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Nonlinear interactions of two compressional hydromagnetic waves

Published online by Cambridge University Press:  13 March 2009

B. Ghosh and
K. P. Das
B. Ghosh
Affiliation:
Department of Physics, R. K. Mission Vidyamandir, Belur Math, Howrah-711202, India
K. P. Das
Affiliation:
Department of Applied Mathematics, Calcutta University, 92, Acharya Prafulla Chandra Road, Calcutta-700009, India
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Abstract

Nonlinear interactions of two azimuthally symmetric compressional hydromagnetic waves propagating in a cylindrical waveguide filled with cold magnetized plasma are investigated. Two cases are considered: the nonlinear interaction of two identical oppositely propagating compressional waves and the nonlinear interaction of two compressional waves propagating with equal group velocities. In the first case the second-order perturbation fields generated through self- and mutual interactions of the waves are calculated and their effect on the otherwise-formed simple linear standing-wave pattern is studied. The possibility of observing a resonant nonlinear interaction is shown. In the second case, in order to describe the nonlinear evolution of the wave amplitudes, two coupled nonlinear Schrödinger (NLS) equations are presented. When excited individually, both the waves are seen to be modulationally stable; but when excited simultaneously, a strong nonlinear wave-wave coupling comes into play, which makes the waves modulationally unstable. The corresponding growth rate of the instability is also calculated.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 2 , April 1988, pp. 215 - 228
Copyright
Copyright © Cambridge University Press 1988

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1970 Handbook of Mathematical Functions. Dover.Google Scholar
Amagishi, Y., Trushima, A. & Inutake, M. 1982 Phys. Rev. Lett. 48, 1183.CrossRefGoogle Scholar
Cramer, N. F. & Sy, W. N.-C. 1979 J. Plasma Phys. 22, 549.CrossRefGoogle Scholar
Das, K. P. 1971 Phys. Fluids, 14, 2235.CrossRefGoogle Scholar
Das, K. P. & Sihi, S. 1979 J. Plasma Phys. 21, 183.CrossRefGoogle Scholar
Davey, A. & Stewartson, K. 1974 Proc. Roy. Soc. A 388, 101.Google Scholar
Fisch, N. J. & Karney, C. F. F. 1981 Phys. Fluids, 24, 27.CrossRefGoogle Scholar
Ghosh, B. & Das, K. P. 1986 J. Plasma Phys. 36, 135.CrossRefGoogle Scholar
Hasegawa, A. & Chen, L. 1976 Phys. Fluids, 19, 1924.CrossRefGoogle Scholar
Hooke, W. M. & Hosea, J. C. 1972 Proceedings of the Fifth European Conference on Controlled Fusion and Plasma Physics, Grenoble, France, (Service d'Ionique Generale, Association EURATOM-commissariat a l'Energie Atomique, Centre d'Etudes Nucleaires de Grenoble, Grenoble, France, 1972), p. 107.Google Scholar
Hosea, J. C. & Hooke, W. M. 1973 Phys. Rev. Lett. 31, 150.CrossRefGoogle Scholar
Hosea, J., Bernabei, S., Colestock, P., Davis, S. L., Efthimion, P., Goldston, R. J., Hwang, D., Medley, S. S., Mueller, D., Strachan, S. K. & Thompson, H. 1979 Phys. Rev. Lett. 43, 1802.CrossRefGoogle Scholar
Inoue, Y. 1977 J. Phys. Soc. Jpn, 43, 243.CrossRefGoogle Scholar
Ivanov, N. V. & Kovan, I. A. 1975 Nucl. Fusion, 13, 653.Google Scholar
Jacquinot, J., McVey, B. D. & Scharer, J. E. 1977 Phys. Rev. Lett. 39, 88.CrossRefGoogle Scholar
Jones, I. R. & Cheetham, A. D. 1977 J. Plasma Phys. 17, 433.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1976 Proc. Roy. Soc. A 347, 311.Google Scholar
Okazaki, T., Maki, K., Kobayashi, T., Sugihara, M. & Fujisawa, N. 1984 Nucl. Fusion, 24, 1451.CrossRefGoogle Scholar
Perkins, F. 1977 Nucl. Fusion, 17, 1197.CrossRefGoogle Scholar
Rutherford, P. 1980 Nucl. Fusion, 20, 1086.CrossRefGoogle Scholar
Sluijter, F. W. & Montgomery, D. 1965 Phys. Fluids, 8, 551.CrossRefGoogle Scholar
Sneddon, I. N. 1951 Fourier Transforms. McGraw-Hill.Google Scholar
Spitzer, L. 1962 Physics of Fully Ionized Gases. Wiley.Google Scholar
Stix, T. H. 1957 Phys. Rev. 106, 1146.CrossRefGoogle Scholar
Stix, T. H. 1975 Nucl. Fusion, 15, 737.CrossRefGoogle Scholar
Swanson, D. G. 1976 Phys. Rev. Lett. 36, 316.CrossRefGoogle Scholar
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar
Woods, L. C. 1962 J. Fluid Mech. 13, 570.CrossRefGoogle Scholar
Woods, L. C. 1964 Phys. Fluids, 7, 1987.CrossRefGoogle Scholar