Magnetic Turbulence in Shocks

  • Charles F. Kennel
  • Harry E. Petschek
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 10)


In this review, we comment upon two apparently diametrically opposed theories of collisionless shock waves which are already partially developed in the literature. These are theories of collisionless shock waves propagating parallel to the upstream in high β plasmas, developed in papers by Parker (1961), Moiseev and Sagdeev (1963) and Kennel and Sagdeev (1967), where Alfvén turbulence provides the dissipation, and theories of collisionless perpendicular shocks in cold plasmas developed by Petschek (1958, 1965), Fishman et al. (1960) and Camac et al. (1962). The theories as presently stated yield quite different predictions; however, we shall suggest that removal of some restrictive assumptions in each may make them converge to similar physical pictures. This paper then divides itself naturally into two parts: Part I, Alfvén Shocks, and Part II, Whistler Shocks.


Solar Wind Mach Number Shock Front Whistler Wave Alfven Wave 
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  1. Abraham-Schrauner, B.: 1968, ‘Conservation Equations for Weakly Turbulent Plasmas’, J. Geophys. Res. 73, 6299–6306.ADSCrossRefGoogle Scholar
  2. Camac, M., Kantrowitz, A. R., Litvak, M. M., Patrick, R. M., and Petschek, H. E.: 1962, ‘Shock waves in collision-free plasmas’, Nucl. Fusion Suppl., part 2, 423–446.Google Scholar
  3. Davidson, R. C. and Volk, H. J.: 1967, ’Quasi-Linear Stabilization of the Firehose Instability in a Fluid Description, paper 3B-12′ Ninth Annual Meeting, Amer. Phys. Soc., Nov. 8–11.Google Scholar
  4. Drummond, W. E. and Pines, D.: 1962, ‘Nonlinear stability of plasma oscillations’, Nucl. Fusion Suppl., part 3, 1049–1058.Google Scholar
  5. Engel, R. D.: 1965, ‘Nonlinear Stability of the Extraordinary Wave in a Plasma’, Phys. Fluids 8, 939–950.CrossRefGoogle Scholar
  6. Fishman, F. J., Kantrowitz, A. R., and Petschek, H. E.: 1960, ‘Magnetohydrodynamic shock wave in a collision-free plasma’, Rev. Mod. Phys. 32, 959–966.MathSciNetADSCrossRefGoogle Scholar
  7. Galeev, A. A. and Karpman, V. I.: 1963, ‘Turbulence theory of a weakly nonequilibrium low density plasma and structure of shock waves’, Sov. Phys. JETP 17, 403–409.zbMATHGoogle Scholar
  8. Galeev, A. A. Karpman, V. I., and Sagdeev, R. Z.: 1965, ‘Multiparticle aspects of turbulent-plasma theory’, Nucl. Fusion 5, 20–39.CrossRefGoogle Scholar
  9. Hundhausen, A. J., Asbridge, J. R., Bame, S. J., and Strong, I. B.: 1966, Distribution Function of Solar Wind Ions, TRANS. AGU, 47, 147.Google Scholar
  10. Hundhausen, A. J., Asbridge, J. R., Bame, S. L, Gilbert, H. E., and Strong, I. B.: 1967, ‘Vela 3 satellite observations of solar wind ions: A preliminary report’, J. Geophys. Res. 72, 87–100.ADSCrossRefGoogle Scholar
  11. Hundhausen, A. J., Bame, S. J., and Ness, N. F.: 1967, ‘Solar Wind Thermal Anisotropies, Vela 3 and IMP 3’, J. Geophys. Res. 72, 5265–5274.ADSCrossRefGoogle Scholar
  12. Kadomtsev, B. B.: 1965, Plasma, Turbulence, Academic Press, London and New York.Google Scholar
  13. Kennel, C. F., and Engelmann, F. E.: 1966, ‘Velocity space diffusion from weak plasma turbulence in a magnetic field’, Phys. Fluids 9, 2377–2388.ADSCrossRefGoogle Scholar
  14. Kennel, C. F. and Petschek, H. E.: 1966, ‘Limit on Stably Trapped Particle Fluxes’, J. Geophys. Res. 71, 1–28.ADSGoogle Scholar
  15. Kennel, C. F. and Sagdeev, R. Z.: 1967, ‘Collisionless Shock Waves in High β Plasmas, I’, J. Geophys. Res. 72, 3303–3326.CrossRefGoogle Scholar
  16. Kennel, C. F. and Scarf, F. L.: 1968, ‘Thermal Anisotropies and Electromagnetic Instabilities in the Solar Wind’, J. Geophys. Res. 73, 6149–6166.ADSCrossRefGoogle Scholar
  17. Litvak, M. M.: 1960, A transport equation for magnetohydrodynamic waves, AVCO-Everett Research Laboratory Res. Rept. 92.Google Scholar
  18. Moiseev, S. S. and Sagdeev, R. Z.: 1963, ‘Collisionless Shock Waves in a Plasma in a Weak Magnetic Field’, (J. Nucl. Energy, Pt. C), Plasma Physics 5, 43–47.Google Scholar
  19. Noerdlinger, P. D.: 1963, Growing Transverse Waves in Plasma in a Magnetic Field’, Ann. Phys. N.Y. 22, 12–53.ADSzbMATHCrossRefGoogle Scholar
  20. Parker, E. N.: 1968, ‘Dynamical instability of an anisotropic ionized gas of low density’, Phys. Rev. 109, 1874–1876.ADSCrossRefGoogle Scholar
  21. Parker, E. N.: 1961, ‘A quasi-linear model of plasma shock structure in a longitudinal magnetic field’, J. Nucl. Energy, C 2, 146–153.ADSCrossRefGoogle Scholar
  22. Parker, E. N.: 1963, Interplanetary dynamical processes, Interscience, New York.zbMATHGoogle Scholar
  23. Petschek, H. E.: 1958, ‘Aerodynamic Dissipation’, Rev. Mod. Phys. 30, 966.ADSCrossRefGoogle Scholar
  24. Petschek, H. E.: 1965, ‘Shock waves in collision-free plasma’, in Plasma Physics, Trieste Seminar Proc., pp. 567–576, IAEA, Vienna.Google Scholar
  25. Roberts, K. V. and Taylor, J. B.: 1962, ‘Magnetohydrodynamic equations for finite Larmor radius’, Phys. Rev. Letters 8, 197–200.ADSzbMATHCrossRefGoogle Scholar
  26. Rosenbluth, M. N., Krall, N. A., and Rostoker, N.: 1962, Finite Larmor radius stabilization of weakly’ unstable plasma, Nucl. Fusion Suppl., part 1, 143–150.Google Scholar
  27. Sagdeev, R. Z. and Shafronov, V. D.: 1961, ‘On the instability of a plasma with an anisotropic distribution of velocities in a magnetic field’, Sov. Phys. JETP English Transl. 12, 130–132.Google Scholar
  28. Scarf, F. L., Wolfe, J. H., and Silva, R. W.: 1967, ‘A plasma instability associated with thermal anisotropies in the solar wind’, J. Geophys. Res. 72, 993–1005.ADSCrossRefGoogle Scholar
  29. Shapiro, V. D. and Shevchenko, V. I.: 1964, ‘Quasi-linear theory of instability of a plasma with an anisotropic ion distribution’, Sov. Physics-JETP 18, 1109–1116.Google Scholar
  30. Tidman, D. A.: 1967, ‘Turbulent shock waves in plasmas’, Phys. Fluids 10, 547–564.ADSCrossRefGoogle Scholar
  31. Tidman, D. A.: 1967, ‘The Earth’s bow shock wave’, J. Geophys. Res. 72, 1799–1808.ADSCrossRefGoogle Scholar
  32. Vedenov, A. A., Velikhov, E. P., and Sagdeev, R. Z.: 1961a, ‘Nonlinear oscillations of rarified plasma’, Nucl. Fusion 1, 83–100.CrossRefGoogle Scholar
  33. Vedenov, A. A., Velikhov, E. P., and Sagdeev, R. Z.: 1961b, ‘Stability of plasma’, Sov. Phys.-Uspekhi 4, 332–369.ADSCrossRefGoogle Scholar
  34. Vedenov, A. A., Velikhov, E. P., and Sagdeev, R. Z.: 1962, ‘Quasi-linear theory of plasma oscillations’, Nucl. Fusion Suppl., part 2, 465–475.Google Scholar
  35. Wolfe, J. H., Silva, R. W., McKibben, D. D., and Mason, R. H.: 1966, ‘The compositional, anisotropic, and non-radical flow characteristics of the solar wind’, J. Geophys. Res. 71, 3329–3335.Google Scholar
  36. Zaslavskii, G. M. and Moiseev, S. S.: 1962, ‘On the influence of magnetic viscosity on the stability of plasma with anisotropic pressure’, Dokl. Acad. Nauk Appl. Mech. Tech. Phys. (in Russian) 6, 119–120.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1968

Authors and Affiliations

  • Charles F. Kennel
    • 1
  • Harry E. Petschek
    • 2
  1. 1.Department of PhysicsUniversity of CaliforniaLos AngelesUSA
  2. 2.AVCO-Everett Research LaboratoryEverettUSA

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