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Physics of Plasmas / Volume 19 / Issue 1 / ARTICLES / Basic Plasma Phenomena, Waves, Instabilities
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Phys. Plasmas 19, 012102 (2012); http://dx.doi.org/10.1063/1.3654030 (9 pages)

Adiabatic nonlinear waves with trapped particles. I. General formalism

I. Y. Dodin and N. J. Fisch

Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA

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(Received 15 July 2011; accepted 28 September 2011; published online 6 January 2012)

A Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic time-averaged Lagrangian density math is expressed in terms of the single-particle oscillation-center Hamiltonians; once those are found, the complete set of geometrical-optics equations is derived without referring to the Maxwell-Vlasov system. The number of trapped particles is assumed fixed; in particular, those may reside close to the bottom of the wave trapping potential, so they never become untrapped. Then their contributions to the wave momentum and the energy flux depend mainly on the trapped-particle density, as an independent parameter, and the phase velocity rather than on the wave amplitude a explicitly; hence, math acquires a-independent terms. Also, the wave action is generally not conserved, because it can be exchanged with resonant oscillations of the trapped-particle density. The corresponding modification of the wave envelope equation is found explicitly and the new action flow velocity is derived. Applications of these results are left to the other two papers of the series, where specific problems are addressed pertaining to properties and dynamics of waves with trapped particles.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. WAVE LAGRANGIAN
    1. Plasma Lagrangian
    2. Routhian
    3. Locally averaged densities
    4. Independent variables
  3. ONE-DIMENSIONAL WAVES WITH TRAPPED PARTICLES
    1. Extended Lagrangian
    2. Action conservation and wave dispersion
  4. LONGITUDINAL WAVES
    1. Single-particle OC Hamiltonians
    2. Parametrization. Wave Lagrangian
    3. Action density
    4. Action flow
  5. DISCUSSION
  6. SUMMARY

EDITORIALLY RELATED

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KEYWORDS and PACS

Keywords

geometrical optics, plasma density, plasma flow, plasma nonlinear waves, plasma oscillations

PACS

  • 52.35.Mw

    Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

  • 52.25.-b

    Plasma properties

  • 52.30.-q

    Plasma dynamics and flow

  • 52.35.Fp

    Electrostatic waves and oscillations (e.g., ion-acoustic waves)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3654030

PUBLICATION DATA

ISSN

1070-664X (print)  
1089-7674 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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