uniform.…”

Section: B Near-adiabatic Limitmentioning

confidence: 99%

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

Bénisti

2016

Physics of Plasmas

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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 VlasovPoisson 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. * Electronic address: didier.benisti@cea.fr

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Section: B Near-adiabatic Limitmentioning

confidence: 99%

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

Bénisti

2016

Physics of Plasmas

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“…Hence, from Eq. (19) we know how to calculate S(v 0 − v φ ) when γ/ω B is small enough by making use of the adiabatic approximation. Moreover, when γ/ω B is large enough, we have the perturbative estimate of S(v 0 − v φ ) given by Eq.…”

Section: Electron Response To a Rapidly Varying Wavementioning

confidence: 99%

“…In the opposite regime, when ω B /γ ≫ 1, the dynamics changes at a rate much smaller than the typical period of an electron orbit. 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).…”

Section: Introductionmentioning

confidence: 99%

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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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“…I B and Refs. [4][5][6][7][8][9][10][11][12][13][14][15], the explanation for this change of action is that the cyclic protocol for λ(t) drives the system through separatrix-associated orbits with arbitrarily long time scales, thereby violating a necessary condition for action being adiabaticly invariant.…”

Section: A Backgroundmentioning

confidence: 99%

Apparent topologically forbidden interchange of energy surfaces under slow variation of a Hamiltonian

Jarzynski

Ott

2015

Phys. Rev. E

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In this paper we consider the motion of point particles in a particular type of one-degree-of-freedom, slowly changing, temporally periodic Hamiltonian. Through most of the time cycle, the particles conserve their action, but when a separatrix is approached and crossed, the conservation of action breaks down, as shown in previous theoretical studies. These crossings have the effect that the numerical solution shows an apparent contradiction. Specifically we consider two initial constant energy phase space curves H=E(A) and H=E(B) at time t=0, where H is the Hamiltonian and E(A) and E(B) are the two initial energies. The curve H=E(A) encircles the curve H=E(B). We then sprinkle many initial conditions (particles) on these curves and numerically follow their orbits from t=0 forward in time by one cycle period. At the end of the cycle the vast majority of points initially on the curves H=E(A) and H=E(B) now appear to lie on two new constant energy curves H=E(A)' and H=E(B)', where the B' curve now encircles the A' curve (as opposed to the initial case where the A curve encircles the B curve). Due to the uniqueness of Hamilton dynamics, curves evolved under the dynamics cannot cross each other. Thus the apparent curves H=E(A)' and H=E(B)' must be only approximate representations of the true situation that respects the topological exclusion of curve crossing. In this paper we resolve this apparent paradox and study its consequences. For this purpose we introduce a "robust" numerical simulation technique for studying the complex time evolution of a phase space curve in a Hamiltonian system. We also consider how a very tiny amount of friction can have a major consequence, as well as what happens when a very large number of cycles is followed. We also discuss how this phenomenon might extend to chaotic motion in higher dimensional Hamiltonian systems.

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Particle capture by a slowly varying periodic potential

Cited by 13 publications

References 2 publications

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

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

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

Apparent topologically forbidden interchange of energy surfaces under slow variation of a Hamiltonian

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