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Collisions of acoustic solitons and their electric fields in plasmas at critical compositions

Published online by Cambridge University Press:  17 January 2019

Frank Verheest Open the ORCID record for Frank Verheest [Opens in a new window]  and
Willy A. Hereman Open the ORCID record for Willy A. Hereman [Opens in a new window]
Frank Verheest*
Affiliation:
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B–9000 Gent, Belgium School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000, South Africa
Willy A. Hereman
Affiliation:
Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401-1887, USA
*
†Email address for correspondence: [email protected]
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Abstract

Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg–de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes. Extending the analytic treatment then leads to a modified KdV (mKdV) equation, which is characterized by a cubic nonlinearity and is even in the electrostatic potential. The mKdV equation admits solitons having opposite electrostatic polarities, in contrast to KdV solitons which can only be of one polarity at a time. A Hirota formalism has been used to derive the two-soliton solution. That solution covers not only the interaction of same-polarity solitons but also the collision of compressive and rarefactive solitons. For the visualization of the solutions, the focus is on the details of the interaction region. A novel and detailed discussion is included of typical electric field signatures that are often observed in ionospheric and magnetospheric plasmas. It is argued that these signatures can be attributed to solitons and their interactions. As such, they have received little attention.

Keywords

plasma nonlinear phenomenaplasma wavesspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 1 , February 2019 , 905850106
Copyright
© Cambridge University Press 2019 

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