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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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References

REFERENCES

Abramowitz, M. & Stegun, I. 1972 Handbook of Mathematical Functions. Dover.Google Scholar
Defouw, R. J. 1976 Astrophys. J. 209, 266.CrossRefGoogle Scholar
Dungey, J. W. & Loughhead, R. E. 1954 Austr. J. Phys. 7, 5.CrossRefGoogle Scholar
Edwin, P. M. & Roberts, B. 1983 Solar Phys. 88, 179.CrossRefGoogle Scholar
Ershkovich, A. I. & Chernikov, A. A. 1973 Planet. Space Sci. 21, 663.CrossRefGoogle Scholar
Merzljakov, E. G. & Ruderman, M. S. 1985 Solar Phys. 95, 51.CrossRefGoogle Scholar
Merzljakov, E. G. & Ruderman, M. S. 1986 a Solar Phys. 103, 259.CrossRefGoogle Scholar
Merzljakov, E. G. & Ruderman, M. S. 1986 b Solar Phys. 105, 265.CrossRefGoogle Scholar
Molotovshchikov, A. L. & Ruderman, M. S. 1987 Solar Phys. 109, 247.CrossRefGoogle Scholar
Pelinovskii, E. N., Fridman, V. E. & Engelbreht, Yu. K. 1984 Nelineinye evolyucionnye uravneniya. Valgus, Tallinn.Google Scholar
Priest, E. R. 1982 Solar Magnetohydrodynamics. Reidel.CrossRefGoogle Scholar
Prudnikov, A. P., Brychkov, Yu. A. & Marichev, O. I. 1981 Integraly i ryady. Elementarnye funkcii. Nauka.Google Scholar
Roberts, B. 1985 Phys. Fluids 28, 3280.CrossRefGoogle Scholar
Roberts, B., Edwin, P. M. & Benz, A. O. 1984 Astrophys. J. 279, 857.CrossRefGoogle Scholar
Roberts, B. & Mangeney, A. 1982 Mon. Not. R. Astron. Soc. 198, 7P.CrossRefGoogle Scholar
Roberts, B. & Webb, A. R. 1978 Solar Phys. 56, 5.CrossRefGoogle Scholar
Ryutov, D. D. & Ryutova, M. P. 1976 Soviet Phys. JETP 43, 491.Google Scholar
Ryutova, M. P. 1981 Soviet Phys. JETP 53, 529.Google Scholar
Shyouni, W., Zhelyazkov, I. & Nenovski, P. 1988 Solar Phys. 115, 17.CrossRefGoogle Scholar
Spruit, H. C. 1982 Solar Phys. 75, 3.CrossRefGoogle Scholar
Taniuti, T. 1974 Progr. Theor. Phys. Suppl. No. 55, 1.Google Scholar