Theory of Vlasov Plasma Oscillation in a Magnetic Field

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  • Watanabe Yoiti
    Institute of Physics College of General Education Osaka University

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  • 磁場中のプラズマ振動と固有値問題
  • ジバ チュウ ノ プラズマ シンドウ ト コユウチ モンダイ
  • Theory of Vlagov Plasma Oscillations in a Magnetic Field

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The eigenvalue theory of plasma oscillations, developed by Case and other authors, is extended for the case, where the waves run obliquely to the direction of external magnetic field. The plasma supposed here is spatially homogeneous, and has a general equilibrium distribution of electron velocity. Many elliptically polarized high harmonic modes overlap in the induced wave of electric field, each of the modes having different characteristic phase velocity. The superposition, unavoidable by the choice of the initial condition, yields anharmonic oscillations. The spectral structure of the characteristic phase velocity is partly identical with the one derived from the dispersion equation of the density waves, but partly, those which being newly introduced, are analogous to the spectrum of atomic energy due to the azimuthal and the magnetic quantum numbers.

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