Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T15:25:17.913Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical solutions for the current driven by a rotating magnetic field in a spherical plasma

Published online by Cambridge University Press:  13 March 2009

Peter A. Watterson
Peter A. Watterson
Affiliation:
School of Physical Sciences, The Flinders University of South Australia, Bedford Park, South Australia 5042, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

The steady currents driven in a spherical plasma by a rotating magnetic field via the Hall effect are studied analytically. The total field is shown to be symmetric across the origin. Integral relationships are obtained between Ohmic dissipation, angular momentum and the oscillating axial current density. The topology of the sum of a Hill's vortex field and a rotating field is documented. Analytical solutions for the driven current are obtained by expansion for the limits corresponding to small rotation frequency, to small number density, to large rotating-field magnitude, to small resistivity, and to small rotating-field magnitude combined with very small resistivity. The latter solution, relevant to the reactor limit, indicates that, with control of the vertical field magnitude, an MHD equilibrium can be generated with total current any fraction of the currentcorresponding to synchronous rotation of the electrons. Oscillating currents sufficient to drive the synchronous current are determined.

Type
Research Article
Information
Journal of Plasma Physics , Volume 46 , Issue 2 , October 1991 , pp. 271 - 298
Copyright
Copyright © Cambridge University Press 1991

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

Bateman, G. 1978 MHD Instabilities. MIT Press.Google Scholar
Bellan, P. M. 1989 Phys. Rev. Lett. 62, 2464.CrossRefGoogle Scholar
Bertram, W. K. 1987 J. Plasma Phys. 37, 423.CrossRefGoogle Scholar
Brotherton-Ratcliffe, D. & Storer, R. G. 1988 Plasma Phys. Contr. Fusion 30, 967.CrossRefGoogle Scholar
Dungey, J. W. 1961 Nucl. Fusion 1, 312.CrossRefGoogle Scholar
Durance, G., Hogg, G. R., Tendys, J. & Watterson, P. A. 1987 Plasma Phys. Contr. Fusion 29, 227.CrossRefGoogle Scholar
Durance, G. & Jones, I. R. 1986 Phys. Fluids 29, 1196.CrossRefGoogle Scholar
Greene, J. M. 1988 J. Geophys. Res. A 93, 8583.CrossRefGoogle Scholar
Hill, M. J. M. 1894 Phil. Trans. R. Soc. Lond. A 185, 213.Google Scholar
Hugrass, W. N. 1985 Aust. J. Phys. 38, 157.CrossRefGoogle Scholar
Hugrass, W. N., Jones, I. R., McKenna, K. F., Phillips, M. G. R., Storer, R. G. & Tuczek, H. 1980 Phys. Rev. Lett. 44, 1676.CrossRefGoogle Scholar
Hugrass, W. N. & Kirolous, H. A. 1984 Aust. J. Phys. 37, 521.CrossRefGoogle Scholar
Johnson, J. L., Dalhed, H. E., Greene, J. M., Grimm, R. C.Hsieh, Y. Y., Jardin, S. C., Manickam, J., Okabayashi, M., Storer, R. G., Todd, M. M., Voss, D. E. & Weimer, K. E. 1979 J. Comp. Phys. 32, 212.CrossRefGoogle Scholar
Jones, I. R., Turley, M. R. E., Wedding, J. E., Durance, G., Hogg, G. R. & Tbndys, J. 1987 Aust. J. Phys. 44, 157.CrossRefGoogle Scholar
Klima, R. 1974 Czech. J. Phys. B 24, 846.CrossRefGoogle Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Percival, I. & Richards, D. 1982 Introduction to Dynamics.Cambridge University Press.Google Scholar
Solov'ev, L. S. 1968 Soviet Phys. JETP 26, 864.Google Scholar
Storer, R. G. 1982 Plasma Phys. 24, 543.CrossRefGoogle Scholar
Taylor, J. B. 1963 Proc. R. Soc. Lond. A 274, 274.Google Scholar
Watterson, P. A. 1988 J. Plasma Phys. 40, 109.CrossRefGoogle Scholar
Watterson, P. A. 1991 J. Plasma Phys. 46, 255.CrossRefGoogle Scholar