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Nonlinear fast sausage waves in homogeneous magnetic flux tubes

Published online by Cambridge University Press:  17 December 2015

Badma B. Mikhalyaev  and
Michael S. Ruderman
Badma B. Mikhalyaev
Affiliation:
Department of Theoretical Physics, Kalmyk State University, 11 Pushkin Str., Elista 358000, Russia
Michael S. Ruderman*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK Space Research Institute (IKI), Russian Academy of Sciences, 84/32 Profsoyuznaya Str., Moscow 117997, Russia
*
†Email address for correspondence: m.s.ruderman@sheffield.ac.uk
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Abstract

We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin–Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810611
Copyright
© Cambridge University Press 2015 

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