Space Science Reviews

, Volume 178, Issue 2–4, pp 535–598 | Cite as

The Dynamic Quasiperpendicular Shock: Cluster Discoveries

  • V. Krasnoselskikh
  • M. Balikhin
  • S. N. Walker
  • S. Schwartz
  • D. Sundkvist
  • V. Lobzin
  • M. Gedalin
  • S. D. Bale
  • F. Mozer
  • J. Soucek
  • Y. Hobara
  • H. Comisel
Article
First Online:
Received:
Accepted:

Abstract

The physics of collisionless shocks is a very broad topic which has been studied for more than five decades. However, there are a number of important issues which remain unresolved. The energy repartition amongst particle populations in quasiperpendicular shocks is a multi-scale process related to the spatial and temporal structure of the electromagnetic fields within the shock layer. The most important processes take place in the close vicinity of the major magnetic transition or ramp region. The distribution of electromagnetic fields in this region determines the characteristics of ion reflection and thus defines the conditions for ion heating and energy dissipation for supercritical shocks and also the region where an important part of electron heating takes place. In other words, the ramp region determines the main characteristics of energy repartition. All these processes are crucially dependent upon the characteristic spatial scales of the ramp and foot region provided that the shock is stationary. The process of shock formation consists of the steepening of a large amplitude nonlinear wave. At some point in its evolution the steepening is arrested by processes occurring within the shock transition. From the earliest studies of collisionless shocks these processes were identified as nonlinearity, dissipation, and dispersion. Their relative role determines the scales of electric and magnetic fields, and so control the characteristics of processes such as ion reflection, electron heating and particle acceleration. The determination of the scales of the electric and magnetic field is one of the key issues in the physics of collisionless shocks. Moreover, it is well known that under certain conditions shocks manifest a nonstationary dynamic behaviour called reformation. It was suggested that the transition from stationary to nonstationary quasiperiodic dynamics is related to gradients, e.g. scales of the ramp region and its associated whistler waves that form a precursor wave train. This implies that the ramp region should be considered as the source of these waves. All these questions have been studied making use observations from the Cluster satellites. The Cluster project continues to provide a unique viewpoint from which to study the scales of shocks. During its lifetime the inter-satellite distance between the Cluster satellites has varied from 100 km to 10000 km allowing scientists to use the data best adapted for the given scientific objective.

The purpose of this review is to address a subset of unresolved problems in collisionless shock physics from experimental point of view making use multi-point observations onboard Cluster satellites. The problems we address are determination of scales of fields and of a scale of electron heating, identification of energy source of precursor wave train, an estimate of the role of anomalous resistivity in energy dissipation process by means of measuring short scale wave fields, and direct observation of reformation process during one single shock front crossing.

Keywords

Collisionless shocks Waves in plasmas Nonstationarity Shock scales Plasma heating and acceleration Wave-particle interactions 

References

  1. J.H. Adlam, J.E. Allen, The structure of strong collision-free hydromagnetic waves. Philos. Mag. 3, 448–455 (1958). doi:10.1080/14786435808236833 ADSMATHGoogle Scholar
  2. U. Ascoli-Bartoli, S. Martellucci, M. Martone, Formation and development of hydromagnetic disturbances during the implosion phase of a preionized theta pinch (cariddi) (cn-21/75), in Plasma Physics and Controlled Nuclear Fusion Research, vol. I (1966), p. 275 Google Scholar
  3. H.U. Auster, K.H. Glassmeier, W. Magnes, O. Aydogar, D. Constantinescu, D. Fischer, K.H. Fornacon, E. Georgescu, P. Harvey, O. Hillenmaier, R. Kroth, M. Ludlam, Y. Narita, K. Okrafka, F. Plaschke, I. Richter, H. Schwarzl, B. Stoll, A. Valavanoglu, M. Wiedemann, The THEMIS fluxgate magnetometer. Space Sci. Rev. 135 (2008). doi:10.1007/s11214-008-9365-9
  4. W.I. Axford, E. Leer, G. Skadron, The acceleration of cosmic rays by shock waves, in International Cosmic Ray Conference, vol. 11 (1977), pp. 132–137 Google Scholar
  5. S.D. Bale, F.S. Mozer, Measurement of large sale parallel and perpendicular electric fields on electron spatial scales in the terrestrial bow shock. Phys. Rev. Lett. 98, 205001 (2007). doi:10.1103/PhysRevLett.98.205001 ADSGoogle Scholar
  6. S.D. Bale, F.S. Mozer, T.S. Horbury, Density-transition scale at quasiperpendicular collisionless shocks. Phys. Rev. Lett. 91(26), 265004 (2003). doi:10.1103/PhysRevLett.91.265004 ADSGoogle Scholar
  7. S.D. Bale, F.S. Mozer, V.V. Krasnoselskikh, Direct measurement of the cross-shock electric potential at low plasma β, quasi-perpendicular bow shocks. ArXiv e-prints (2008) Google Scholar
  8. S.D. Bale, P.J. Kellogg, D.E. Larson, R.P. Lin, K. Goetz, R.P. Lepping, Bipolar electrostatic structures in the shock transition region: evidence of electron phase space holes. Geophys. Res. Lett. 25, 2929–2932 (1998). doi:10.1029/98GL02111 ADSGoogle Scholar
  9. S.D. Bale, M.A. Balikhin, T.S. Horbury, V.V. Krasnoselskikh, H. Kucharek, E. Möbius, S.N. Walker, A. Balogh, D. Burgess, B. Lembége, E.A. Lucek, M. Scholer, S.J. Schwartz, M.F. Thomsen, Quasi-perpendicular shock structure and processes. Space Sci. Rev. 118(1–4), 161–203 (2005). doi:10.1007/s11214-005-3827-0 ADSGoogle Scholar
  10. M. Balikhin, M. Gedalin, Kinematic mechanism of electron heating in shocks: theory vs observations. Geophys. Res. Lett. 21, 841–844 (1994). doi:10.1029/94GL00371 ADSGoogle Scholar
  11. M. Balikhin, M. Gedalin, A. Petrukovich, New mechanism for heating in shocks. Phys. Rev. Lett. 70, 1259–1262 (1993). doi:10.1103/PhysRevLett.70.1259 ADSGoogle Scholar
  12. M. Balikhin, V. Krasnosselskikh, M. Gedalin, The scales in quasiperpendicular shocks. Adv. Space Res. 15(8–9), 247–260 (1995). doi:10.1016/0273-1177(94)00105-A ADSGoogle Scholar
  13. M.A. Balikhin, T. Dudok de Wit, L.J.C. Woolliscroft, S.N. Walker, H. Alleyne, V. Krasnoselskikh, W.A.C. Mier–Jedrzejowicz, W. Baumjohann, Experimental determination of the dispersion of waves observed upstream of a quasi-perpendicular shock. Geophys. Res. Lett. 24, 787–790 (1997a). doi:10.1029/97GL00671 ADSGoogle Scholar
  14. M.A. Balikhin, S.N. Walker, T. Dudok de Witt, H.S.C. Alleyne, L.J.C. Woolliscroft, W.A.C. Mier-Jedrzejowicz, W. Baumjohann, Nonstationarity and low frequency turbulence at a quasi-perpendicular shock front. Adv. Space Res. 20, 729–734 (1997b) ADSGoogle Scholar
  15. M.A. Balikhin, V. Krasnoselskikh, L.J.C. Woolliscroft, M. Gedalin, A study of the dispersion of the electron distribution in the presence of e and b gradients: application to electron heating at quasi-perpendicular shocks. J. Geophys. Res., Atmos. 103, 2029–2040 (1998). doi:10.1029/97JA02463 ADSGoogle Scholar
  16. M.A. Balikhin, M. Nozdrachev, M. Dunlop, V. Krasnoselskikh, S.N. Walker, H.S.C.K. Alleyne, V. Formisano, M. André, A. Balogh, A. Eriksson, K. Yearby, Observation of the terrestrial bow shock in quasi-electrostatic sub-shock regime. J. Geophys. Res., Atmos. 107(8), 10 (2002). doi:10.1029/2001JA000327 Google Scholar
  17. M.A. Balikhin, O.A. Pokhotelov, S.N. Walker, E. Amata, M. Andre, M. Dunlop, H.S.C.K. Alleyne, Minimum variance free wave identification: application to cluster electric field data in the magnetosheath. Geophys. Res. Lett. 30(10) (2003). doi:10.1029/2003GL016918
  18. M. Balikhin, S. Walker, R. Treumann, H. Alleyne, V. Krasnoselskikh, M. Gedalin, M. Andre, M. Dunlop, A. Fazakerley, Ion sound wave packets at the quasiperpendicular shock front. Geophys. Res. Lett. 32(24), 24106 (2005). doi:10.1029/2005GL024660 ADSGoogle Scholar
  19. A. Balogh, M.W. Dunlop, S.W.H. Cowley, D.J. Southwood, J.G. Thomlinson, K.H. Glassmeier, G. Musmann, H. Lühr, S. Buchert, M.H. Acuña, D.H. Fairfield, J.A. Slavin, W. Riedler, K. Schwingenschuh, M.G. Kivelson, The cluster magnetic field investigation. Space Sci. Rev. 79, 65–91 (1997). doi:10.1023/A:1004970907748 ADSGoogle Scholar
  20. A. Bamba, R. Yamazaki, M. Ueno, K. Koyama, Small-scale structure of the sn 1006 shock with chandra observations. Astrophys. J. 589, 827–837 (2003). doi:10.1086/374687 ADSGoogle Scholar
  21. F. Begenal, J.W. Belcher, E.C. Sittler, R.P. Lepping, The uranian bow shock—Voyager 2 inbound observations of a high Mach number shock. J. Geophys. Res. 92, 8603–8612 (1987). doi:10.1029/JA092iA08p08603 ADSGoogle Scholar
  22. A.R. Bell, The acceleration of cosmic rays in shock fronts, I. Mon. Not. R. Astron. Soc. 182, 147–156 (1978a) ADSGoogle Scholar
  23. A.R. Bell, The acceleration of cosmic rays in shock fronts, II. Mon. Not. R. Astron. Soc. 182, 443–455 (1978b) ADSGoogle Scholar
  24. D. Biskamp, H. Welter, Ion heating in high-Mach-number, oblique, collisionless shock waves. Phys. Rev. Lett. 28, 410–413 (1972). doi:10.1103/PhysRevLett.28.410 ADSGoogle Scholar
  25. R.D. Blandford, J.P. Ostriker, Particle acceleration by astrophysical shocks. Astrophys. J. Lett. 221, 29–32 (1978). doi:10.1086/182658 ADSGoogle Scholar
  26. K.D. Cole, Effects of crossed magnetic and /spatially dependent/ electric fields on charged particle motion. Planet. Space Sci. 24, 515–518 (1976). doi:10.1016/0032-0633(76)90096-9 ADSGoogle Scholar
  27. H. Comişel, M. Scholer, J. Soucek, S. Matsukiyo, Non-stationarity of the quasi-perpendicular bow shock: comparison between cluster observations and simulations. Ann. Geophys. 29, 263–274 (2011). doi:10.5194/angeo-29-263-2011 ADSGoogle Scholar
  28. N. Cornilleau-Wehrlin, P. Chauveau, S. Louis, A. Meyer, J.M. Nappa, S. Perraut, L. Rezeau, P. Robert, A. Roux, C. De Villedary, Y. de Conchy, L. Friel, C.C. Harvey, D. Hubert, C. Lacombe, R. Manning, F. Wouters, F. Lefeuvre, M. Parrot, J.L. Pinçon, B. Poirier, W. Kofman, P. Louarn, The STAFF investigator team, the cluster spatio-temporal analysis of field fluctuations (staff) experiment. Space Sci. Rev. 79, 107–136 (1997) ADSGoogle Scholar
  29. F.V. Coroniti, Dissipation discontinuities in hydromagnetic shock waves. J. Plasma Phys. 4, 265 (1970) ADSGoogle Scholar
  30. R.C. Davidson, N.T. Gladd, C.S. Wu, J.D. Huba, Effects of finite beta plasma on the lower hybrid instability. Phys. Fluids 20, 301 (1977) ADSGoogle Scholar
  31. L. Davis, R. Lüst, A. Schlüter, The structure of hydromagnetic shock waves, I: nonlinear hydromagnetic waves in a cold plasma. Z. Naturforsch. Teil A 13, 916 (1958) ADSMATHGoogle Scholar
  32. F. de Hoffmann, E. Teller, Magneto-hydrodynamic shocks. Phys. Rev. 80, 692–703 (1950). doi:10.1103/PhysRev.80.692 MathSciNetADSMATHGoogle Scholar
  33. P.M.E. Décréau, P. Fergeau, V. Krannosels’kikh, M. Leveque, P. Martin, O. Randriamboarison, F.X. Sene, J.G. Trotignon, P. Canu, P.B. Mogensen, Whisper, a resonance sounder and wave analyser: performances and perspectives for the cluster mission. Space Sci. Rev. 79, 157–193 (1997). doi:10.1023/A:1004931326404 ADSGoogle Scholar
  34. A.P. Dimmock, M.A. Balikhin, V.V. Krasnoselskikh, S.N. Walker, S.D. Bale, Y. Hobara, A statistical study of the cross-shock electric potential at low Mach number, quasi-perpendicular bow shock crossings using cluster data. J. Geophys. Res., Space Phys. 117(A2), 2210 (2012). doi:10.1029/2011JA017089 ADSGoogle Scholar
  35. C.P. Escoubet, R. Schmidt, M.L. Goldstein, Cluster—science and mission overview. Space Sci. Rev. 79, 11–32 (1997) ADSGoogle Scholar
  36. V.G. Eselevich, A.G. Eskov, R.C. Kurtmullaev, A.I. Malyutin, Isomagnetic discontinuity in a collisionless shock wave. Sov. Phys. JETP 33, 1120 (1971) ADSGoogle Scholar
  37. M.H. Farris, S.M. Petrinec, C.T. Russell, The thickness of the magnetosheath: constraints on the polytropic index. Geophys. Res. Lett. 18, 1821 (1991). doi:10.1029/91GL02090 ADSGoogle Scholar
  38. M.H. Farris, C.T. Russell, M.F. Thomsen, Magnetic structure of the low beta, quasi-perpendicular shock. J. Geophys. Res., Atmos. 98, 15285–15294 (1993). doi:10.1029/93JA00958 ADSGoogle Scholar
  39. W.C. Feldman, R.C. Anderson, J.R. Asbridge, S.J. Bame, J.T. Gosling, R.D. Zwickl, Plasma electron signature of magnetic connection to the Earth’s bow shock—isee 3. J. Geophys. Res., Atmos. 87(A2), 632–642 (1982) ADSGoogle Scholar
  40. W.C. Feldman, R.C. Anderson, S.J. Bame, S.P. Gary, J.T. Gosling, D.J. McComas, M.F. Thomsen, G. Paschmann, M.M. Hoppe, Electron velocity distributions near the Earth’s bow shock. J. Geophys. Res., Atmos. 88, 96–110 (1983) ADSGoogle Scholar
  41. V. Formisano, Measurement of the potential drop across the Earth’s collisionless bow shock. Geophys. Res. Lett. 9, 1033 (1982) ADSGoogle Scholar
  42. V. Formisano, Collisionless shock waves in space and astrophysical plasmas, in Proc. ESA Workshop on Future Missions in Solar, Heliospheric and Space Plasma Physics, vol. ESA SP-235 (1985), p. 83 Google Scholar
  43. V. Formisano, R. Torbert, Ion acoustic wave forms generated by ion-ion streams at the Earth’s bow shock. Geophys. Res. Lett. 9, 207 (1982) ADSGoogle Scholar
  44. S.A. Fuselier, D.A. Gurnett, R.J. Fitzenreiter, The downshift of electron plasma oscillations in the electron foreshock region. J. Geophys. Res. 90, 3935–3946 (1985). doi:10.1029/JA090iA05p03935 ADSGoogle Scholar
  45. A.A. Galeev, Collisionless shocks, in Physics of Solar Planetary Environment; Proceedings of the International Symposium on Solar-Terrestrial Physics, Boulder, CO, June 7–18, 1976, ed. by D.J. Williams (AGU, Washington, 1976), pp. 464–490 Google Scholar
  46. A.A. Galeev, R.Z. Sagdeev, Current instabilities and anomalous resistivity of plasma, in Basic Plasma Physics: Selected Chapters, Handbook of Plasma Physics, vol. 1, ed. by A.A. Galeev, R.N. Sudan (1984), p. 271 Google Scholar
  47. A.A. Galeev, R.N. Sudan, Basic Plasma Physics. Selected Chapters. Handbook of Plasma Physics, vols. 1 and 2 (1989) Google Scholar
  48. A.A. Galeev, V.V. Krasnoselskikh, V.V. Lobzin, Fine structure of the front of a quasi-perpendicular supercritical collisionless shock wave. Sov. J. Plasma Phys. 14, 1192–1200 (1988) Google Scholar
  49. A.A. Galeev, C.F. Kennel, V.V. Krasnoselskikh, V.V. Lobzin, The role of whistler oscillations in the formation of the structure of high Mach number collisionless shock, in Plasma Astrophysics (1989), pp. 165–171 Google Scholar
  50. M. Gedalin, Ion reflection at the shock front revisited. J. Geophys. Res. 101, 4871 (1996). doi:10.1029/95JA03669 ADSGoogle Scholar
  51. M. Gedalin, Ion heating in oblique low-Mach number shocks. Geophys. Res. Lett. 24, 2511 (1997) ADSGoogle Scholar
  52. M. Gedalin, K. Gedalin, M. Balikhin, V. Krasnosselskikh, L.J.C. Woolliscroft, Demagnetization of electrons in inhomogeneous E ⊥ B: implications for electron heating in shocks. J. Geophys. Res. 100, 19911–19918 (1995a). doi:10.1029/95JA01399 ADSGoogle Scholar
  53. M. Gedalin, K. Gedalin, M. Balikhin, V. Krasnosselskikh, Demagnetization of electrons in the electromagnetic field structure, typical for quasi-perpendicular collisionless shock front. J. Geophys. Res. 100, 9481–9488 (1995b). doi:10.1029/94JA03369 ADSGoogle Scholar
  54. G. Goldenbaum, E. Hintz, Experimental study of shock wave formation in an almost collisionfree plasma. Phys. Plasmas 8, 2111–2112 (1965). doi:10.1063/1.1761164 Google Scholar
  55. C.C. Goodrich, J.D. Scudder, The adiabatic energy change of plasma electrons and the frame dependence of the cross shock potential at collisionless magnetosonic shock waves. J. Geophys. Res., Atmos. 89, 6654–6662 (1984) ADSGoogle Scholar
  56. E.W. Greenstadt, R.W. Fredricks, Shock systems in collisionless space plasmas, in Solar System Plasma Physics, vol. 3, ed. by L.J. Lanzerotti, C.F. Kennel, E.N. Parker (North Holland, Amsterdam, 1979), pp. 3–43 Google Scholar
  57. D.A. Gurnett, Plasma waves and instabilities, in Collisionless Shocks in the Heliosphere: Reviews of Current Research, ed. by B.T. Tsurutani, R.G. Stone Geophysical Monograph (AGU, Washington, 1985), pp. 207–224 Google Scholar
  58. G. Gustafsson, R. Bostrom, B. Holback, G. Holmgren, A. Lundgren, K. Stasiewicz, L. Ahlen, F.S. Mozer, D. Pankow, P. Harvey, P. Berg, R. Ulrich, A. Pedersen, R. Schmidt, A. Butler, A.W.C. Fransen, D. Klinge, C.-G. Falthammar, P.-A. Lindqvist, S. Christenson, J. Holtet, B. Lybekk, T.A. Sten, P. Tanskanen, K. Lappalainen, J. Wygant, The electric field and wave experiment for the cluster mission. Space Sci. Rev. 79, 137–156 (1997) ADSGoogle Scholar
  59. P. Hellinger, A. Mangeney, Upstream whistlers generated by protons reflected from a quasi-perpendicular shock. J. Geophys. Res., Space Phys. 102(A5), 9809–9819 (1997). doi:10.1029/96JA03826 ADSGoogle Scholar
  60. P. Hellinger, P. Trávnícek, H. Matsumoto, Reformation of perpendicular shocks: hybrid simulations. Geophys. Res. Lett. 29(24), 240000 (2002). doi:10.1029/2002GL015915 Google Scholar
  61. P. Hellinger, P. Trávníček, B. Lembège, P. Savoini, Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: hybrid versus full particle simulations. Geophys. Res. Lett. 34, 14109 (2007). doi:10.1029/2007GL030239 ADSGoogle Scholar
  62. J.P. Heppner, N.C. Maynard, T.L. Aggson, Early results from isee-1 electric field measurements. Space Sci. Rev. 22, 777–789 (1978) ADSGoogle Scholar
  63. Y. Hobara, S.N. Walker, M. Balikhin, O.A. Pokhotelov, M. Gedalin, V. Krasnoselskikh, M. Hayakawa, M. André, M. Dunlop, H. Rème, A. Fazakerley, Cluster observations of electrostatic solitary waves near the Earth’s bow shock. J. Geophys. Res., Atmos. 113, 05211 (2008). doi:10.1029/2007JA012789 ADSGoogle Scholar
  64. Y. Hobara, M. Balikhin, V. Krasnoselskikh, M. Gedalin, H. Yamagishi, Statistical study of the quasi-perpendicular shock ramp widths. J. Geophys. Res. 115, 11106 (2010). doi:10.1029/2010JA015659 Google Scholar
  65. T.S. Horbury, P.J. Cargill, E.A. Lucek, A. Balogh, M.W. Dunlop, T.M. Oddy, C. Carr, P. Brown, A. Szabo, K.-H. Fornaçon, Cluster magnetic field observations of the bowshock: orientation, motion and structure. Ann. Geophys. 19, 1399–1409 (2001). doi:10.5194/angeo-19-1399-2001 ADSGoogle Scholar
  66. T.S. Horbury, P.J. Cargill, E.A. Lucek, J. Eastwood, A. Balogh, M.W. Dunlop, K.-H. Fornaçon, E. Georgescu, Four spacecraft measurements of the quasi-perpendicular terrestrial bowshock: orientation and motion. J. Geophys. Res., Atmos. 107(A8), 10–11 (2002). doi:10.1029/2001JA000273 Google Scholar
  67. V.I. Karpman, Structure of the shock front propagating at an angle of the magnetic field in a low density plasma. Sov. Phys. Tech. Phys. Engl. Transl. 8, 715 (1964) Google Scholar
  68. V.I. Karpman, J.K. Alekhin, N.D. Borisov, N.A. Rjabova, Electrostatic waves with frequencies exceeding gyrofrequency in magnetosphere. Astrophys. Space Sci. 22(2), 267–278 (1973). doi:10.1007/BF00647426 ADSGoogle Scholar
  69. C.F. Kennel, J.P. Edmiston, T. Hada, A quarter century of collisionless shock research, in Collisionless Shocks in the Heliosphere: A Tutorial Review, ed. by R.G. Stone, B.T. Tsurutani Geophysical Monograph, vol. 34 (American Geophysical Union, Washington, 1985), pp. 1–36 Google Scholar
  70. S. Klimov, S. Savin, Y. Aleksevich, G. Avanesova, V. Balebanov, M. Balikhin, A. Galeev, B. Gribov, M. Nozdrachev, V. Smirnov, A. Sokolov, O. Vaisberg, P. Oberc, Z. Krawczyk, S. Grzedzielski, J. Juchniewicz, K. Nowak, D. Orlowski, B. Parfianovich, D. Wozniak, Z. Zbyszynski, Y. Voita, P. Triska, Extremely-low-frequency plasma waves in the environment of comet Halley. Nature 321, 292–293 (1986) ADSGoogle Scholar
  71. K. Koyama, R. Petre, E.V. Gotthelf, U. Hwang, M. Matsuura, M. Ozaki, S.S. Holt, Evidence for shock acceleration of high-energy electrons in the supernova Remnant sn1006. Nature 378, 255–258 (1995). doi:10.1038/378255a0 ADSGoogle Scholar
  72. V. Krasnoselskikh, Nonlinear motions of a plasma across a magnetic field. Sov. Phys. JETP 62, 282–294 (1985) Google Scholar
  73. V.V. Krasnoselskikh, E.N. Kruchina, A.S. Volokitin, G. Thejappa, Fast electron generation in quasiperpendicular shocks and type II solar radiobursts. Astron. Astrophys. 149, 323–329 (1985) ADSGoogle Scholar
  74. V.V. Krasnoselskikh, M.A. Balikhin, H.S.C. Alleyne, S.I. Klimov, W.A.C. Mier-Jedrzejowicz, A.K. Pardaens, A. Petrukovich, D.J. Southwood, T. Vinogradova, L.J.C. Woolliscroft, On the nature of low frequency turbulence in the foot of strong quasi-perpendicular shocks. Adv. Space Res. 11(9), 15–18 (1991) ADSGoogle Scholar
  75. V.V. Krasnoselskikh, B. Lembége, P. Savoini, V.V. Lobzin, Nonstationarity of strong collisionless quasiperpendicular shocks: theory and full particle numerical simulations. Phys. Plasmas 9(4), 1192–1209 (2002). doi:10.1063/1.1457465 MathSciNetADSGoogle Scholar
  76. G.F. Krymskii, A regular mechanism for the acceleration of charged particles on the front of a shock wave. Dokl. Akad. Nauk SSSR 234, 1306–1308 (1977) ADSGoogle Scholar
  77. R.H. Kurtmullaev, J.E. Nesterikhin, V.I. Pilsky, Shock waves in partially ionized plasma, in Phenomena in Ionized Gases, VIII International Conference (1967), p. 459 Google Scholar
  78. R.K. Kurtmullaev, V.K. Malinovskii, Y.E. Nesterikhin, A.G. Ponomarenko, Excitation of strong collisionless shock waves in a plasma. J. Appl. Mech. Tech. Phys. 6, 68–73 (1965). doi:10.1007/BF00915616 ADSGoogle Scholar
  79. C. Lacombe, A. Mangeney, C. Harvey, J. Scudder, Electron plasma waves upstream of the Earth’s bow shock. J. Geophys. Res. 90, 73–94 (1985). doi:10.1029/JA090iA01p00073 ADSGoogle Scholar
  80. J.M. Laming, Accelerated electrons in Cassiopeia A: an explaination for the hard x-ray tail. Astrophys. J. 546, 1149–1158 (2001) ADSGoogle Scholar
  81. B. Lefebvre, S.J. Schwartz, A.F. Fazakerley, P. Décréau, Electron dynamics and cross-shock potential at the quasi-perpendicular Earth’s bow shock. J. Geophys. Res. 112, 09212 (2007). doi:10.1029/2007JA012277 Google Scholar
  82. B. Lembège, S.N. Walker, P. Savoini, M.A. Balikhin, V. Krasnoselskikh, The spatial sizes of electric and magnetic field gradients in a simulated shock. Adv. Space Res. 24, 109–112 (1999) ADSGoogle Scholar
  83. B. Lembège, J. Giacalone, M. Scholer, T. Hada, M. Hoshino, V. Krasnoselskikh, H. Kucharek, P. Savoini, T. Terasawa, Selected problems in collisionless-shock physics. Space Sci. Rev. 110, 161–226 (2004). doi:10.1023/B:SPAC.0000023372.12232.b7 ADSGoogle Scholar
  84. M.M. Leroy, A. Mangeney, A theory of energization of solar wind electrons by the Earth’s bow shock. Ann. Geophys. 2, 449–456 (1984) ADSGoogle Scholar
  85. M.M. Leroy, D. Winske, C.C. Goodrich, C.S. Wu, K. Papadopoulos, The structure of perpendicular bow shocks. J. Geophys. Res. 87(A7), 5081–5094 (1982). doi:10.1029/JA087iA07p05081 ADSGoogle Scholar
  86. P.C. Liewer, V.K. Decyk, J.M. Dawson, B. Lembège, Numerical studies of electron dynamics in oblique quasi-perpendicular collisionless shock waves. J. Geophys. Res., Atmos. 96(A6), 9455 (1991) ADSGoogle Scholar
  87. W.A. Livesey, C.T. Russell, C.F. Kennel, A comparison of specularly reflected gyrating ion orbits with observed shock foot thicknesses. J. Geophys. Res., Atmos. 89(A8), 6824–6828 (1984) ADSGoogle Scholar
  88. V.V. Lobzin, V.V. Krasnoselskikh, S.J. Schwartz, I. Cairns, B. Lefebvre, P. Décréau, A. Fazakerley, Generation of downshifted oscillations in the electron foreshock: a loss-cone instability. Geophys. Res. Lett. 32, 18101 (2005). doi:10.1029/2005GL023563 ADSGoogle Scholar
  89. V.V. Lobzin, V.V. Krasnoselskikh, J.-M. Bosqued, J.-L. Pinçon, S.J. Schwartz, M. Dunlop, Nonstationarity and reformation of high-Mach-number quasiperpendicular shocks: cluster observations. Geophys. Res. Lett. 34, 5107 (2007). doi:10.1029/2006GL029095 ADSGoogle Scholar
  90. E. Mach, J. Arbes, Einige versuche über totale Reflexion und anomale Dispersion. Ann. Phys. 263, 436–444 (1886). doi:10.1002/andp.18862630307 Google Scholar
  91. E. Mach, P. Salcher, Photographische fixirung der durch Projectile in der Luft eingeleiteten Vorgänge. Ann. Phys. 268, 277–291 (1887). doi:10.1002/andp.18872681008 Google Scholar
  92. S. Matsukiyo, M. Scholer, On microinstabilities in the foot of high Mach number perpendicular shocks. J. Geophys. Res., Space Phys. 111(A6), 6104 (2006). doi:10.1029/2005JA011409 ADSGoogle Scholar
  93. C. Mazelle, B. Lembége, A. Morgenthaler, K. Meziane, T.S. Horbury, V. Génot, E.A. Lucek, I. Dandouras, Self-reformation of the quasi-perpendicular shock: cluster observations, in Twelfth International Solar Wind Conference, vol. 1216 (2010), pp. 471–474. doi:10.1063/1.3395905 Google Scholar
  94. J.D. Means, Use of the three-dimensional covariance matrix in analyzing the polarization properties of plane waves. J. Geophys. Res. 77, 5551–5559 (1972) ADSGoogle Scholar
  95. M.M. Mellott, Subcritical collisionless shock waves, in Washington DC American Geophysical Union Geophysical Monograph Series, vol. 35 (1985), pp. 131–140 Google Scholar
  96. J.J. Mitchell, S.J. Schwartz, U. Auster, Electron cross talk and asymmetric electron distributions near the Earth’s bow shock. Ann. Geophys. 30, 503–513 (2012). doi:10.5194/angeo-30-503-2012 ADSGoogle Scholar
  97. D.L. Morse, W.W. Destler, P.L. Auer, Nonstationary behavior of collisionless shocks. Phys. Rev. Lett. 28, 13–16 (1972). doi:10.1103/PhysRevLett.28.13 ADSGoogle Scholar
  98. N.F. Ness, K.W. Behannon, R.P. Lepping, Y.C. Whang, K.H. Schatten, Magnetic field observations near venus: preliminary results from Mariner 10. Science 183, 1301–1306 (1974). doi:10.1126/science.183.4131.1301 ADSGoogle Scholar
  99. N.F. Ness, M.H. Acuna, R.P. Lepping, J.E.P. Connerney, K.W. Behannon, L.F. Burlaga, F.M. Neubauer, Magnetic field studies by Voyager 1—preliminary results at saturn. Science 212, 211–217 (1981). doi:10.1126/science.212.4491.211 ADSGoogle Scholar
  100. J.A. Newbury, C.T. Russell, Observations of a very thin collisionless shock. Geophys. Res. Lett. 23, 781 (1996). doi:10.1029/96GL00700 ADSGoogle Scholar
  101. J.A. Newbury, C.T. Russell, M. Gedalin, The ramp widths of high-Mach-number, quasi-perpendicular collisionless shocks. J. Geophys. Res., Atmos. 103(A12), 29581–29593 (1998). doi:10.1029/1998JA900024 ADSGoogle Scholar
  102. M. Oka, T. Terasawa, Y. Seki, M. Fujimoto, Y. Kasaba, H. Kojima, I. Shinohara, H. Matsui, H. Matsumoto, Y. Saito, T. Mukai, Whistler critical Mach number and electron acceleration at the bow shock: geotail observation. Geophys. Res. Lett. 33, 24104 (2006). doi:10.1029/2006GL028156 ADSGoogle Scholar
  103. K. Papadopoulos, Electron acceleration in magnetosonic shock fronts. Technical report, 1981 Google Scholar
  104. K. Papadopoulos, Microinstabilities and anomalous transport in collisionless shocks, in Advances in Space Plasma Physics, ed. by W. Grossmann, E.M. Campbell, B. Buti (1985a), p. 289 Google Scholar
  105. K. Papadopoulos, Microinstabilities and anomolous transport, in Collisionless Shocks in the Heliosphere: A Tutorial Review, ed. by R.G. Stone, B.T. Tsurutani Geophysical Monograph, vol. 34 (American Geophysical Union, Washington, 1985b), pp. 59–90 Google Scholar
  106. G. Paschmann, P.W. Daly, Analysis Methods for Multi-spacecraft Data. ISSI Scientific Reports Series sr-001, esa/issi, vol. 1 (1998). ISSN:1608-280x Google Scholar
  107. J.W.M. Paul, L.S. Holmes, M.J. Parkinson, J. Sheffield, Experimental observations on the structure of collisionless shock waves in a magnetized plasma. Nature 208, 133–135 (1965). doi:10.1038/208133a0 ADSGoogle Scholar
  108. J.W.M. Paul, G.C. Goldenbaum, A. Iiyoshi, L.S. Holmes, R.A. Hardcastle, Measurement of electron temperatures produced by collisionless shock waves in a magnetized plasma. Nature 216, 363–364 (1967). doi:10.1038/216363a0 ADSGoogle Scholar
  109. J.-L. Pinçon, K.-H. Glassmeier, Multi-spacecraft methods of wave field characterisation, in ISSI Scientific Reports Series, vol. 8 (2008), pp. 47–54 Google Scholar
  110. J.-L. Pinçon, P.M. Kintner, P.W. Schuck, C.E. Seyler, Observation and analysis of lower hybrid solitary structures as rotating eigenmodes. J. Geophys. Res., Atmos. 102, 17283–17296 (1997) ADSGoogle Scholar
  111. T. Piran, Magnetic fields in gamma-ray bursts: a short overview. in American Institute of Physics Conference Series, vol. 784, ed. by E.M. de Gouveia dal Pino, G. Lugones, A. Lazarian, 2005, pp. 164–174. doi:10.1063/1.2077181 Google Scholar
  112. K.B. Quest, Simulations of high mach number perpendicular shocks with resistive electrons. J. Geophys. Res., Atmos. 91(A8), 8805–8815 (1986) ADSGoogle Scholar
  113. H. Reme, J.M. Bosqued, J.A. Sauvaud, A. Cros, J. Dandouras, C. Aoustin, J. Bouyssou, T. Camus, J. Cuvilo, C. Martz, J.L. Médale, H. Perrier, D. Romefort, J. Rouzaud, D. D’Uston, E. Möbius, K. Crocker, M. Granoff, L.M. Kistler, M. Popecki, D. Hovestadt, B. Klecker, G. Paschmann, M. Scholer, C.W. Carlson, D.W. Curtis, R.P. Lin, J.P. McFadden, V. Formisano, E. Amata, M.B. Bavassano-Cattaneo, P. Baldetti, G. Belluci, R. Bruno, G. Chionchio, A. di Lellis, E.G. Shelley, A.G. Ghielmetti, W. Lennartsson, A. Korth, U. Rosenbauer, R. Lundin, S. Olsen, G.K. Parks, M. McCarthy, H. Balsiger, The cluster ion spectrometry (cis) experiment. Space Sci. Rev. 79, 303–350 (1997) ADSGoogle Scholar
  114. C.T. Russell, On the relative locations of the bow shocks of the terrestrial planets. Geophys. Res. Lett. 4, 387–390 (1977). doi:10.1029/GL004i010p00387 ADSGoogle Scholar
  115. C.T. Russell, Planetary bow shocks, in Washington DC American Geophysical Union Geophysical Monograph Series, vol. 35 (1985), pp. 109–130 Google Scholar
  116. C.T. Russell, M.M. Mellot, E.J. Smith, J.H. King, Multiple spacecraft observations on interplanetary shocks: four spacecraft determination of shock normals. J. Geophys. Res., Atmos. 88, 4739–4748 (1983) ADSGoogle Scholar
  117. R.Z. Sagdeev, Asymptotic methods in the hydrodynamic theory of stability, in Lectures Presented at the Trieste Seminar on Plasma Physics (1965a), p. 625 Google Scholar
  118. R.Z. Sagdeev, Landau damping and finite resistivity instability in plasmas, in Lectures Presented at the Trieste Seminar on Plasma Physics (1965b), p. 555 Google Scholar
  119. R.Z. Sagdeev, Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23 (1966) ADSGoogle Scholar
  120. R.Z. Sagdeyev, “Shock” waves in rarefied plasma, in Ionization Phenomena in Gases, vol. II, ed. by N.R. Nilsson (1960), p. 1081 Google Scholar
  121. J.C. Samson, J.V. Olson, Some comments on the descriptions of the polarization states of waves. Geophys. J. R. Astron. Soc. 61, 115–129 (1980). doi:10.1111/j.1365-246X.1980.tb04308.x MATHGoogle Scholar
  122. M. Scholer, D. Burgess, Transition scale at quasiperpendicular collisionless shocks: full particle electromagnetic simulations. Phys. Plasmas 13(6), 062101 (2006). doi:10.1063/1.2207126 ADSGoogle Scholar
  123. M. Scholer, S. Matsukiyo, Nonstationarity of quasi-perpendicular shocks: a comparison of full particle simulations with different ion to electron mass ratio. Ann. Geophys. 22, 2345–2353 (2004) ADSGoogle Scholar
  124. M. Scholer, I. Shinohara, S. Matsukiyo, Quasi-perpendicular shocks: length scale of the cross-shock potential, shock reformation, and implication for shock surfing. J. Geophys. Res., Space Phys. 108, 1014 (2003). doi:10.1029/2002JA009515 ADSGoogle Scholar
  125. S.J. Schwartz, Shock and discontinuity normals, mach numbers, and related parameters, in ISSI Scientific Reports Series, vol. 1 (1998), pp. 249–270 Google Scholar
  126. S.J. Schwartz, M.F. Thomsen, J.T. Gosling, Ions upstream of the Earth’s bow shock—a theoretical comparison of alternative source populations. J. Geophys. Res. 88, 2039–2047 (1983). doi:10.1029/JA088iA03p02039 ADSGoogle Scholar
  127. S.J. Schwartz, M.F. Thomsen, S.J. Bame, J. Stansberry, Electron heating and the potential jump across fast mode shocks. J. Geophys. Res. 93(A11), 12923–12931 (1988). doi:10.1029/JA093iA11p12923 ADSGoogle Scholar
  128. S.J. Schwartz, E. Henley, J. Mitchell, V. Krasnoselskikh, Electron temperature gradient scale at collisionless shocks. Phys. Rev. Lett. 107(21), 215002 (2011). doi:10.1103/PhysRevLett.107.215002 ADSGoogle Scholar
  129. N. Sckopke, G. Paschmann, S.J. Bame, J.T. Gosling, C.T. Russell, Evolution of ion distributions across the nearly perpendicular bow shock—specularly and non-specularly reflected-gyrating ions. J. Geophys. Res., Atmos. 88(A8), 6121–6136 (1983) ADSGoogle Scholar
  130. J.D. Scudder, A review of the physics of electron heating at collisionless shocks. Adv. Space Res. 15, 181 (1995) ADSGoogle Scholar
  131. J.D. Scudder, A. Mangeney, C. Lacombe, C.C. Harvey, T.L. Aggson, R.R. Anderson, J.T. Gosling, G. Paschmann, C.T. Russell, The resolved layer of a collisionless high β supercritical quasi-perpendicular shock wave, 1: Rankine–Hugoniot geometry currents and stationarity. J. Geophys. Res., Atmos. 91, 11019–11052 (1986a) ADSGoogle Scholar
  132. J.D. Scudder, A. Mangeney, C. Lacombe, C.C. Harvey, T.L. Aggson, The resolved layer of a collisionless high β supercritical quasi-perpendicular shock wave, 2: dissipative fluid electrodynamics. J. Geophys. Res., Atmos. 91, 11053 (1986b) ADSGoogle Scholar
  133. J.D. Scudder, A. Mangeney, C. Lacombe, C.C. Harvey, C.S. Wu, R.R. Anderson, The resolved layer of a collisionless high β supercritical quasi-perpendicular shock wave, 3: Vlasov electrodynamics. J. Geophys. Res., Atmos. 91, 11075 (1986c) ADSGoogle Scholar
  134. V. Smirnov, O. Vaisberg, Evidence of the nonlinear structure at the bow shock front, in Collisionless Shocks, Budapest, ed. by K. Szego (1987), pp. 70–76 Google Scholar
  135. D. Sundkvist, V. Krasnoselskikh, S.D. Bale, S.J. Schwartz, J. Soucek, F. Mozer, Dispersive nature of high mach number collisionless plasma shocks: Poynting flux of oblique whistler waves. Phys. Rev. Lett. 108(2), 025002 (2012). doi:10.1103/PhysRevLett.108.025002 ADSGoogle Scholar
  136. M.F. Thomsen, J.T. Gosling, S.J. Bame, K.B. Quest, D. Winske, On the noncoplanarity of the magnetic field within a fast collisionless shock. J. Geophys. Res., Atmos. 92(A3), 2305–2314 (1987) ADSGoogle Scholar
  137. D.A. Tidman, N.A. Krall, Shockwaves in Collisionless Plasmas (Wiley, New York, 1971) Google Scholar
  138. A. Tjulin, A.I. Eriksson, M. André, Lower hybrid cavities in the inner magnetosphere. Geophys. Res. Lett. 30, 17–21 (2003). doi:10.1029/2003GL016915 Google Scholar
  139. O.L. Vaisberg, A.A. Galeev, G.N. Zastenker, S.I. Klimov, M.N. Nozdrachev, R.Z. Sagdeev, A.I. Sokolov, V.D. Shapiro, Electron acceleration at the front of strong collisionless shock waves. Zh. Èksp. Teor. Fiz. 85, 1232–1243 (1983) ADSGoogle Scholar
  140. O. Vaisberg, S. Klimov, G. Zastenker, M. Nozdrachev, A. Sokolov, V. Smirnov, S. Savin, L. Avanov, Relaxation of plasma at the shock front. Adv. Space Res. 4, 265–275 (1984). doi:10.1016/0273-1177(84)90320-X ADSGoogle Scholar
  141. P. Veltri, G. Zimbardo, Electron whistler interaction at the Earths bow shock, 2: electron pitch-angle diffusion. J. Geophys. Res. 98(A8), 13335–13346 (1993) ADSGoogle Scholar
  142. S.N. Walker, M.A. Balikhin, M.N. Nozdrachev, Ramp nonstationarity and the generation of whistler waves upstream of a strong quasiperpendicular shock. Geophys. Res. Lett. 26(10), 1357–1360 (1999a). doi:10.1029/1999GL900210 ADSGoogle Scholar
  143. S.N. Walker, M.A. Balikhin, H.S.C.K. Alleyne, W. Baumjohann, M. Dunlop, Observations of a very thin shock. Adv. Space Res. 24, 47–50 (1999b) ADSGoogle Scholar
  144. S.N. Walker, M.A. Balikhin, H.S.C.K. Alleyne, Y. Hobara, M. André, M.W. Dunlop, Lower hybrid waves at the shock front: a reassessment. Ann. Geophys. 26, 699–707 (2008). http://www.ann-geophys.net/26/699/2008/ ADSGoogle Scholar
  145. S. Walker, H. Alleyne, M. Balikhin, M. André, T. Horbury, Electric field scales at quasi-perpendicular shocks. Ann. Geophys. 22(7), 2291–2300 (2004). http://www.ann-geophys.net/22/2291/2004/ ADSGoogle Scholar
  146. L.B. Wilson III, A. Koval, A. Szabo, A. Breneman, C.A. Cattell, K. Goetz, P.J. Kellogg, K. Kersten, J.C. Kasper, B.A. Maruca, M. Pulupa, Observations of electromagnetic whistler precursors at supercritical interplanetary shocks. Geophys. Res. Lett. 39, 8109 (2012). doi:10.1029/2012GL051581 ADSGoogle Scholar
  147. L.C. Woods, On the structure of collisionless magneto-plasma shock waves at super-critical Alfvèn-Mach numbers. J. Plasma Phys. 3(3), 435–447 (1969) ADSGoogle Scholar
  148. L.C. Woods, On double-structured, perpendicular, magneto-plasma shock waves. Plasma Phys. 13, 289–302 (1971). doi:10.1088/0032-1028/13/4/302 ADSGoogle Scholar
  149. L.J.C. Woolliscroft, H.S.C. Alleyne, C.M. Dunford, A. Sumner, J.A. Thompson, S.N. Walker, K.H. Yearby, A. Buckley, S. Chapman, M.P. Gough, The digital wave-processing experiment on cluster. Space Sci. Rev. 79, 209–231 (1997) ADSGoogle Scholar
  150. C.S. Wu, A fast Fermi process—energetic electrons accelerated by a nearly perpendicular bow shock. J. Geophys. Res. 89, 8857–8862 (1984). doi:10.1029/JA089iA10p08857 ADSGoogle Scholar
  151. J.R. Wygant, M. Bensadoun, F.S. Mozer, Electric field measurements at subcritical, oblique bow shock crossings. J. Geophys. Res., Atmos. 92(A10), 11109–11121 (1987) ADSGoogle Scholar
  152. G. Zank, H. Pauls, I. Cairns, G. Webb, Interstellar pickup ions and quasi-perpendicular shocks: implications for the termination shock and interplanetary shocks. J. Geophys. Res. 101, 457–477 (1996) ADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • V. Krasnoselskikh
    • 1
  • M. Balikhin
    • 2
  • S. N. Walker
    • 2
  • S. Schwartz
    • 3
  • D. Sundkvist
    • 4
  • V. Lobzin
    • 5
  • M. Gedalin
    • 6
  • S. D. Bale
    • 4
  • F. Mozer
    • 4
  • J. Soucek
    • 7
  • Y. Hobara
    • 8
  • H. Comisel
    • 9
  1. 1.LPC2ECNRS-University of OrleansOrleansFrance
  2. 2.ACSEUniversity of SheffieldSheffieldUK
  3. 3.Blackett LaboratoryImperial College LondonLondonUK
  4. 4.Space Sciences LaboratoryUniversity of CaliforniaBerkeleyUSA
  5. 5.School of PhysicsUniversity of SydneySydneyAustralia
  6. 6.Department of PhysicsBen-Gurion UniversityBeer-ShevaIsrael
  7. 7.Institute of Atmospheric PhysicsAcademy of Sciences of the Czech RepublicPragueCzech Republic
  8. 8.Research Center of Space Physics and Radio EngineeringUniversity of Electro-CommunicationsTokyoJapan
  9. 9.Institute for Space SciencesBucharestRomania

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