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Relaxed states in a spheromak with inhomogeneous boundary fields

Published online by Cambridge University Press:  13 March 2009

A. M. Dixon ,
P. K. Browning ,
M. K. Bevir ,
C. G. Gimblett  and
E. R. Priest
A. M. Dixon
Affiliation:
Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
P. K. Browning
Affiliation:
Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
M. K. Bevir
Affiliation:
Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
C. G. Gimblett
Affiliation:
Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
E. R. Priest
Affiliation:
Department of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland
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Abstract

In this paper we consider force-free equilibrium solutions of the MHD equations in a spherical geometry for the case in which magnetic flux crosses the boundary of the containing vessel. The main motivation is to model more faithfully actual spheromak experiments in the laboratory, for which boundaries are unlikely to be magnetic surfaces. We show how a general inhomogeneous boundary field may be constructed from individual components. In particular, we consider the cases of a boundary field of dipolar form and one of quadrupolar form. We then go on to discuss solutions for fields embedded in point or ring electrodes using the ‘general solution’, some of which can be used to model experiments such as the PS-1- or CTX-type spheromaks.

Type
Research Article
Information
Journal of Plasma Physics , Volume 43 , Issue 3 , June 1990 , pp. 357 - 383
Copyright
Copyright © Cambridge University Press 1990

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References

REFERENCES

Berger, M. A. & Field, G. B. 1984 J. Fluid Mech. 147, 133.CrossRefGoogle Scholar
Browning, P. K. 1988 Plasma Phys. 30, 1.Google Scholar
Browning, P. K., Cunningham, G. C. & Rusbridge, M. C. 1987 Proceedings of Varenna Summer School (ed. S. Ortolani & E. Sindoni) Commission of European Communities (EUR 11335 EN), p. 559.Google Scholar
Chandrasekhar, S. & Kendall, P. C. 1957 Astrophys. J. 126, 457.CrossRefGoogle Scholar
Chin-Fatt, C., De Silva, A. W., Goldenbaum, G. C., Hess, R., Shaw, R., Filuk, A. & Singam, K. 1987 Proceedings of 8th U.S. Compact Torus Symposium, Maryland (ed. A. W. De Silva & G. C. Goldenbaum), p. 31.Google Scholar
Dixon, A. M., Browning, P. K. & Priest, E. R. 1989 Astron. Astrophys. 225, 156–166.Google Scholar
Goldenbaum, G. C., Irby, J. H., Chong, Y. P. & Hart, G. W. 1980 Phys. Rev. Lett. 44, 393.CrossRefGoogle Scholar
Hammer, J. H. 1984 Magnetic Reconnection in Space and Laboratory Plasmas (ed. Hones, E. W.), p. 319. American Geophysical Union.CrossRefGoogle Scholar
Hart, G. W., Janos, A., Meyerhofer, D. D. & Yamada, M. 1986 Phys. Fluids, 29, 1994.CrossRefGoogle Scholar
Janos, A., Hart, G. W., Nam, C. H. & Yamada, M. 1985 Phys. Fluids, 28, 3667.CrossRefGoogle Scholar
Jarboe, T. R., Barnes, C. W., Henins, I., Hoida, H. W., Knox, S. O., Linford, R. K. & Sherwood, A. R. 1984 Phys. Fluids, 27, 13.CrossRefGoogle Scholar
Jarboe, T. R., Henins, I., Sherwood, A. R., Barnes, C. W. & Hoida, H. W. 1983 Phys. Rev. Lett. 51, 39.CrossRefGoogle Scholar
Jensen, T. H. & Chu, M. S. 1984 Phys. Fluids, 27, 281.CrossRefGoogle Scholar
Knox, S. O., Barnes, C. W., Marklin, G. J., Jarboe, T. R., Henins, I., Hoida, H. W. & Wright, B. L. 1986 Phys. Rev. Lett. 56, 842.CrossRefGoogle Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Ono, Y., Chu, T. K., Janos, A. C., Levinton, F. M., Ueda, Y. & Yamada, M. 1987 Proceedings of 8th U.S. Compact Torus Symposium, Maryland (ed. A. W. De Silva & G. C. Goldenbaum), p. 85.Google Scholar
Priest, E. R. 1982 Solar Magnetohydrodynamics (Reidei).CrossRefGoogle Scholar
Reiman, A. 1981 Phys. Fluids, 24, 596.Google Scholar
Rosenbluth, M. N. & Bussac, M. N. 1979 Nucl. Fusion, 19, 489.CrossRefGoogle Scholar
Taylor, J. B. 1974 Phys. Rev. Lett. 33, 1139.CrossRefGoogle Scholar
Taylor, J. B. 1986 Rev. Mod. Phys. 58, 741.CrossRefGoogle Scholar
Turner, L. 1984 Phys. Fluids, 27, 1677.CrossRefGoogle Scholar
Turner, W. C., Goldenbaum, G. C., Granneman, E. H. A., Hammer, J. H., Hartman, C. W., Prono, D. S. & Taska, T. 1983 Phys. Fluids, 26, 1965.CrossRefGoogle Scholar
Yamada, M., Furth, H. P., Hsu, W., Janos, A., Jardin, S. C., Okabayashi, M., Sinnis, J., Stix, T. H. & Yamakazi, K. 1981 Phys. Rev. Lett. 46, 188.CrossRefGoogle Scholar