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Critical densities for Korteweg–de Vries-like acoustic solitons in multi-ion plasmas

Published online by Cambridge University Press:  20 November 2015

Frank Verheest
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
*
†Email address for correspondence: frank.verheest@ugent.be
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Abstract

A generic proof has been given that, for the acoustic mode with the highest velocity in a plasma comprising a number of fluid species and one kind of inertialess electrons, even though there can be critical densities (making the coefficient of the quadratic nonlinearity in a Korteweg–de Vries equation vanish), no supercritical densities exist (requiring the simultaneous annulment of both the quadratic and cubic nonlinearities in a reductive perturbation treatment). Similar conclusions hold upon expansion of the corresponding Sagdeev pseudopotential treatment. When there is only one (hot) electron species, the highest-velocity mode is an ion-acoustic one, but if there is an additional cool electron species, with its inertia taken into account, the highest-velocity mode is an electron-acoustic mode in a two-temperature plasma. The cool fluid species can have various polytropic pressure–density relations, including adiabatic and/or isothermal variations, whereas the hot inertialess electrons are modelled by extensions of the usual Boltzmann description that include non-thermal effects through Cairns, kappa or Tsallis distributions. Together, in this way quite a number of plasma models are covered. Unfortunately, there seems to be no equivalent generic statement for the slow modes, so that these have to be studied on a case-by-case basis, which for models with more than three species is far from straightforward, given the parameter ranges to be discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810605
Copyright
© Cambridge University Press 2015 

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