Landau damping and transittime damping of localized plasma waves in general geometries
Abstract
Landau`s original derivation of the collisionless damping of smallamplitude 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 firstorder quantities. More recent generalizations of Landau damping to localized fields, often called ``transittime damping,`` have followed the physical approach, and thus also required secondorder calculations, which can be quite lengthy. In this paper it is shown that when the equilibrium distribution function depends solely on the energy, invoking the timereversal invariance of the Vlasov equation allows transittime damping to be analyzed using only firstorder 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 transittime damping of plasma waves confined in slabs, cylinders, and spheres, analyzing the dependence on size, radius, and mode number, and demonstrating the approachmore »
 Authors:

 Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, New York, 146231299 (United States)
 Publication Date:
 OSTI Identifier:
 300087
 Resource Type:
 Journal Article
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 5; Journal Issue: 12; Other Information: PBD: Dec 1998
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION; BOLTZMANNVLASOV EQUATION; PLASMA WAVES; DAMPING; LANDAU DAMPING; LANGMUIR FREQUENCY; RAMAN EFFECT; FOCUSING; LASERPRODUCED PLASMA
Citation Formats
Short, R W, and Simon, A. Landau damping and transittime damping of localized plasma waves in general geometries. United States: N. p., 1998.
Web. doi:10.1063/1.873146.
Short, R W, & Simon, A. Landau damping and transittime damping of localized plasma waves in general geometries. United States. doi:10.1063/1.873146.
Short, R W, and Simon, A. Tue .
"Landau damping and transittime damping of localized plasma waves in general geometries". United States. doi:10.1063/1.873146.
@article{osti_300087,
title = {Landau damping and transittime damping of localized plasma waves in general geometries},
author = {Short, R W and Simon, A},
abstractNote = {Landau`s original derivation of the collisionless damping of smallamplitude 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 firstorder quantities. More recent generalizations of Landau damping to localized fields, often called ``transittime damping,`` have followed the physical approach, and thus also required secondorder calculations, which can be quite lengthy. In this paper it is shown that when the equilibrium distribution function depends solely on the energy, invoking the timereversal invariance of the Vlasov equation allows transittime damping to be analyzed using only firstorder 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 transittime 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 transittime damping in a cylinder in more detail, with applications to the problem of stimulated Raman scattering in selffocused light filaments in laserproduced plasmas. {copyright} {ital 1998 American Institute of Physics.}},
doi = {10.1063/1.873146},
journal = {Physics of Plasmas},
number = 12,
volume = 5,
place = {United States},
year = {1998},
month = {12}
}