Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-14T21:32:11.616Z Has data issue: false hasContentIssue false
  • English
  • Français

Collisionless relaxation of non-gyrotropic downstream ion distributions: dependence on shock parameters

Published online by Cambridge University Press:  12 October 2015

M. Gedalin
M. Gedalin*
Affiliation:
Department of Physics, Ben-Gurion University, Beer-Sheva 8410501, Israel
*
†Email address for correspondence: gedalin@bgu.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

Upon crossing the shock front, ions begin to gyrate. The ion distribution just behind the ramp is manifestly non-gyrotropic. The gyration of the ion distribution as a whole results in spatially periodic oscillations of the ion pressure. The magnetic pressure must oscillate in the opposite phase to ensure the maintenance of the pressure balance throughout the shock front. The ion non-gyrotropy and the pressure oscillations gradually damp due to the collisionless gyrophase mixing. The rate of this relaxation depends on the basic shock parameters. The most influential are the angle between the shock normal and the magnetic field, the upstream ion temperature and the magnetic compression.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810603
Copyright
© Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bale, S. D., Balikhin, M. A., Horbury, T. S., Krasnoselskikh, V. V., Kucharek, H., Möbius, E., Walker, S. N., Balogh, A., Burgess, D., Lembège, B. et al. 2005 Quasi-perpendicular shock structure and processes. Space Sci. Rev. 118 (1), 161–203.CrossRefGoogle Scholar
Bale, S. D., Hull, A., Larson, D. E., Lin, R. P., Muschietti, L., Kellogg, P. J., Goetz, K. & Monson, S. J. 2002 Electrostatic turbulence and Debye-scale structures associated with electron thermalization at collisionless shocks. Astrophys. J. 575 (1), L25–L28.Google Scholar
Bale, S. & Mozer, F. 2007 Measurement of large parallel and perpendicular electric fields on electron spatial scales in the terrestrial bow shock. Phys. Rev. Lett. 98, 205001.Google Scholar
Balikhin, M. A., Zhang, T. L., Gedalin, M., Ganushkina, N. Y & Pope, S. A. 2008 Venus Express observes a new type of shock with pure kinematic relaxation. Geophys. Res. Lett. 35 (1), 01103.Google Scholar
Burgess, D. 1987 Simulations of backstreaming ion beams formed at oblique shocks by direct reflection. Ann. Geophys. 5, 133–145.Google Scholar
Burgess, D. 2006 Interpreting multipoint observations of substructure at the quasi-perpendicular bow shock: simulations. J. Geophys. Res. 111, 10210.Google Scholar
Burgess, D., Lucek, E. A., Scholer, M., Bale, S. D., Balikhin, M. A., Balogh, A., Horbury, T. S., Krasnoselskikh, V. V., Kucharek, H., Lembège, B. et al. 2005 Quasi-parallel shock structure and processes. Space Sci. Rev. 118 (1), 205–222.Google Scholar
Burgess, D. & Scholer, M. 2007 Shock front instability associated with reflected ions at the perpendicular shock. Phys. Plasmas 14 (1), 012108.Google Scholar
Burgess, D. & Scholer, M. 2013 Microphysics of quasi-parallel shocks in collisionless plasmas. Space Sci. Rev. 178 (2–4), 513–533.Google Scholar
Burgess, D., Wilkinson, W. P. & Schwartz, S. J. 1989 Ion distributions and thermalization at perpendicular and quasi-perpendicular supercritical collisionless shocks. J. Geophys. Res. 94, 8783–8792.Google Scholar
Dasgupta, B., Burrows, R., Zank, G. P. & Webb, G. M. 2006 Hydrodynamics of shock waves with reflected particles. I. Rankine–Hugoniot relations and stationary solutions. Phys. Plasmas 13 (8), 082112.Google Scholar
Dimmock, A. P., Balikhin, M. A., Krasnoselskikh, V. V., Walker, S. N., Bale, S. D. & Hobara, Y. 2012 A statistical study of the cross-shock electric potential at low Mach number, quasi-perpendicular bow shock crossings using Cluster data. J. Geophys. Res. A 117, 02210.Google Scholar
Farris, M., Russell, C. & Thomsen, M 1993 Magnetic structure of the low beta, quasi-perpendicular shock. J. Geophys. Res. 98, 15285–15294.Google Scholar
Gedalin, M. 1996 Transmitted ions and ion heating in nearly perpendicular low-Mach number shocks. J. Geophys. Res. 101, 15569–15578.Google Scholar
Gedalin, M. 1997a Ion dynamics and distribution at the quasiperpendicular collisionless shock front. Surv. Geophys. 18, 541–566.Google Scholar
Gedalin, M. 1997b Ion heating in oblique low-Mach number shocks. Geophys. Res. Lett. 24 (2), 2511–2514.Google Scholar
Gedalin, M. 1998 Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description. Phys. Plasmas 5 (1), 127–132.Google Scholar
Gedalin, M. & Balikhin, M. 2008 Rankine–Hugoniot relations for shocks with demagnetized ions. J. Plasma Phys. 74 (0), 207–214.Google Scholar
Gedalin, M. & Dröge, W. 2013 Ion dynamics in quasi-perpendicular collisionless interplanetary shocks: a case study. Front. Phys. 1, 29.Google Scholar
Gedalin, M., Dröge, W. & Kartavykh, Y. Y. 2015a Scatttering of high-energy particles at a collisionless shock front: dependence on the shock angle. Astrophys. J. 807 (2), 126.Google Scholar
Gedalin, M., Friedman, Y. & Balikhin, M. 2015b Collisionless relaxation of downstream ion distributions in low-Mach number shocks. Phys. Plasmas 22, 072301.Google Scholar
Gedalin, M., Liverts, M. & Balikhin, M. A. 2008 Distribution of escaping ions produced by non-specular reflection at the stationary quasi-perpendicular shock front. J. Geophys. Res. 113, 05101.Google Scholar
Gedalin, M., Newbury, J. A. & Russell, C. T. 1998 Shock profile analysis using wavelet transform. J. Geophys. Res. 103, 6503–6511.Google Scholar
Greenstadt, E. W., Coroniti, F. V., Moses, S. L., Tsurutani, B. T., Omidi, N., Quest, K. B. & Krauss-Varban, D. 1991 Weak, quasiparallel profiles of Earth’s bow shock – a comparison between numerical simulations and ISEE 3 observations on the far flank. Geophys. Res. Lett. 18, 2301–2304.Google Scholar
Greenstadt, E. W., Scarf, F. L., Russell, C. T., Formisano, V. & Neugebauer, M. 1975 Structure of the quasi-perpendicular laminar bow shock. J. Geophys. Res. 80, 502–514.Google Scholar
Hobara, Y., Balikhin, M., Krasnoselskikh, V., Gedalin, M. & Yamagishi, H. 2010 Statistical study of the quasi-perpendicular shock ramp widths. J. Geophys. Res. 115, 11106.Google Scholar
Hull, A. J., Larson, D. E., Wilber, M., Scudder, J. D., Mozer, F. S., Russell, C. T. & Bale, S. D. 2006 Large-amplitude electrostatic waves associated with magnetic ramp substructure at Earth’s bow shock. Geophys. Res. Lett. 33 (15), 4.Google Scholar
Kajdič, P., Blanco-Cano, X., Aguilar-Rodriguez, E., Russell, C. T., Jian, L. K. & Luhmann, J. G. 2012 Waves upstream and downstream of interplanetary shocks driven by coronal mass ejections. J. Geophys. Res. 117 (A6), A06103.Google Scholar
Kennel, C. F., Edmiston, J. P., Russell, C. T., Scarf, F. L., Coroniti, F. V., Smith, E. J., Tsurutani, B. T., Scudder, J. D., Feldman, W. C. & Anderson, R. R. 1984 Structure of the November 12, 1978, quasi-parallel interplanetary shock. J. Geophys. Res. 89, 5436–5452.CrossRefGoogle Scholar
Krasnoselskikh, V., Balikhin, M., Walker, S. N., Schwartz, S., Sundkvist, D., Lobzin, V., Gedalin, M., Bale, S. D., Mozer, F., Soucek, J. et al. 2013 The dynamic quasiperpendicular shock: Cluster discoveries. Space Sci. Rev. 178, 535–598.Google Scholar
Krasnoselskikh, V., Lembège, B., Savoini, P. & Lobzin, V. 2002 Nonstationarity of strong collisionless quasiperpendicular shocks: theory and full particle numerical simulations. Phys. Plasmas 9, 1192–1209.Google Scholar
Lembège, B., Savoini, P., Hellinger, P. & Trávníček, P. M. 2009 Nonstationarity of a two-dimensional perpendicular shock: competing mechanisms. J. Geophys. Res. 114, 3217.Google Scholar
Leroy, M. M. 1983 Structure of perpendicular shocks in collisionless plasma. Phys. Fluids 26, 2742–2753.Google Scholar
Li, X., Lewis, H. R., LaBelle, J. & Phan, T. D. 1995 Characteristics of the ion pressure tensor in the Earth’s magnetosheath. Geophys. Res. Lett. 22, 667–670.Google Scholar
Lobzin, V. V., Krasnoselskikh, V. V., Bosqued, J.-M., Pinçon, J.-L., Schwartz, S. J. & Dunlop, M. 2007 Nonstationarity and reformation of high-Mach-number quasiperpendicular shocks: Cluster observations. Geophys. Res. Lett. 34 (5), 6.Google Scholar
Lobzin, V. V., Krasnoselskikh, V. V., Musatenko, K. & de Wit, T. Dudok 2008 On nonstationarity and rippling of the quasiperpendicular zone of the Earth bow shock: cluster observations. Ann. Geophys. 26, 2899.Google Scholar
Lowe, R. & Burgess, D. 2003 The properties and causes of rippling in quasi-perpendicular collisionless shock fronts. Ann. Geophys. 21, 671–679.Google Scholar
Mandt, M. E., Kan, J. R. & Russell, C. T. 1986 Comparison of magnetic field structures in quasi-parallel interplanetary shocks: observations versus simulations. J. Geophys. Res. 91, 8981–8985.Google Scholar
Mellott, M. M. & Greenstadt, E. W. 1984 The structure of oblique subcritical bow shocks – ISEE 1 and 2 observations. J. Geophys. Res. 89, 2151–2161.Google Scholar
Moullard, O., Burgess, D., Horbury, T. S. & Lucek, E. A. 2006 Ripples observed on the surface of the Earth’s quasi-perpendicular bow shock. J. Geophys. Res. 111, A09113.Google Scholar
Neugebauer, M. 2013 Propagating shocks. Space Sci. Rev. 176, 125–132.Google Scholar
Newbury, J. A., Russell, C. T. & Gedalin, M. 1998 The ramp widths of high-Mach-number, quasi-perpendicular collisionless shocks. J. Geophys. Res. 103, 29581–29594.CrossRefGoogle Scholar
Ofman, L., Balikhin, M., Russell, C. T. & Gedalin, M. 2009 Collisionless relaxation of ion distributions downstream of laminar quasi-perpendicular shocks. J. Geophys. Res. 114, 09106.Google Scholar
Ofman, L. & Gedalin, M. 2013 Two-dimensional hybrid simulations of quasi-perpendicular collisionless shock dynamics: gyrating downstream ion distributions. J. Geophys. Res. 118, 1828–1836.Google Scholar
Russell, C. T., Hoppe, M. M., Livesey, W. A., Gosling, J. T. & Bame, S. J. 1982 ISEE-1 and -2 observations of laminar bow shocks – velocity and thickness. Geophys. Res. Lett. 9, 1171–1174.Google Scholar
Russell, C. T., Jian, L. K., Blanco-Cano, X. & Luhmann, J. G. 2009 STEREO observations of upstream and downstream waves at low Mach number shocks. Geophys. Res. Lett. 36, 03106.Google Scholar
Scholer, M. 1993 Upstream waves, shocklets, short large-amplitude magnetic structures and the cyclic behavior of oblique quasi-parallel collisionless shocks. J. Geophys. Res. 98, 47–57.Google Scholar
Scholer, M. & Fujimoto, M. 1993 Low-Mach number quasi-parallel shocks – upstream waves. J. Geophys. Res. 98, 15275–15283.Google Scholar
Scholer, M., Fujimoto, M. & Kucharek, H. 1993 Two-dimensional simulations of supercritical quasi-parallel shocks: upstream waves, downstream waves, and shock re-formation. J. Geophys. Res. 98, 18971–18984.Google Scholar
Scholer, M., Kucharek, H. & Shinohara, I. 2003 Short large-amplitude magnetic structures and whistler wave precursors in a full-particle quasi-parallel shock simulation. J. Geophys. Res. 108, 1273–1273.Google Scholar
Schwartz, S. J. & Burgess, D. 1991 Quasi-parallel shocks – a patchwork of three-dimensional structures. Geophys. Res. Lett. 18, 373–376.CrossRefGoogle Scholar
Schwartz, S. J., Henley, E., Mitchell, J. & Krasnoselskikh, V. 2011 Electron temperature gradient scale at collisionless shocks. Phys. Rev. Lett. 107, 215002.Google Scholar
Schwartz, S. J., Thomsen, M. F., Bame, S. J. & Stansberry, J. 1988 Electron heating and the potential jump across fast mode shocks. J. Geophys. Res. 93, 12923–12931.CrossRefGoogle Scholar
Sckopke, N., Paschmann, G., Bame, S. J., Gosling, J. T. & Russell, C. T. 1983 Evolution of ion distributions across the nearly perpendicular bow shock – specularly and non-specularly reflected-gyrating ions. J. Geophys. Res. 88, 6121–6136.Google Scholar
Sckopke, N., Paschmann, G., Brinca, A. L., Carlson, C. W. & Luehr, H. 1990 Ion thermalization in quasi-perpendicular shocks involving reflected ions. J. Geophys. Res. 95, 6337–6352.Google Scholar
Scudder, J. D., Aggson, T. L., Mangeney, A., Lacombe, C. & Harvey, C. C. 1986 The resolved layer of a collisionless, high beta, supercritical, quasi-perpendicular shock wave. I – Rankine–Hugoniot geometry, currents, and stationarity. J. Geophys. Res. 91, 11019–11052.Google Scholar
Thomsen, M. F., Gosling, J. T., Bame, S. J. & Russell, C. T. 1990 Magnetic pulsations at the quasi-parallel shock. J. Geophys. Res. 95, 957–966.CrossRefGoogle Scholar
Woods, L. 1971 On double-structured, perpendicular, magneto-plasma shock waves. Plasma Phys. 13, 289–302.Google Scholar
Yang, Z. W., Lembège, B. & Lu, Q. M. 2011 Impact of the nonstationarity of a supercritical perpendicular collisionless shock on the dynamics and energy spectra of pickup ions. J. Geophys. Res. 116, 08216.Google Scholar
Yang, Z. W., Lembège, B. & Lu, Q. M. 2012 Impact of the rippling of a perpendicular shock front on ion dynamics. J. Geophys. Res. 117, A07222.Google Scholar
Zilbersher, D., Gedalin, M., Newbury, J. A. & Russell, C. T. 1998 Direct numerical testing of stationary shock model with low Mach number shock observations. J. Geophys. Res. 103, 26775–26782.Google Scholar