Advertisement

Landau Damping an Initial-Value Problem

  • W. D. Jones
  • H. J. Doucet
  • J. M. Buzzi

Abstract

As we have seen in the preceding five chapters, many wave phenomena in plasmas can be studied using only the fluid-theory model in which the plasma is considered as two or more interpenetrating fluids (one for the electrons and one for each ion species). The main disadvantage of this model, as has been pointed out several times, is that only the velocity average of each plasma specie can be taken into account, so that any velocity-dependent effects, such as the Landau damping to be discussed in this chapter, are not predicted by the theory. From a mathematical point of view, the main advantage of the model is that it is a much simpler model than the kinetic-theory model to be used in the present and remaining chapters of the book. Because of this relative simplicity, unless velocity-dependent phenomena are of specific interest, the fluid-theory model is always used. For non-velocity-dependent effects, the fluid-theory model and the kinetic-theory model give identical results. As we employ the kinetic theory in the remaining chapters of the book, we shall see that not only are velocity-dependent effects predicted, but that we will recover many of the fluid-theory wave phenomena already found.

Keywords

Dispersion Relation Real Axis Initial Perturbation Density Perturbation Cold Plasma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York (1965); Tenth Edition (1972).Google Scholar
  2. B. D. Fried and S. D. Conte, The Plasma Dispersion Function, Academic, New York (1961).Google Scholar
  3. B. D. Fried and R. W. Gould, Longitudinal Ion Oscillations in a Hot Plasma, Phys. Fluids 4, 139 (1961).MathSciNetADSCrossRefGoogle Scholar
  4. R. W. Motley, Q Machines, Academic, New York (1975).Google Scholar
  5. D. R. Nicholson, Introduction to Plasma Theory, Wiley, New York (1983).Google Scholar
  6. B. W. Roos, Analytic Functions and Distributions in Physics and Engineering, Wiley, New York (1969).Google Scholar
  7. G. M. Sessler and G. Pearson, Propagation of ion waves in weakly ionized gases, Phys. Rev. 162, 108 (1967).ADSCrossRefGoogle Scholar
  8. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge (1902); Fourth Edition (1965).MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • W. D. Jones
    • 1
  • H. J. Doucet
    • 2
  • J. M. Buzzi
    • 2
  1. 1.Physics DepartmentUniversity of South FloridaTampaUSA
  2. 2.Laboratorie de Physique des Milieux IonisésEcole PolytechniquePalaiseauFrance

Personalised recommendations