Connection between elementary collective coordinates and the vlasov equation

Jerome Percus, George J. Yevick

Research output: Contribution to journalArticle

Abstract

A naive collective coordinate analysis leads to no damping of the acoustic modes of a classical fluid. A similar analysis of the linearized Vlasov equation leads to the well-known phenomenon of Landau damping. The qualitative form of Landau damping is, however, inaccurate for nonsingular forces and probably for low-k propagation in plasmas. Comparison of the two approaches shows that retention of the velocity variable in the Vlasov equation allows for an accurate description of positional fluctuations due to velocity dispersion by itself, but a poor assessment of collective forces. If, instead, the phase mixing of collective modes due to velocity dispersion is taken into account, a damping mechanism is introduced with the anticipated hydrodynamic form in fluids at low k, and with a k4 dependence for plasmas.

Original languageEnglish (US)
Pages (from-to)1526-1532
Number of pages7
JournalPhysical Review A
Volume2
Issue number4
DOIs
StatePublished - 1970

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vlasov equations
Landau damping
damping
fluids
hydrodynamics
propagation
acoustics

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Connection between elementary collective coordinates and the vlasov equation. / Percus, Jerome; Yevick, George J.

In: Physical Review A, Vol. 2, No. 4, 1970, p. 1526-1532.

Research output: Contribution to journalArticle

Percus, Jerome ; Yevick, George J. / Connection between elementary collective coordinates and the vlasov equation. In: Physical Review A. 1970 ; Vol. 2, No. 4. pp. 1526-1532.
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