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Long, nonlinear, non-axisymmetric surface-wave propagation in a magnetic tube

Published online by Cambridge University Press:  13 March 2009

M. S. Ruderman
M. S. Ruderman
Affiliation:
Institute for Problems in Mechanics, Academy of Sciences, 101 Vernadski Avenue, 117526 Moscow, U.S.S.R.
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Abstract

The propagation of long, nonlinear, non-axisymmetric surface waves in a magnetic cylinder is considered. It is supposed that the electrical conductivity is infinite, the fluid is incompressible and there is no magnetic field outside the cylinder. The nonlinear integro-differential equation governing the wave propagation is derived using the reductive perturbation method. The interesting and important point is that this equation governs the evolution of all nonaxisymmetric modes simultaneously. This is because the phase velocities of all non-axisymmetric modes are equal to the kink speed in the linear, infinitely long-wavelength approximation, and as a result all non-axisymmetric modes interact strongly in the nonlinear case. Solutions of the governing equation in the form of periodic helical waves of permanent form are obtained numerically.

Type
Research Article
Information
Journal of Plasma Physics , Volume 47 , Issue 2 , April 1992 , pp. 175 - 191
Copyright
Copyright © Cambridge University Press 1992

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