Nonlinear travelling waves in a homogeneous cold collisionless plasma

Decoster, A.

doi:10.1016/0370-1573(78)90129-1

Cited by 52 publications

(21 citation statements)

References 38 publications

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“…These first integrals have been obtained before in various guises (Decoster, 1978;Dubinin et al, 2003;Mace et al, 2007).…”

Section: Nonlinear Modes and First Integralsmentioning

confidence: 70%

“…Such a solitary wave Ansatz excludes the consideration of periodic nonlinear waves with constant amplitudes, which do not vanish for the undisturbed conditions at x=−∞. This applies in particular to the large amplitude circularly polarized transverse modes at parallel propagation, discussed by many authors and reviewed by Decoster (1978).…”

Section: Nonlinear Modes and First Integralsmentioning

confidence: 99%

“…The discussion is typical for the Sagdeev pseudopotential analysis and runs along lines found in many plasma wave treatments, as discussed specifically for pair plasmas by Decoster (1978).…”

Section: Appendix B Elements Of the Pair Plasmas Treatmentmentioning

confidence: 99%

“…Thus there was no simple reduction to one single differential equation for one of the field variables, except in rather special cases, as reviewed by Decoster (1978) with particular emphasis on parallel and perpendicular propagation with respect to the ambient magnetic field. 50 F. Verheest: Oblique large solitary waves in charge neutral plasmas Recently, McKenzie and coworkers (McKenzie and Doyle, 2001;Sauer et al, 2001;Dubinin et al, 2002;McKenzie et al, 2004) have revived interest in these approaches, by focussing on the fluid dynamic interpretation of how various first integrals limit the available parameter space, rather than relying on numerical work to find these limitations, as had mostly been the case before.…”

Section: Introductionmentioning

confidence: 99%

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Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Verheest

2007

Nonlin. Processes Geophys.

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Abstract. This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons) cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not) of the phase, since the amplitude or envelope graphs look very similar.

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“…These first integrals have been obtained before in various guises (Decoster, 1978;Dubinin et al, 2003;Mace et al, 2007).…”

Section: Nonlinear Modes and First Integralsmentioning

confidence: 70%

Section: Nonlinear Modes and First Integralsmentioning

confidence: 99%

Section: Appendix B Elements Of the Pair Plasmas Treatmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Verheest

2007

Nonlin. Processes Geophys.

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“…and Clemmow [4], Kennal and Pellat [5], Shih [6], Decoster [7], Lee and Lerche [8][9][10][11], Clemmow and Harding [12] halve used the special Lorentz transformation to study nonlinear problems in plasma dynamics. On the other hand, Akhiezer and Polovin [13], Wong [14], Wong and Lojko [15] (…”

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confidence: 99%

Study of nonlinear wave processes in plasmas using the formalism of a special Lorntz transformation for a space‐independent fram

Paul

Chakraborty

Debnath

1984

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. A study is made of pot;linear waves in plasmas using the formalism of a special Lorentz transformation for a space-independent frame, S'. This special transformation is used to transform the space-time dependent equations in a cold, relativistic, magnetized plasma to the S' frame. Then the transformed equations are employed to derive the expressions for the Lagrangian and the Hamiltonian in the S' frame. The Lagrengian and the llamiltonian for a strong circularly polarized laser beam have also been obtained in the S' frame. The exact form of the nonlinear dispersion 'elation is derived for circularly polarized waves. Then the results for the frequency and the wave number shifts of these waves in a cold, magnetized relativistic plasma are obtained with some Discussion

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Relativistic Electromagnetic Waves in an Electron-Ion Plasma

Chian

Kennel

1984

Laser Interaction and Related Plasma Phenomena

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High power laser beams can drive plasma particles to relativistic energies. An accurate description of strong waves requires the inclusion of ion dynamics in the anal y sis. The e q uations governing the propagation cf relativistic alectroiagnetic waves in a cold electron-ion plasma can be reduced to two equations expressing conservation of energy-momentum of the system. The two conservtion constants are functions of the plasma stream velocity, the wave velocity, the wave amplitude and the electrbn-ion mass ratio. The'--dynamic parameter, expressing electron-ion momentum conservation in the laboratory frame, can.be regarded as an adjustable quantity, a suitable c1-oic-e , of which will yield self-consistent solutior.s when other plasma parameters have been specified. Circularly pQlarized.. electromagnetic waves and electrostatic plasma waves are used as illustrations.

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Nonlinear travelling waves in a homogeneous cold collisionless plasma

Cited by 52 publications

References 38 publications

Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Study of nonlinear wave processes in plasmas using the formalism of a special Lorntz transformation for a space‐independent fram

Relativistic Electromagnetic Waves in an Electron-Ion Plasma

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