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Simple waves in a plasma with anisotropic pressure

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Abstract

Fast and slow simple waves are studied in the framework of the anisotropic magnetohydrodynamics of Chew, Goldberger, and Low [1]. Baranov [2] has constructed fields of integral curves for fast and slow waves and in two special cases has shown that such waves break in the compression section. The possibility of breaking of a slow wave in a rarefaction section was noted by Akhiezer et al. [3]. However, their general relations in simple waves [3] have been shown to be incorrect [2, 4]. In the present paper the nature of the variation of the longitudinal and transverse plasma pressures is determined, and the problem of the breaking of fast and slow waves is completely solved. Conditions under which a slow wave breaks in a rarefaction section are found. A fast wave always breaks in a rarefaction section.

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Literature cited

  1. 1.

    G. F. Chew, M. L. Goldberger, and F. E. Low, “The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions,” Proc. R. Soc. London, Ser. A:236, 112 (1956).

  2. 2.

    V. B. Baranov, “Investigation of simple waves in a plasma with anisotropic pressure,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 6 (1970).

  3. 3.

    I. A. Akhiezer, R. V. Polovich, and N. L. Tsiniadze, “Simple waves in the Chew-Goldberger-Low approximation,” Zh. Eksp. Teor. Fiz.,37, 756 (1959).

  4. 4.

    Y. Kato, M. Tajiri, and T. Taniuti, “Propagation of hydromagnetic waves in collisionless plasma I,” J. Phys. Soc. Jpn.,21, 765 (1966).

  5. 5.

    V. B. Baranov and K. V. Krasnobaev, Hydrodynamic Theory of Cosmic Plasmas [in Russian], Nauka, Moscow (1977).

  6. 6.

    R. Z. Sagdeev, “Collective processes and shock waves in a rarefied plasma,” in: Reviews of Plasma Physics, Vol. 4, Consultants Bureau, New York (1966), p. 23.

  7. 7.

    I. S. Shikin, “Wave theory in Chew-Goldberger-Low relativistic magnetohydrodynamics,” Fiz. Plazmy,2, 24 (1976).

  8. 8.

    Shr. Abraham, “Propagation of hydromagnetic waves through in anisotropic plasma,” J. Plasma Phys.,1, 361 (1967).

  9. 9.

    A. G. Kulikovskii and G. A. Lyubimov, Magnetohydrodynamics [in Russian], Fizmatgiz, Moscow (1962).

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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 181–183, July–August, 1988.

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Zakharov, V.Y., Shikin, I.S. Simple waves in a plasma with anisotropic pressure. Fluid Dyn 23, 637–639 (1988). https://doi.org/10.1007/BF01055093

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Keywords

  • General Relation
  • Slow Wave
  • Plasma Pressure
  • Integral Curf
  • Fast Wave