Geomagnetism and Aeronomy

, Volume 58, Issue 6, pp 728–736 | Cite as

Structure of the Front of a Collisionless Oblique Interplanetary Shock Wave from High Time Resolution Measurements of Solar-Wind Plasma Parameters

  • V. G. EselevichEmail author
  • N. L. Borodkova
  • O. V. Sapunova
  • G. N. Zastenker
  • Yu. I. Yermolaev


Data from the Fast Solar Wind Monitor (BMSW) of the science payload onboard the SPEKTR-R satellite and data from instruments on board the WIND spacecraft are used to study statistically the structure of the front of oblique interplanetary shock waves with respect to the θBn angle and the fulfillment of the Rankine–Hugoniot conditions at the fronts of collisionless shock waves. The experimental wavelength of oscillations upstream of the ramp is compared with the estimated theoretical wavelength to determine that the dispersion of oblique magnetosonic waves plays the decisive role in the formation of the fronts of quasiperpendicular (45° ≤ θBn < 90°) collisionless interplanetary shock waves with small Mach numbers МA < 3 and a parameter of β1 < 1. Comparison of the Rankine–Hugoniot relations MA21), which were measured at the fronts of 47 interplanetary shock waves with β1 < 5 and Alfven Mach numbers of 1 < МА < 10 by calculations performed within the ideal magnetic hydrodynamics (MHD), has revealed that the effective adiabatic index γ, which characterizes the processes inside the shock front, lies mainly within the range from 2 to 5/3.



The authors thank NASA CDAWEB for granting the opportunity to use data on the plasma and magnetic-field parameters measured onboard ACE, WIND, IMP 8, Cluster, Geotail, THEMIS-B, and THEMIS-C. This work was supported by the Russian Science Foundation, project no. 16-12-10062, and within 2018 State Assignment no. 007-00163-18-00 of January 12, 2018.


  1. 1.
    Alikhanov, S.G., Belan, V.G., and Sagdeev, R.Z., Non-linear ion-acoustic waves in plasma, JETP Lett., 1968, vol. 7, no. 11, pp. 318–319.Google Scholar
  2. 2.
    Bale, S.D., Balikhin, M.A., Horbury, T.S., Krasnoselskikh, V.V., Kucharek, H., Mobius, E., Walker, S.N., Balogh, A., Burgess, D., and Lembège, B., Quasi-perpendicular shock structure and processes, Space Sci. Rev., 2005, vol. 118. doi 10.1007/s11214-005-3827-0Google Scholar
  3. 3.
    Bame, S.J., Asbridge, J.R., Gosling, J.T., Halbig, M., Paschmann, G., Scopke, N., and Rosenbauer, H., High temporal resolution observations of electron heating at the bow shock, Space Sci. Rev., 1979, vol. 23, pp. 75–92.CrossRefGoogle Scholar
  4. 4.
    Burlaga, L.F., Interplanetary Magnetohydrodynamics, New York: Oxford University Press, 1995.Google Scholar
  5. 5.
    Burlaga, L., Sitteler, E., Mariani, F., and Schwenn, R., Magnetic loop behind an interplanetary shock: Voyager, Helios, and IMP 8 observations, J. Geophys. Res., 1981, vol. 86, no. 8, pp. 6673–6684.CrossRefGoogle Scholar
  6. 6.
    Colburn, D.S. and Sonett, C.P., Discontinuities in the solar wind, Space Sci. Rev., 1966, vol. 5, no. 4, pp. 439–506.CrossRefGoogle Scholar
  7. 7.
    Eselevich, M.V. and Eselevich, V.G., Relations estimated at shock discontinuities excited by coronal mass ejections, Astron. Rep., 2011, vol. 5, no. 4, pp. 359–373.CrossRefGoogle Scholar
  8. 8.
    Eselevich, V.G., Eselevich, M.V., Borodkova, N.L., Zastenker, G.N., Šafránkova, J., Němeček, Z., and Přech, L., Fine structure of the interplanetary shock front according to measurements of the ion flux of the solar wind with high time resolution, Cosmic Res., 2017, vol. 55, no. 1, pp. 30–45.CrossRefGoogle Scholar
  9. 9.
    Formisano, V., Hedgecoc, P.C., Moreno, G., Palmiotto, F., and Chao, J.K., Solar wind interaction with the earth’s magnetic field. 2. Magnetohydrodynamic bow shock, J. Geophys. Res., 1973, vol. 78, no. 19, pp. 3731–3744.CrossRefGoogle Scholar
  10. 10.
    Galeev, A.A. and Sagdeev, R.Z., Lecture on the Nonlinear Theory of Plasma, Trieste, Italy, 1966.Google Scholar
  11. 11.
    Gold, T., Discussion on Shock Waves and Rarefied Gases. Gas Dynamics of Cosmic Clouds, Amsterdam: North Holland, 1955.Google Scholar
  12. 12.
    Gosling, J.T. and Robson, A.E., Ion reflection, gyration and dissipation at supercritical shocks, in Collisionless Shocks in the Heliosphere: Reviews of Current Research, Tsurutani, B.T. and Stone, R.G., Eds., Washington, D.C.: Am. Geophys. Union, 1985, pp. 141–152.Google Scholar
  13. 13.
    Greenstadt, E.W., Russell, C.T., Gosling, J.T., Bame, S.J., Pashmann, G., Parks, G.K., Andersen, K.A., Scarf, F.L., Andersen, R.R., and Gurnett, D.A., Macroscopic profile of the typical quasi-perpendicular bow shock: ISEE 1 and 2, J. Geophys. Res., 1980, vol. 85, no. A5, pp. 2124–2130.CrossRefGoogle Scholar
  14. 14.
    Iskoldsky, A.M., Kurtmullayev, R.Kh., Nesterikhin, Yu.E., and Ponomarenko, A.G., Experiments in collisionless shock wave in plasma, Zh. Exp. Teor. Fiz., 1964, vol. 47, no. 2, pp. 774–776.Google Scholar
  15. 15.
    Kantrowitz, A.R. and Petschec, H.E., MHD characteristics and shock waves, in Plasma Physics in Theory and Application, Kunkel, W.B., Ed., New York: McGraw-Hill, 1966.Google Scholar
  16. 16.
    Kennel S.F., Edmiston J.P., Hada T. A quarter century of collisionless shock research, in Collisionless Shocks in the Heliosphere: A Tutorial Review, Tsurutani, B.T. and Stone, R.G., Eds., Washington, D.C.: Am. Geophys. Union, 1985, pp. 1–36.Google Scholar
  17. 17.
    Korolev, A.S., Boshenyatov, B.V., Druker, I.G., and Zatoloka, V.V., Pulsed Tunnels in Aerodynamic Research, Novosibirsk: Nauka, 1978, pp. 5–80.Google Scholar
  18. 18.
    Krasnoselskikh, V., Balikhin, M., Walker, S.N., et al., The dynamic quasiperpendicular shock: Cluster discoveries, Space Sci. Rev., 2013, vol. 178, nos. 2–4, pp. 535–598.CrossRefGoogle Scholar
  19. 19.
    Landau, L.D. and Lifshits, E.M., Gidrodinamika (Fluid Dynamics), Moscow: Gostekhteoretizdat, 1953.Google Scholar
  20. 20.
    Lepping, R.P., Acuna, M.H., Burlaga, L.F., Farrell, W.M., Slavin, J.A., Schatten, K.H., Mariani, F., Ness, N.F., Neubauer, F.M., and Whang, Y.C., The WIND magnetic field investigation, Space Sci. Rev., 1995, vol. 71, nos. 1–4, pp. 207–229.CrossRefGoogle Scholar
  21. 21.
    Lin, R.P., Anderson, K.A., Ashford, S., Carlson, C., Curtis, D., Ergun, R., Larson, D., McFadden, J., McCarthy, M., and Parks, G.K., A three-dimensional (3-D) plasma and energetic particle experiment for the WIND spacecraft of the ISTP/GGS mission, Space Sci. Rev., 1995, vol. 71, pp. 125–153.CrossRefGoogle Scholar
  22. 22.
    Mellott, M., Subcritical collisionless shock waves, in Collisionless Shocks in the Heliosphere: Reviews of Current Research, Tsurutani, B.T. and Stone, R.G., Eds., Washington, D.C.: Am. Geophys. Union, 1985, pp. 131–140.Google Scholar
  23. 23.
    Němeček, Z., Šafránkova, J., Goncharov, O., Přech, L., and Zastenker, G.N., Ion scales of quasi-perpendicular low-Mach-number interplanetary shocks, Geophys. Res. Lett., 2013, vol. 40, pp. 4133–4137.CrossRefGoogle Scholar
  24. 24.
    Ogilvie, K.W., Chorney, D.J., Fitzenreiter, R.J., et al., SWE, a comprehensive plasma instrument for the wind spacecraft, Space Sci. Rev., 1995, vol. 71, nos. 1–4, pp. 55–77.CrossRefGoogle Scholar
  25. 25.
    Oliveira, D.M. and Samsonov, A.A., Geoeffectiveness of interplanetary shocks controlled by impact angles: A review, Adv. Space Res., 2018, vol. 61, pp. 1–44.CrossRefGoogle Scholar
  26. 26.
    Paul, J.W.H., Holmes, L.S., Parkinson, M.J., and Sheffield, J., Experimental observations on the structure of collisionless shock waves in a magnetized plasma, Nature, 1965, vol. 2, pp. 367–385.Google Scholar
  27. 27.
    Sagdeev, R.Z., Voprosy teorii plazmy (Issues in the Plasma Theory), Moscow: Atomizdat, 1964.Google Scholar
  28. 28.
    Sagdeev, R.Z., Cooperative phenomena and shock waves in collisionless plasmas, Rev. Plasma Phys., 1966, vol. 4, pp. 23–91.Google Scholar
  29. 29.
    Song, P. and Russell, C.T., Time series data analysis in space physics, Space Sci. Rev., 1999, vol. 87, nos. 3–4, pp. 387–463.CrossRefGoogle Scholar
  30. 30.
    Šafránkova, J., Němeček, Z., Přech, L., et al., Fast Solar Wind Monitor (BMSW): Description and first results, Space Sci. Rev., 2013, vol. 175, pp. 165–182.CrossRefGoogle Scholar
  31. 31.
    Tidman, D.A., Turbulent shock waves in plasma, Phys. Fluids, 1967, vol. 10, pp. 547–568.CrossRefGoogle Scholar
  32. 32.
    Totten, T.L., Freeman, J.W., and Arya, S., An empirical determination of the polytropic index for the free-streaming solar wind using HELIOS 1 data, J. Geophys. Res., 1995, vol. 100, no. A1, pp. 13–17.CrossRefGoogle Scholar
  33. 33.
    Tsurutani, B.T. and Stone, R.G., Collisionless Shocks in the Heliosphere: Reviews of Current Research. Geophysical Monograph No. 35, Washington, D.C.: Am. Geophys. Union, 1985.CrossRefGoogle Scholar
  34. 34.
    Volkov, O.L., Eselevich, V.G., Kichigin, G.N., and Paperny, V.L., Turbulent shock waves in rarefied nonmagnetised plasma, Zh. Eksp. Teor. Fiz., 1974, vol. 67, pp. 1689–1692.Google Scholar
  35. 35.
    Zagorodnikov, S.P., Rudakov, L.I., Smolkin, G.E., and Sholin, G.V., Observation of shock waves in collisionless plasma, Zh. Eksp. Teor. Fiz., 1964, vol. 47, no. 5, pp. 1770–1720.Google Scholar
  36. 36.
    Zastenker, G.N., Borodkova, N.L., Vaisberg, O.L., Omel’chenko, A.N., Yermolaev, Yu.I., and Balebanov, V.M., Interplanetary shock waves in the period after the solar maximum year: Prognoz-8 satellite, Preprint of the Space Research Institute, Russ. Acad. Sci., Moscow, 1983, no. 841.Google Scholar
  37. 37.
    Zastenker, G.N., Šafránkova, J., Němeček, Z., et al., Fast measurements of parameters of the solar wind using the BMSW instrument, Cosmic. Res., 2013, vol. 51, no. 2, pp. 78–89.CrossRefGoogle Scholar
  38. 38.
    Zeldovich, Ya.B. and Raiser, Yu.P., Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii (Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena), Moscow: Nauka, 1966, pp. 398–406.Google Scholar
  39. 39.
    Zimbardo, G., More than mass proportional heating of heavy ions by collisionless quasi-perpendicular shocks in the solar corona, in Solar Wind 12, Proceedings of the International Conference, Saint-Malo, France, 21–26 June 2009, AIP Proc. Conf., 2009, vol. 1216, pp. 52–55.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. G. Eselevich
    • 1
    Email author
  • N. L. Borodkova
    • 2
  • O. V. Sapunova
    • 2
  • G. N. Zastenker
    • 2
  • Yu. I. Yermolaev
    • 2
  1. 1.Institute of Solar–Terrestrial Physics, Siberian Branch, Russian Academy of SciencesIrkutskRussia
  2. 2.Space Research Institute, Russian Academy of SciencesMoscowRussia

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