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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 4
Nonlin. Processes Geophys., 11, 421–425, 2004
https://doi.org/10.5194/npg-11-421-2004
© Author(s) 2004. 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., 11, 421–425, 2004
https://doi.org/10.5194/npg-11-421-2004
© Author(s) 2004. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  24 Sep 2004

24 Sep 2004

Trans-sonic cusped shaped, periodic waves and solitary waves of the electrostatic ion-cyclotron type

J. F. McKenzie1,2,3 and T. B. Doyle2 J. F. McKenzie and T. B. Doyle
  • 1Max-Planck-Institute for Solarsystems Research, Katlenburg-Lindau, Germany
  • 2School of Physics & School of Mathematical and Statistical Sciences, Univ. of KwaZulu-Natal, Durban, 4041, South Africa
  • 3Department of Physics, University of Alabama at Huntsville, USA

Abstract. By adopting an essentially fluid dynamic viewpoint we derive the wave structure equation for stationary, fully nonlinear, electrostatic, ion-cyclotron waves. The existence of two fundamental constants of the motion, namely, conservation of momentum flux parallel to the ambient magnetic field, and energy flux parallel to the direction of wave propagation, enables the wave structure equation to be reduced to a first order differential equation, which has solutions that are physically transparent. The analysis shows that sufficiently oblique waves, propagating at sub-ion acoustic speeds, form soliton pulse-like solutions whose amplitudes are greatest for perpendicular propagation. Waves that propagate supersonically have periodic cnoidal waveforms, which are asymmetric about the compressive and rarefactive phases of the wave. It is also shown that there exist critical driver fields for which the end point of the compressive phase goes sonic (in the wave frame), with the consequence that the wave form develops a cusp. It is possible that this trans-sonic, choked flow feature provides a mechanism for the "spiky" waveforms observed in auroral electric field measurements.

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