Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T04:48:51.200Z Has data issue: false hasContentIssue false
  • English
  • Français

Cylindrically symmetric waves in the magnetohydrodynamic approximation

Published online by Cambridge University Press:  13 March 2009

M. L. Woolley
M. L. Woolley
Affiliation:
96 Highdown Road, Hove BN3 6EA, Sussex, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The equations of motion of an ideally conducting medium, in the magnetohydrodynamic approximation, are solved exactly under the hypotheses that (i) one component of the magnetic field is constant everywhere, (ii) the magnetic and hydrodynamic pressures are in equilibrium, and (iii) the solution is invariant under a continuous group of transformations which preserves the symmetry of the uniform magnetic field. It is seen that the invariants of the group of transformations form the basis for a parametric description of the full solution that describes the propagation of cylindrically symmetric magneto-sonic waves in the direction of the uniform field. A number of general features of the motion are deduced, and an integral expression is given for the amplitude of the component of velocity, perpendicular to the uniform magnetic field, which undergoes potential well oscillations.

Type
Research Article
Information
Journal of Plasma Physics , Volume 8 , Issue 3 , December 1972 , pp. 331 - 340
Copyright
Copyright © Cambridge University Press 1972

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

Budden, K. G. 1961 Radio Waves in the Ionosphere. Cambridge University Press.Google Scholar
Campbell, J. E. 1966 Introductory Treatise on Lie's Theory of Continuous Transformation Groups. Bronx, N.Y.: Chelsea.Google Scholar
Ginzburgh, V. L. 1964 Propagation of Electromagnetic Waves in Plasmas. Pergamon.Google Scholar
Laird, M. J. 1968 J. Plasma Phys. 2, 59.Google Scholar
Lee, J. C. 1969 Institute for Plasma Research, Stanford University, Tech. Rep. 318.Google Scholar
Kondratenko, A. N. 1966 Soviet Phys. Tech. Phys. 11, 590.Google Scholar
Roberts, C. S. & Buchsbaum, S. J. 1964 Phys. Rev. A 135, 381.Google Scholar
Van, Kampen N. G. & Felderhof, B. V. 1967 Theoretical Methods in Plasma Physics. North Holland.Google Scholar
Woolley, M. L. 1970 Plasma Phys. 12, 779.CrossRefGoogle Scholar
Woolley, M. L. 1973 Plasma Phys. 15, 89.CrossRefGoogle Scholar