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Relativistic plasma viscosity of the Burnett kind
Phys. Rev. E 60, 4754 – Published 1 October, 1999
DOI: https://doi.org/10.1103/PhysRevE.60.4754
Abstract
Hydrodynamic equations to describe relativistic and ultrarelativistic plasma dynamics were obtained by Dzhavakhishvili and Tsintsadze [Sov. Phys. JETP 37, 666 (1973)] using the Chapman and Enskog scheme to solve the relativistic kinetic equations for the different plasma species. This approach leads to a representation of the particle viscosities in the Navier-Stokes form and, therefore, some relevant physical processes, such as the Burnett type of particle viscosity, cannot be properly dealt with in this scheme. In this paper we employ the extended Grad method to derive hydrodynamic equations which include ultrarelativistic viscosities of the Burnett type, i.e., viscosities that depend not only on derivatives of the particle macroscopic velocities but also on derivatives of particle heat fluxes.
References (17)
- S. I. Braginskii, in Review of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1965), Vol. 1, p. 205.
- Ya. B. Zeldovich and I. D. Novikov, in Relativistic Astrophysics, edited by K. S. Thorne and W. D. Arnett (The University of Chicago Press, Chicago, 1971), Vols. 1 and 2.
- P. K. Shukla, N. N. Rao, My Yu, and N. L. Tsintsadze, Phys. Rep. 138, 1 (1986).
- D. I. Dzhavakhishvili and N. L. Tsintsadze, Zh. Eksp. Teor. Fiz. 64, 1314 (1973) [Sov. Phys. JETP 37, 666 (1973)].
- S. Chapman and T. G. Cowling, Mathematical Theory of Nonuniform Gases (Cambridge University Press, New York, 1960).
- M. N. Kogan, V. Galkin, and O. G. Fridlender, Usp. Fiz. Nauk 119, 111 (1976) [Sov. Phys. Usp. 19, 420 (1976)].
- S. M. Dikman and L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 78, 1752 (1980) [Sov. Phys. JETP 51, 879 (1980)].
- D. Burnett, Proc. London Math. Soc. 39, 385; ibid.40, 382 (1935).
- A. B. Mikhailovskii and V. S. Tsypin, Plasma Phys. 13, 785 (1971).
- A. B. Mikhailovskii and V. S. Tsypin, Beitr. Plasmaphys. 24, 317 (1984).
- R. D. Hazeltine, Phys. Fluids 17, 961 (1974).
- A. B. Mikhailovskii and V. S. Tsypin, Zh. Eksp. Teor. Fiz. 83, 139 (1982) [Sov. Phys. JETP 56, 75 (1982)].
- F. L. Hinton and M. N. Rosenbluth, Phys. Fluids 16, 836 (1973).
- H. Grad, Commun. Pure Appl. Math. 2, 331 (1949).
- S. T. Belyaev and G. I. Budker, Dokl. Akad. Nauk 106, 807 (1956) [Sov. Phys. Dokl. 1, 218 (1956)].
- M. Abramovitz and I. A. Stegan, in Handbook of Mathematical Functions (Dover, New York, 1972).
- L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975).