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Title: Landau damping


Landau damping is calculated using real variables, clarifying the physical mechanism.

  1. CCFE, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB (United Kingdom)
Publication Date:
OSTI Identifier:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2015 EURATOM; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States

Citation Formats

Wesson, John. Landau damping. United States: N. p., 2015. Web. doi:10.1063/1.4913426.
Wesson, John. Landau damping. United States. doi:10.1063/1.4913426.
Wesson, John. 2015. "Landau damping". United States. doi:10.1063/1.4913426.
title = {Landau damping},
author = {Wesson, John},
abstractNote = {Landau damping is calculated using real variables, clarifying the physical mechanism.},
doi = {10.1063/1.4913426},
journal = {Physics of Plasmas},
number = 2,
volume = 22,
place = {United States},
year = 2015,
month = 2
  • The question of whether the Landau-fluid'' description of wave-particle resonances (e.g., Hammett and Perkins, Phys. Rev. Lett. {bold 64}, 3019 (1990)) can describe nonlinear Landau damping is addressed. It is found that this model can provide an adequate description of the Compton scattering of electron drift waves, but fails in the case of ion-temperature-gradient-driven modes near the threshold. The general conclusion is that Landau-fluid models have difficulty describing the dynamics associated with the product of two or more deeply resonant propagators.
  • For linear Langmuir waves, it is well known that the energy exchanges generally lead to a continuous dissipation, on average, from the electric form to the kinetic one. Many papers have estimated these exchanges and indeed shown that the classical Landau value {gamma}{sub L}, characterizing the electric field damping, can be derived from this estimation. The paper comes back to this demonstration and its implicit assumption of 'forgetting the initial conditions'. The limits of the usual energy calculations have become much apparent recently when non-Landau solutions, decreasing with damping rates smaller than {gamma}{sub L}, have been evidenced [Belmont et al.,more » Phys. Plasmas 15, 052310 (2008)]. Taking advantage of the explicit form provided in this paper for the perturbed distribution function, the dissipation process is revisited here in a more general way. It is shown that the energy calculations, when complete (i.e., when the role of the initial conditions is not excluded by the very hypotheses of the calculations), are indeed in full agreement with the existence of non-Landau solutions; Landau damping, by the way, appears as a particular mode of dissipation, in which the ballistic transport of the initial plasma perturbation leads to negligible effects. Two approaches are presented for this demonstration, Eulerian and Lagrangian, the first one starting from the Vlasov equation and the second from the dynamics of the individual particles. The specific role of the so-called resonant particles is investigated in both formalisms, which provides complementary pictures of the microphysics involved in the energy transfers between field and particles for Landau as well as for non-Landau solutions.« less
  • Landau`s original derivation of the collisionless damping of small-amplitude Langmuir waves in an infinite homogeneous plasma relied on the introduction of complex velocities and was therefore somewhat difficult to interpret physically. This has inspired many subsequent derivations of Landau damping that involve only real physical quantities throughout. These ``physical`` derivations, however, have required the calculation of quantities to second order in the wave field, whereas Landau`s approach involved only first-order quantities. More recent generalizations of Landau damping to localized fields, often called ``transit-time damping,`` have followed the physical approach, and thus also required second-order calculations, which can be quite lengthy.more » In this paper it is shown that when the equilibrium distribution function depends solely on the energy, invoking the time-reversal invariance of the Vlasov equation allows transit-time damping to be analyzed using only first-order physical quantities. This greatly simplifies the calculation of the damping of localized plasma waves and, in the limit of an infinite plasma, provides a derivation of Landau damping that is both physical and linear in the wave field. This paper investigates the transit-time damping of plasma waves confined in slabs, cylinders, and spheres, analyzing the dependence on size, radius, and mode number, and demonstrating the approach to Landau damping as the systems become large. It is also shown that the same approach can be extended to more general geometries. A companion paper analyzes transit-time damping in a cylinder in more detail, with applications to the problem of stimulated Raman scattering in self-focused light filaments in laser-produced plasmas. {copyright} {ital 1998 American Institute of Physics.}« less
  • The propagation and damping of small-amplitude waves in a plasma of relativistic electrons and/or protons is studied. As in the analogous nonrelativistic problem, the damping is found to be large except for particular angles of propagation. The results are applied, in the ultrarelativistic limit, to the problem of the heating of the high-energy electrons in the Crab Nebula. Some aspects of the morphology of the propagating disturbances near the center of the nebula can be understood in terms of the magnitude and angular dependence of the calculated damping. (auth)