### Abstract

Original language | English |
---|---|

Journal | Plasma Physics and Controlled Fusion |

Volume | 20 |

Issue number | 10 |

Pages (from-to) | 997-1010 |

ISSN | 0741-3335 |

DOIs | |

Publication status | Published - 1978 |

### Cite this

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*Plasma Physics and Controlled Fusion*, vol. 20, no. 10, pp. 997-1010. https://doi.org/10.1088/0032-1028/20/10/003

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

Research output: Contribution to journal › Journal article › Research

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 -