Single-mode saturation of a linearly unstable plasma

C. Burnap, M. Miklavčič, B. L. Willis, P. F. Zweifel

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth [Phys. Fluids 19, 1567 (1976)]. It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of "secular regularization" is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the "eigenmode dominance" approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.

Original languageEnglish (US)
Pages (from-to)110-115
Number of pages6
JournalPhysics of Fluids
Volume28
Issue number1
DOIs
StatePublished - Jan 1 1985

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saturation
Plasmas
oscillations
vlasov equations
subsidiaries
energy conservation
Vlasov equation
electron plasma
Perturbation techniques
boxes
conservation
continuums
momentum
perturbation
Conservation
Momentum
fluids
approximation
Fluids
Electrons

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Single-mode saturation of a linearly unstable plasma. / Burnap, C.; Miklavčič, M.; Willis, B. L.; Zweifel, P. F.

In: Physics of Fluids, Vol. 28, No. 1, 01.01.1985, p. 110-115.

Research output: Contribution to journalArticle

Burnap, C, Miklavčič, M, Willis, BL & Zweifel, PF 1985, 'Single-mode saturation of a linearly unstable plasma', Physics of Fluids, vol. 28, no. 1, pp. 110-115. https://doi.org/10.1063/1.865190
Burnap, C. ; Miklavčič, M. ; Willis, B. L. ; Zweifel, P. F. / Single-mode saturation of a linearly unstable plasma. In: Physics of Fluids. 1985 ; Vol. 28, No. 1. pp. 110-115.
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