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Relativistic Jet Flow from a One Dimensional Magnetic Nozzle—Analytic Solutions

Published online by Cambridge University Press:  05 March 2013

Kurt Liffman
Kurt Liffman*
Affiliation:
Advanced Fluid Dynamics Laboratory, CSIRO/BCE, PO Box 56, Highett, Vic 3190, Australia; [email protected]
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Abstract

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Magnetohydrodynamic devices that can accelerate plasmas to speeds of the order of hundreds of kilometres per second have been designed and built for nearly forty years. Up to the time of writing, however, the theory for such devices has been exclusively non-relativistic. In this paper we derive the special relativistic magnetohydrodynamic (SRMHD) equations and use them to obtain the relativistic, magnetic nozzle equation which describes the production of jet flows with speeds approaching the speed of light.We obtain analytic solutions to this equation and show that, in principle, magnetic field gradients can accelerate a plasma to highly relativistic speeds. We also show that the exit kinetic energy, EK, of a particle is given by the equation EK = m0C2FR, where m0 is the rest mass of the particle and CFR is the fast magnetosonic speed at the start of the flow.

The relativistic nozzle differs in a number of ways from the non-relativistic case.A non-relativistic nozzle has a relatively symmetric converging/diverging shape, while a highly relativistic nozzle converges in the usual manner, but diverges, in an abrupt fashion, at the very end of the nozzle. The gentle divergence of non-relativistic nozzles causes the exit plasma densities and magnetic fields of the flow to have values that are small relative to their values at the start of the nozzle. The abrupt divergence of a highly relativistic nozzle implies that, for a less than perfect nozzle, the exit values of the mass density and the magnetic field strength are comparable to their initial values. This unexpected dichotomy in behaviour may have future application in understanding the ‘radio-loud’ and ‘radio-quiet’ relativistic jets that are produced from astrophysical sources.

Keywords

plasmasrelativitygalaxies:jetsstars: winds, outflows
Type
Research Article
Information
Publications of the Astronomical Society of Australia , Volume 18 , Issue 3 , 2001 , pp. 267 - 280
Copyright
Copyright © Astronomical Society of Australia 2001

References

Ardavan, H. 1976, ApJ, 203, 226 CrossRefGoogle Scholar
Battaner, E. 1996, Astrophysical Fluid Dynamics (Cambridge: Cambridge University Press)CrossRefGoogle Scholar
Blackman, E. G., & Field, G. B. 1993, Phys. Rev. Lett., 71, 3481 CrossRefGoogle Scholar
Camenzind, M. 1990, in Accretion and Winds, Reviews in Modern Astronomy 3, ed. G. Klare (Berlin: Springer-Verlag), 234 Google Scholar
Chow, E., & Monaghan, J. J. 1997, J. Comp. Phys., 134, 296 CrossRefGoogle Scholar
Contopoulos, J. 1995, ApJ, 450, 616 CrossRefGoogle Scholar
Ducati, A. C., Giannini, G. M., & Muehlberger, E. 1964, AIAA Journal, 2, 1452 CrossRefGoogle Scholar
Ellis, G. F. R., & Williams, R. M. 1988, Flat and Curved Space—Times (Oxford: Clarendon Press)Google Scholar
Goldreich, P., & Julian, W. H. 1970, ApJ, 160, 971 CrossRefGoogle Scholar
Hughes, W. F., & Brighton, J. A. 1991, Schaum's Outline Series, Theory and Problems of Fluid Dynamics (New York: McGraw-Hill)Google Scholar
Jahn, R. G. 1968, Physics of Electric Propulsion (NewYork: McGraw-Hill)Google Scholar
Kennel, C. F., Fujimura, F. S., & Okamoto, I. 1983, Geophys. Ap. Fluid Dyn., 26, 147 CrossRefGoogle Scholar
Khanna, R. 1998, MNRAS, 294, 673 CrossRefGoogle Scholar
Koide, S., Nishikawa, K.-I., & Mutel, R. L. 1996, ApJ, 463, L71 CrossRefGoogle Scholar
Landau, L. D., & Lifshitz, E. M. 1975, The Classical Theory of Fields (Oxford: Butterworth-Heinemann)Google Scholar
Landau, L. D., & Lifshitz, E. M. 1997, Fluid Mechanics (Oxford: Butterworth-Heinemann)Google Scholar
Liffman, K., & Siora, A. 1997, MNRAS, 290, 629 CrossRefGoogle Scholar
Liffman, K. 1998, PASA, 15, 259 CrossRefGoogle Scholar
Martí, J. Ma., & Müller, E. 1996, J. Comp. Phys., 123, 1 CrossRefGoogle Scholar
Melatos, A., & Melrose, D. B. 1996, MNRAS, 279, 1168 CrossRefGoogle Scholar
Michel, F. C. 1969, ApJ, 158, 727 CrossRefGoogle Scholar
Mirabel, I. F., & Rodriguez, L. F. 1998, Nature, 392, 673 CrossRefGoogle Scholar
Morozov, A. L., & Solov'ev, L. S. 1980, in Reviews of Plasma Physics, Volume 8, ed. M. A. Leontovitch (New York: Consul-tants Bureau), 1 Google Scholar
Morozov, A. I. 1990, Sov. J. Plasma Phys., 16, 69 Google Scholar
Pai, S.-I. 1962, Magnetogasdynamics and Plasma Dynamics (Vienna: Springer-Verlag)CrossRefGoogle Scholar
Schoenberg, K., Gerwin, R., Barnes, C., Henins, I., Mayo, R., Moses, R. Jr, Scarberry, R., & Wurden, G. 1991, American Institute of Aeronautics and Astronautics 91–3570 Google Scholar
Sutton, G. W., & Sherman, A. 1965, Engineering Magnetohydro-dynamics (New York: McGraw-Hill)Google Scholar
Thorne, K. S., & Macdonald, D. 1982, MNRAS, 198, 339 CrossRefGoogle Scholar
Weinberg, S. 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (New York: John Wiley and Sons)Google Scholar
Wolfram, S. 1996, The Mathematica Book, 3rd edition, Wolfram Media/Cambridge University PressGoogle Scholar