Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T04:29:26.260Z Has data issue: false hasContentIssue false
  • English
  • Français

General two-dimensional magnetohydrodynamic equilibria with mass flow

Published online by Cambridge University Press:  13 March 2009

Y. Z. Agim  and
J. A. Tataronis
Y. Z. Agim
Affiliation:
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
J. A. Tataronis
Affiliation:
Department of Electrical Engineering, University of Wisconsin, Madison, Wisconsin 53706
Get access Rights & Permissions [Opens in a new window]

Abstract

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.

Type
Research Article
Information
Journal of Plasma Physics , Volume 34 , Issue 3 , December 1985 , pp. 337 - 360
Copyright
Copyright © Cambridge University Press 1985

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

Agim, Y. Z. & Tataronis, J. A. 1983 Bull. Am. Phys. Soc. 28, p. 1073.Google Scholar
Asano, N. & Taniuti, T. 1972 Phys. Fluids, 15, 423.CrossRefGoogle Scholar
Cattanei, G. et al. 1982 Proceedings of 9th International Conference on Plasma Physics and Controlled Fusion, Baltimore, vol. 2, p. 241. IAEA.Google Scholar
Cattanei, G. et al. 1984 Proceedings of 10th International Conference on Plasma Physics and Controlled Fusion, London, vol. 2, p. 371. IAEA.Google Scholar
Correa, D. & Lortz, D. 1972 Nucl. Fusion, 12, 127.Google Scholar
Dobrott, D. & Greene, J. M. 1970 Phys. Fluids, 13, 2391.CrossRefGoogle Scholar
Friedrichs, K. O. & Kranzer, H. 1958 Report No. NYO-6486, AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York University.Google Scholar
Grad, H. 1960 Rev. Mod. Phys. 32, 830.CrossRefGoogle Scholar
Green, B. J. & Zehrfeld, H. P. 1973 Nucl. Fusion, 13, 750.Google Scholar
Hameiri, E. 1981 J. Math. Phys. 22, 2080.CrossRefGoogle Scholar
Hameiri, E. 1983 Phys. Fluids, 26, 230.CrossRefGoogle Scholar
Hazeltine, R. D., Lee, E. P. & Rosenbluth, M. N. 1971 Phys. Fluids, 14, 361.CrossRefGoogle Scholar
Hellsten, T. A. K. & Spies, G. O. 1979 Phys. Fluids, 22, 743.CrossRefGoogle Scholar
Kerner, W. & Jandl, O. 1984 Comp. Phys. Comm. 31, 269.CrossRefGoogle Scholar
Maschke, E. K. & Perrin, H. 1980 Plasma Phys. 22, 579.Google Scholar
Mercier, C. 1964 Nucl. Fusion, 4, 213.CrossRefGoogle Scholar
Morozov, A. I. & Solov'Ev, L. S. 1963 Soviet Phys. 8, 243.Google Scholar
Pashnev, V. K., Ponomarenko, N. P. & Kharchenko, L. P. 1982 Soviet J. Plasma Phys. 8, 391.Google Scholar
Semenzato, S., Gruber, R. & Zehrfeld, H. P. 1984 C.R.P.P. École polytechnique fédérale de Lausanne-Suisse L.R.P. 233/84.Google Scholar
Spies, G. O. 1978 Phys. Fluids, 21, 580.CrossRefGoogle Scholar
Suckewer, S., Eubank, H. P., Goldston, R. J., McEnerney, J., Sauthoff, N. R. & Towner, H. H. 1981 Nucl. Fusion, 21, 1301.CrossRefGoogle Scholar
Taniuti, T. 1970 Phys. Rev. Lett. 25, 1478.CrossRefGoogle Scholar
Voslamber, D. & Callebaut, D. K. 1962 Phys. Rev. 128, 2016.CrossRefGoogle Scholar
Woltjer, L. 1959 Astrophys. 130, 405.CrossRefGoogle Scholar
Zehrfeld, H. P. & Green, B. J. 1972 Nucl. Fusion, 12, 569.Google Scholar