Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T07:00:03.466Z Has data issue: false hasContentIssue false
  • English
  • Français

Magneto-viscous resistive tearing of cylindrical flux surfaces

Published online by Cambridge University Press:  13 March 2009

R. J. Hosking
R. J. Hosking
Affiliation:
University of Waikato, Hamilton, New Zealand
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of cylindrical flux surfaces in the presence of finite resistivity and parallel ion viscosity is reconsidered, and in particular the increment in the logarithmic derivative Δ(Q) over the inner dissipative region. Correction of the viscosity coefficient removes the branch-point behaviour at large growth rates reported earlier. Numerical results for real Q in the high-beta hard-core pinch are supported by mathematical analysis to show that parallel ion viscosity renders Δ(Q) positive definite provided D < 0, with a positive minimum increasing with temperature. This stabilization is associated with coupling of the parallel plasma motion in the presence of magnetic field curvature. The viscous compressible value of Δ(Q) is somewhat less than its inviscid compressible counterpart at small real Q, so that relative to purely compressible theory parallel ion viscosity can be slightly destabilizing.

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 2 , October 1979 , pp. 329 - 338
Copyright
Copyright © Cambridge University Press 1979

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

Braginskii, S. I. 1965 Reviews of Plasma Physics (ed. Leontovich, M. A.), vol. 1, p. 205. Consultants Bureau.Google Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn.Cambridge University Press.Google Scholar
Coppi, B., Greene, J. M. & Johnson, J. L. 1966 Nucl. Fusion, 6, 101.CrossRefGoogle Scholar
Dagazian, R. Y. & Paris, R. B. 1977 Phys. Fluids, 20, 917.CrossRefGoogle Scholar
Furth, H. P., Killeen, J. & Rosenbluth, M. N. 1963 Phys. Fluids, 6, 459.CrossRefGoogle Scholar
Grad, H. 1949 Communs. Pure Appl. Math. 2, 231.Google Scholar
Grimm, R. C. & Johnson, J. L. 1972 Plasma Phys. 14, 617.Google Scholar
Hellberg, M. A., Winsor, N. K. & Johnson, J. L. 1974 Phys. Fluids, 17, 1528.Google Scholar
Herdan, R. & Liley, B. S. 1960 Rev. Mod. Phys. 32, 731.CrossRefGoogle Scholar
Hosking, R. J. 1967 Phys. Fluids, 10, 1654.CrossRefGoogle Scholar
Hosking, R. J. 1975 J. Plasma Phys. 13, 27.Google Scholar
Hosking, R. J. & Marinoff, G. M. 1973 Plasma Phys. 15, 327.Google Scholar
Liley, B. S. 1972 University of Waikato, Physics Research Report 103.Google Scholar
Mikhaliovskii, A. B. & Tsypin, V. S. 1971 Plasma Phys. 13, 785.CrossRefGoogle Scholar
Marinoff, G. M. 1974 J. Plasma Phys. 11, 253.Google Scholar
Shkarofsky, I. P., Bernstein, I. B. & Robinson, B. B. 1963 Phys. Fluids, 6, 40.Google Scholar
Stringer, T. E. & Connor, J. W. 1971 Phys. Fluids, 14, 2177.CrossRefGoogle Scholar
Suydam, B. R. 1958 Proceedings of Second Geneva Conference on Peaceful Use8 of Atomic Energy, vol. 31, p. 157.Google Scholar
Ware, A. A. 1966 Phys. Fluids 9, 816.CrossRefGoogle Scholar