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Elements of magnetohydrodynamics with the Hall current. Part 1. Nonlinear phenomena

Published online by Cambridge University Press:  13 March 2009

P. Rosenau ,
J. A. Tataronis  and
G. Conn
P. Rosenau
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
J. A. Tataronis
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
G. Conn
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, N.Y. 10012
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Abstract

The elements of magnetohydrodynamics (MHD) with the Hall current are presented. The governing partial differential equations are, like those of ideal MHD, quasi-linear, but unlike ideal MHD, are not hyperbolic. However, they do possess real characteristics which are shown to be associated with the sound wave and the surfaces ø(r, t) = const. determined by B. ∇ø = 0. Properties of weak and strong discontinuities are discussed, and comparisons are made with ideal MHD. It is shown that generalizations of dipole layers appear as a result of discontinuities in the magnetic field.

Type
Research Article
Information
Journal of Plasma Physics , Volume 21 , Issue 3 , June 1979 , pp. 385 - 399
Copyright
Copyright © Cambridge University Press 1979

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References

REFERENCES

Bhowmix, G. & Talwar, S. P. 1972 Canadian J. Phys. 50, 1487.CrossRefGoogle Scholar
Buti, B., Dipit, M. S., Nayyar, N. K. & Trehan, S. K. 1965 Nucl. Fusion, 5, 17.CrossRefGoogle Scholar
Friedman, A. 1964 Partial Differential Equations of the Parabolic Type. Prentice-Hall.Google 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
Golitsyn, G. S. & Stantukovich, K. P. 1958 Soviet Phys. JETP, 6 (33), 1090.Google Scholar
Hosking, R. J. 1965 Phys. Rev. Lett. 15, 344.CrossRefGoogle Scholar
Hosking, R. J. & Kalra, G. L. 1972 University of Waikato Report No. 5, Mathematics Department, Hamilton, New Zealand.Google Scholar
Kadish, A. 1976 Phys. Fluids, 19, 141.CrossRefGoogle Scholar
Kulikovsky, A. G. & Lyubimov, G. A. 1965 Magnetohydrodynamics. Addison-Wesley.Google Scholar
Lax, P. D. 1957 Comm. Pure Appl. Math. 10, 537.CrossRefGoogle Scholar
Lighthill, M. J. 1960 Proc. R. Soc. A252, 397.Google Scholar
Malik, S. K. 1971 J. Plasma Phys. 5, 65.Google Scholar
McKenzie, J. F. 1971 J. Plasma Phys. 5, 275.CrossRefGoogle Scholar
Schram, P. P. J. M. & Tasso, H. 1967 Nucl. Fusion, 7, 91.CrossRefGoogle Scholar
Spitzer, L. 1956 Physics of Fully Ionized Gases. Interscience.Google Scholar
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.Google Scholar
Talwar, S. P. & Kalra, G. L. 1967 J. Plasma Phys. 1, 145.CrossRefGoogle Scholar
Tasso, H. 1970 Max-Planck-Institut für Plasmaphysik Report No. IPP6/84, Garching.Google Scholar
Tasso, H. & Schram, P. P. J. M. 1966 Nucl. Fusion, 6, 284.Google Scholar
Tayler, R. J. 1962 Nucl. Fusion Suppl. Part 1, 877.Google Scholar
Tayler, R. J. 1963 J. Nucl. Energy, Part C 5, 345.CrossRefGoogle Scholar
Trehan, S. K., Malik, S. K. & Dixit, M. S. 1965 Phys. Fluids, 8, 1461.CrossRefGoogle Scholar
Ware, A. A. 1961 J. Nucl. Energy, Part C 3, 93.CrossRefGoogle Scholar