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The Dynamic Quasiperpendicular Shock: Cluster Discoveries

  • Chapter
Microphysics of Cosmic Plasmas

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.

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References

  • J.H. Adlam, J.E. Allen, The structure of strong collision-free hydromagnetic waves. Philos. Mag. 3, 448–455 (1958). doi:10.1080/14786435808236833

    ADS  MATH  Google Scholar 

  • 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 

  • 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

  • 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 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • A.R. Bell, The acceleration of cosmic rays in shock fronts, I. Mon. Not. R. Astron. Soc. 182, 147–156 (1978a)

    ADS  Google Scholar 

  • A.R. Bell, The acceleration of cosmic rays in shock fronts, II. Mon. Not. R. Astron. Soc. 182, 443–455 (1978b)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • R.D. Blandford, J.P. Ostriker, Particle acceleration by astrophysical shocks. Astrophys. J. Lett. 221, 29–32 (1978). doi:10.1086/182658

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • F.V. Coroniti, Dissipation discontinuities in hydromagnetic shock waves. J. Plasma Phys. 4, 265 (1970)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  MATH  Google Scholar 

  • F. de Hoffmann, E. Teller, Magneto-hydrodynamic shocks. Phys. Rev. 80, 692–703 (1950). doi:10.1103/PhysRev.80.692

    ADS  MATH  MathSciNet  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • C.P. Escoubet, R. Schmidt, M.L. Goldstein, Cluster—science and mission overview. Space Sci. Rev. 79, 11–32 (1997)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • V. Formisano, Measurement of the potential drop across the Earth’s collisionless bow shock. Geophys. Res. Lett. 9, 1033 (1982)

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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 

  • A.A. Galeev, R.N. Sudan, Basic Plasma Physics. Selected Chapters. Handbook of Plasma Physics, vols. 1 and 2 (1989)

    Google Scholar 

  • 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 

  • 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 

  • M. Gedalin, Ion reflection at the shock front revisited. J. Geophys. Res. 101, 4871 (1996). doi:10.1029/95JA03669

    ADS  Google Scholar 

  • M. Gedalin, Ion heating in oblique low-Mach number shocks. Geophys. Res. Lett. 24, 2511 (1997)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • J.P. Heppner, N.C. Maynard, T.L. Aggson, Early results from isee-1 electric field measurements. Space Sci. Rev. 22, 777–789 (1978)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • V. Krasnoselskikh, Nonlinear motions of a plasma across a magnetic field. Sov. Phys. JETP 62, 282–294 (1985)

    Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  MathSciNet  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • J.M. Laming, Accelerated electrons in Cassiopeia A: an explaination for the hard x-ray tail. Astrophys. J. 546, 1149–1158 (2001)

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • M.M. Mellott, Subcritical collisionless shock waves, in Washington DC American Geophysical Union Geophysical Monograph Series, vol. 35 (1985), pp. 131–140

    Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • J.A. Newbury, C.T. Russell, Observations of a very thin collisionless shock. Geophys. Res. Lett. 23, 781 (1996). doi:10.1029/96GL00700

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • K. Papadopoulos, Electron acceleration in magnetosonic shock fronts. Technical report, 1981

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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 

  • K.B. Quest, Simulations of high mach number perpendicular shocks with resistive electrons. J. Geophys. Res., Atmos. 91(A8), 8805–8815 (1986)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • C.T. Russell, Planetary bow shocks, in Washington DC American Geophysical Union Geophysical Monograph Series, vol. 35 (1985), pp. 109–130

    Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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 

  • 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 

  • R.Z. Sagdeev, Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23 (1966)

    ADS  Google Scholar 

  • 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 

  • 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

    MATH  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • J.D. Scudder, A review of the physics of electron heating at collisionless shocks. Adv. Space Res. 15, 181 (1995)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • D.A. Tidman, N.A. Krall, Shockwaves in Collisionless Plasmas (Wiley, New York, 1971)

    Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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/

    ADS  Google Scholar 

  • 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/

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

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Krasnoselskikh, V. et al. (2013). The Dynamic Quasiperpendicular Shock: Cluster Discoveries. In: Balogh, A., Bykov, A., Cargill, P., Dendy, R., Dudok de Wit, T., Raymond, J. (eds) Microphysics of Cosmic Plasmas. Space Sciences Series of ISSI, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7413-6_18

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