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Locally excited magnethohydrodynamic waves in a uniform cylindrical plasma waveguide

Published online by Cambridge University Press:  13 March 2009

W. N-C. Sy
W. N-C. Sy
Affiliation:
School of Physical Sciences, The Flinders University of South Australia, Bedford Park, S. A. 5042, Australia
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Abstract

The guided modes of Woods' magnetohydrodynamic waveguide for a uniform, cylindrical plasma are shown to satisfy a homogeneous wave equation whose differential operator is the product of eight Helmholtz operators. The propagation constants of the Helmholtz operators are the characteristic roots of an 8 × 8 matrix which is derived and written down explicitly. This reformulated theory is extended to include localized sources which excite the guided modes. For certain cases, the Green's functions for the differential operators can be represented by Dini expansions in terms of modal eigenfunctions, which manifestly satisfy the boundary conditions. For the case of MHD waves excited by an azimuthally symmetric current source in a resistive, pressureless, inviscid, fully ionized plasma, a detailed solution is obtained which is in good qualitative agreement with experiments.

Type
Research Article
Information
Journal of Plasma Physics , Volume 17 , Issue 2 , April 1977 , pp. 281 - 300
Copyright
Copyright © Cambridge University Press 1977

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References

REFERENCES

Bernnan, M. H., Cheetham, A. D. & Jones, I. R. 1974 Phys. Lett. 46A, 437.CrossRefGoogle Scholar
Cheetham, A. D. 1976 Unpublished thesis, Flinders University of South Australia.Google Scholar
Gould, R. W. 1960 Space Technology Laboratories, Inc., Report STL/TR/60–0000–09143.Google Scholar
Lighthill, M. J. 1960 Phil. Trans. Roy. Soc. A 252A, 397.Google Scholar
Morrow, R. M. & Brennan, M. H. 1974 Aust. J. Phys. 27, 181.CrossRefGoogle Scholar
Müller, G. 1974 Plasma Phys. 16, 813.CrossRefGoogle Scholar
Newcomb, W. A. 1957 Magnetohydrodynamics (ed. Landshoff, R.) p. 109. Stanford University Press.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar
Wilcox, J. M., De Silva, A. W. & Cooper, W. S. 1961 Phys. Fluids, 4, 1506.CrossRefGoogle Scholar
Woods, L. C. 1962 J. Fluid Mech. 13, 570.CrossRefGoogle Scholar