Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T13:57:02.459Z Has data issue: false hasContentIssue false

Quasi-static modes of oscillation of a cold toroidal plasma

Published online by Cambridge University Press:  13 March 2009

John D. Love
Affiliation:
Mathematical Institute, University of Oxford

Abstract

The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Erdélyi, A., Magnus, W., Oberhettinger, P. & Tricomi, F. G. (ed.) 1953 Higher Transcendental Functions. McGraw-Hill.Google Scholar
Hansen, W. S. 1935 Phys. Rev. 47, 139.CrossRefGoogle Scholar
Hansen, W. S. 1936 Physics, 7, 460.CrossRefGoogle Scholar
Hansen, W. S. 1937 J. Appl. Phys. 8, 282.CrossRefGoogle Scholar
Hobson, E. W. 1955 The Theory of Spherical and Ellipsoidal Harmonics. Chelsea.Google Scholar
Moon, P. & Spencer, D. E. 1952 a J. Franklin Inst. 253, 227.CrossRefGoogle Scholar
Moon, P. & Spencer, D. E. 1952 b J. Franklin Inst. 253, 585.CrossRefGoogle Scholar
Talmadge, S., Marshall, T. C. & Schlesinger, S. P. 1973 Phys. Fluids, 16, 1171.CrossRefGoogle Scholar
Weston, V. H. 1960 J. Math. Phys. 8, 282.Google Scholar