Theory of the Parametric Oscillation in an Electron Beam-Plasma System

Tomokazu Kato, Takashi Okazaki, Takashi Ohsawa

研究成果: Article

1 引用 (Scopus)

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The density oscillations in a system composed of a one-dimensional cold electron plasma and a cold electron beam are considered where the beam is assumed to be modulated sinusoidally and also to be bounded by a repeller in the plasma. A nonlinear differential equation which describes the density oscillations in the beam-plasma system is derived from the Vlasov and Poisson equations. The equation does not take the so-called van der Pol-type, but is, as one of the linear approximations, reduced to a Mathieu-type equation with an inhomogeneous term: d2ρ⁄dt2e 2[1−σ cos (ωt)]ρ=σ(ω2−ωe 2) cos (ωt). This inhomogeneous Mathieu equation is analyzed by the method of Bogoliubov and Mitropolsky. The spectrum of the characteristic frequency obtained from the analysis is compared with the experimental results.

元の言語English
ページ(範囲)277-284
ページ数8
ジャーナルjournal of the physical society of japan
46
発行部数1
DOI
出版物ステータスPublished - 1979 1 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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