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The dispersion and attenuation of helicon waves in a uniform cylindrical plasma

Published online by Cambridge University Press:  28 March 2006

J. P. Klozenberg ,
B. McNamara  and
P. C. Thonemann
J. P. Klozenberg
Affiliation:
Culham Laboratory, Culham, Abingdon, Berkshire
B. McNamara
Affiliation:
Culham Laboratory, Culham, Abingdon, Berkshire
P. C. Thonemann
Affiliation:
Culham Laboratory, Culham, Abingdon, Berkshire
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Abstract

A systematic account is given of the derivation of the dispersion relation for helicon waves in a uniform cylindrical plasma bounded by a vacuum. By retaining finite resistivity in the equations, boundary conditions present no difficulties, since the wave magnetic field is continuous through the plasma-vacuum interface. Two unexpected results are found. First, the wave attenuation remains finite in the limit of vanishing resistivity. This is due to the energy dissipated at the interface by the surface currents required to match the plasma wave field to the vacuum wave field. Zero wave attenuation for zero resistivity is recovered if electron inertia is included. Secondly, it is found that waves with azimuthal numbers m of opposite sign propagate differently, but the sense of polarization at the axis of the cylinder is independent of the sign of m.

The argument of the dispersion function is complex and numerical results were obtained using a computer. The method of programming is described, and results are given applicable to propagation in metals at low temperatures, or in a typical gas discharge plasma for the m = 0 and m = ± 1 modes.

An example of the amplitude of the wave fields as a function of radius is given for the axisymmetric mode, and of amplitude and phase for the m = ± 1 modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 3 , March 1965 , pp. 545 - 563
Copyright
© 1965 Cambridge University Press

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References

Aigrain, P. 1960 Proc. of International conf. on Semiconductor Physics, Prague, p. 224.
Barkhausen, H. 1919 Physik. Z. 20, 401.
Bernstein, I. B. & Trehan, S. K. 1960 Nuclear Fusion, 1, 3.
Bowers, R., Legendy, C. & Rose, F. E. 1961 Phys. Rev. Lett. 7, 339.
Budden, K. G. 1961 Radio Waves in the Ionosphere. Cambridge University Press.
Chambers, R. G. & Jones, B. K. 1962 Proc. Roy. Soc. A, 270, 417.
Cotti, P., Wyder, P. & Quattropani, A. 1962 Phys. Lett. 1, 50.
Eckersley, T. L. 1935 Nature, Lond., 135, 104.
Formato, P. & Gilardini, A. 1962 J. Res. Nat. Bureau of Standards, 66 D, 543.
McNamara, B. 1964 Gulham Report (to be published).
Ratcliffe, J. A. 1959 The Magneto-Ionic Theory. Cambridge University Press.
Rose, F. E., Taylor, M. T. & Bowers, R. 1962 Phys. Rev. 127, 1122.
Spitzer, L. 1962 Physics of Fully Ionised Gases, 2nd edition. New York: Interscience.
Stix, T. H. 1962 The Theory of Plasma Waves. New York: McGraw-Hill.
Storey, L. R. O. 1953 Phil. Trans. A, 246, 113.
Stratton, J. A. 1941 Electromagnetic Theory, p. 190. New York: McGraw-Hill.
Woods, L. C. 1962 J. Fluid Mech. 13, 570.
Woods, L. C. 1964 J. Fluid Mech. 18, 401.