[en] The terminologies, decoherence and Landau damping, are often used concerning the damping of a collective instability. This article revisits the difference and relation between decoherence and Landau damping. A model is given to demonstrate how Landau damping affects the rate of damping coming from decoherence

[en] Landau damping, as the term is used in accelerator science, is a physical process in which an ensemble of harmonic oscillators--an accelerator beam, for example--that would otherwise be unstable is stabilized by a spread in the natural frequencies of the oscillators. This is a study of the most basic aspects of that process. It has two main goals: to gain a deeper insight into the mechanism of Landau damping and to find the coherent motion of the ensemble and thus the dependence of the total damping rate on the frequency spread

[en] The equations of nonlinear three-wave interaction, with special emphasis on the backscatter situation are studied, and the effect of damping included. Since a general analytic solution of this problem does not exist, various limiting situations are investigated, e.g. the reflection coefficient for the backscatter process is obtained explicitly in the cases of weak and strong damping. (author)

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[en] The case of three parametrically coupled and damped oscillators is considered. One (with natural frequency ω₀) is externally driven at a frequency Ω close to the sum (ω₁ + ω₂) of the other two. In the vicinity of the parametric instability threshold, we determine the time-asymptotic oscillator amplitudes and nonlinear frequency shifts by using secular-free perturbation analysis. The resulting amplitudes are sensitive to the mismatch delta (= Ω - ω₁ - ω₂), if Ω and ω₀ are dissimilar, and rise sharply as delta → 0. If Ω is close to ω₀, the behavior is quite insensitive to delta, and models results obtained for parametric instabilities in plasma. The single parametrically-driven oscillator threshold result is also obtained and compared to a general small amplitude result of Landau. This Landau result is then generalized to two coupled oscillators and compared to a result obtained by perturbation analysis. These two cases all behave as the three-oscillator does when ω₀ and Ω are dissimilar. All solutions are shown to be stable

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[en] Systematic perturbation methods are used to derive formulas for the Landau damping rates of electron-plasma and ion-acoustic waves. These formulas are more accurate than the standard formulas found in textbooks. copyright 1999 American Institute of Physics

[en] It is shown that damping of a 3-D Langmuir caviton can be due to both Landau damping and the damping due to inhomogeneities in the fields and particle distribution function. The latter we call transitional damping. It is found that the damping of the waves in the cavity considered as a whole structure, differs essentially from the damping obtained by considering only the field at the center. Arrest of the collapse seems to be very sensitive to inhomogeneities in the field structure and particle distribution function. (author)