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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 12, issue 3
Nonlin. Processes Geophys., 12, 407–423, 2005
https://doi.org/10.5194/npg-12-407-2005
© Author(s) 2005. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Nonlinear plasma waves-solitons, periodic waves and...

Nonlin. Processes Geophys., 12, 407–423, 2005
https://doi.org/10.5194/npg-12-407-2005
© Author(s) 2005. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  18 Mar 2005

18 Mar 2005

Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas

I. Kourakis1,2 and P. K. Shukla1 I. Kourakis and P. K. Shukla
  • 1Institut für Theoretische Physik IV, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
  • 2Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse, D-85740 Garching, Germany

Abstract. Abundant evidence for the occurrence of modulated envelope plasma wave packets is provided by recent satellite missions. These excitations are characterized by a slowly varying localized envelope structure, embedding the fast carrier wave, which appears to be the result of strong modulation of the wave amplitude. This modulation may be due to parametric interactions between different modes or, simply, to the nonlinear (self-)interaction of the carrier wave. A generic exact theory is presented in this study, for the nonlinear self-modulation of known electrostatic plasma modes, by employing a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The (moderately) nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrödinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright-(pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness (with respect to the propagation direction), finite temperature and defect (dust) concentration are explicitly considered. Relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.

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