Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide

    Research output: Contribution to journalJournal articleResearch

    Abstract

    The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations. It is further shown that an oscillatory solution of the Korteweg-de Vries equation, which is derived in the small wavenumber region, satisfies the small wavenumber limit of the nonlinear Schrodinger equation
    Original languageEnglish
    JournalPlasma Physics and Controlled Fusion
    Volume20
    Issue number10
    Pages (from-to)997-1010
    ISSN0741-3335
    DOIs
    Publication statusPublished - 1978

    Cite this

    @article{9f984564be144135afc3a180d2e4e7b7,
    title = "Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide",
    abstract = "The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations. It is further shown that an oscillatory solution of the Korteweg-de Vries equation, which is derived in the small wavenumber region, satisfies the small wavenumber limit of the nonlinear Schrodinger equation",
    author = "{Juul Rasmussen}, Jens",
    year = "1978",
    doi = "10.1088/0032-1028/20/10/003",
    language = "English",
    volume = "20",
    pages = "997--1010",
    journal = "Plasma Physics and Controlled Fusion",
    issn = "0741-3335",
    publisher = "IOP Publishing",
    number = "10",

    }

    Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide. / Juul Rasmussen, Jens.

    In: Plasma Physics and Controlled Fusion, Vol. 20, No. 10, 1978, p. 997-1010.

    Research output: Contribution to journalJournal articleResearch

    TY - JOUR

    T1 - Finite Amplitude Electron Plasma Waves in a Cylindrical Waveguide

    AU - Juul Rasmussen, Jens

    PY - 1978

    Y1 - 1978

    N2 - The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations. It is further shown that an oscillatory solution of the Korteweg-de Vries equation, which is derived in the small wavenumber region, satisfies the small wavenumber limit of the nonlinear Schrodinger equation

    AB - The nonlinear behaviour of the electron plasma wave propagating in a cylindrical plasma waveguide immersed in an infinite axial magnetic field is investigated using the Krylov-Bogoliubov-Mitropolsky perturbation method, by means of which is deduced the nonlinear Schrodinger equation governing the long-time slow modulation of the wave amplitude. From this equation the amplitude-dependent frequency and wavenumber shifts are calculated, and it is found that the electron waves with short wavelengths are modulationally unstable with respect to long-wavelength, low-frequency perturbations. It is further shown that an oscillatory solution of the Korteweg-de Vries equation, which is derived in the small wavenumber region, satisfies the small wavenumber limit of the nonlinear Schrodinger equation

    U2 - 10.1088/0032-1028/20/10/003

    DO - 10.1088/0032-1028/20/10/003

    M3 - Journal article

    VL - 20

    SP - 997

    EP - 1010

    JO - Plasma Physics and Controlled Fusion

    JF - Plasma Physics and Controlled Fusion

    SN - 0741-3335

    IS - 10

    ER -