Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-11T06:29:25.104Z Has data issue: false hasContentIssue false
  • English
  • Français

Whistler precursor and intrinsic variability of quasi-perpendicular shocks

Part of: Focus on Space Plasmas

Published online by Cambridge University Press:  15 February 2018

Gilad Granit  and
Michael Gedalin Open the ORCID record for Michael Gedalin [Opens in a new window]
Gilad Granit
Affiliation:
Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Michael Gedalin*
Affiliation:
Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
*
†Email address for correspondence: gedalin@bgu.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

The structure of a whistler precursor in a quasi-perpendicular shock is studied within two-fluid approach in one-dimensional case. The complete set of equations is reduced to the KdV equation, if no dissipation is included. With a phenomenological resistive dissipation the structure is described with the KdV–Burgers equation. The shock profile is intrinsically time dependent. For sufficiently strong dissipation, temporal evolution of a steepening profile results in generation of a stationary decaying whistler ahead of the shock front. With the decrease of the dissipation parameter, whistler wave trains begin to detach and propagate toward the upstream and the ramp is weakly time dependent. In the weakly dissipative regime the shock front experiences reformation.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 1 , February 2018 , 905840113
Copyright
© Cambridge University Press 2018 

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

Ablowitz, M. J. 2011 Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons. Cambridge University Press.Google Scholar
Ablowitz, M. J. & Baldwin, D. E. 2013 Dispersive shock wave interactions and asymptotics. Phys. Rev. E 87, 022906.Google Scholar
Ablowitz, M. J., Baldwin, D. E. & Hoefer, M. A. 2009 Soliton generation and multiple phases in dispersive shock and rarefaction wave interaction. Phys. Rev. E 80, 016603.Google Scholar
Ascher, U. M. 2008 Numerical Methods for Evolutionary Differential Equations. SIAM.Google Scholar
Balikhin, M. A., Pokhotelov, O. A., Walker, S. N. & André, M. 2003 Identification of low frequency waves in the vicinity of the terrestrial bow shock. Planet. Space Sci. 51, 693–702.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, L01103.Google Scholar
Blanco-Cano, X., Kajdič, P., Aguilar-Rodriguez, E., Russell, C. T., Jian, L. K. & Luhmann, J. G. 2013 STEREO interplanetary shocks and foreshocks. In SOLAR WIND 13: Proceedings of the Thirteenth International Solar Wind Conference. AIP Conference Proceedings, pp. 131–134. AIP, Instituto de Geofísica, UNAM, CU, Coyoacán 04510 DF, Mexico.Google Scholar
Blanco-Cano, X., Kajdič, P., Aguilar-Rodriguez, E., Russell, C. T., Jian, L. K. & Luhmann, J. G. 2016 Interplanetary shocks and foreshocks observed by STEREO during 2007–2010. J. Geophys. Res. 121, 992–1008.Google Scholar
Blanco-Cano, X., Omidi, N. & Russell, C. T. 2006 Macrostructure of collisionless bow shocks: 2. ULF waves in the foreshock and magnetosheath. J. Geophys. Res. 111, 10205.Google Scholar
Burgess, D. & Scholer, M. 2007 Shock front instability associated with reflected ions at the perpendicular shock. Phys. Plasmas 14, 012108.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. 1993 Nonlinear waves in two-fluid hydrodynamics. Phys. Fluids B 5, 2062–207s.Google Scholar
Gedalin, M. 1994 Nonlinear waves in hot magnetized plasma. Phys. Plasmas 1, 1159–1167.Google Scholar
Gedalin, M. 1998 Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description. Phys. Plasmas 5, 127–132.Google Scholar
Gedalin, M., Friedman, Y. & Balikhin, M. 2015a Collisionless relaxation of downstream ion distributions in low-Mach number shocks. Phys. Plasmas 22, 072301.Google Scholar
Gedalin, M., Kushinsky, Y. & Balikhin, M. 2015b Profile of a low-Mach-number shock in two-fluid plasma theory. Ann. Geophys. 33, 1011–1017.Google Scholar
Gingell, I., Schwartz, S. J., Burgess, D., Johlander, A., Russell, C. T., Burch, J. L., Ergun, R. E., Fuselier, S., Gershman, D. J., Giles, B. L. et al. 2017 MMS observations and hybrid simulations of surface ripples at a marginally quasi-parallel shock. J. Geophys. Res. 77, 736.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
Gurevich, A. V. & Pitayevsky, L. P. 1974 Nonstationary structure of a collisionless shock wave. Sov. Phys. JETP 38, 291–297.Google Scholar
Hull, A. J., Muschietti, L., Oka, M., Larson, D. E., Mozer, F. S., Chaston, C. C., Bonnell, J. W. & Hospodarsky, G. B. 2012 Multiscale whistler waves within Earth’s perpendicular bow shock. J. Geophys. Res. 117, A12104.Google Scholar
Jeffrey, A. & Kakutani, T. 1972 Weak nonlinear dispersive waves: a discussion centered around the Korteweg-de Vries equation. SIAM Rev. 14 (4), 582–643.Google Scholar
Jeffrey, A. & Mohamad, M. N. B. 1991 Exact solutions to the KdV–Burgers’ equation. Wave Motion 14, 369–375.Google Scholar
Johlander, A., Schwartz, S. J., Vaivads, A., Khotyaintsev, Y. V., Gingell, I., Peng, I. B., Markidis, S., Lindqvist, P. A., Ergun, R. E., Marklund, G. T. et al. 2016 Rippled quasiperpendicular shock observed by the magnetospheric multiscale spacecraft. Phys. Rev. Lett. 117, 165101.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, A06103.Google Scholar
Karpman, V. I. 1975 Non-Linear Waves in Dispersive Media. Pergamon Press.Google Scholar
Kassam, A.-K. & Trefethen, L. N. 2005 Fourth-order time-stepping for stiff PDEs. SIAM J. Sci. Comput. 26 (4), 1214–1233.Google Scholar
Kennel, C. F., Edmiston, J. P. & Hada, T. 1985 A quarter century of collisionless shock research. In Collisionless Shocks in the Heliosphere: A Tutorial Review, Geophysical Monograph Series, vol. 34, pp. 1–36. American Geophysical Union.Google Scholar
Krasnoselskikh, V., Balikhin, M. & Walker, S. N. 2013 The dynamic quasiperpendicular shock: cluster discoveries. Space Sci. Rev. 178, 535–598.Google Scholar
Krasnoselskikh, V. V., Lembège, B., Savoini, P. & Lobzin, V. 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, A03217.Google Scholar
Lobzin, V. V., Krasnoselskikh, V. V., Musatenko, K. & de Wit, T. D. 2008 On nonstationarity and rippling of the quasiperpendicular zone of the earth bow shock: cluster observations. Ann. Geophys. 26, 2899–2910.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
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
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
Oka, M., Wilson, L. B. I., Phan, T. D., Hull, A. J., Amano, T., Hoshino, M., Argall, M. R., Le Contel, O., Agapitov, O., Gershman, D. J. et al. 2017 Electron scattering by high-frequency whistler waves at earth’s bow shock. Astrophys. J. Lett. 842, L11.Google Scholar
Ramírez Vélez, J. C., Blanco-Cano, X., Aguilar-Rodriguez, E., Russell, C. T., Kajdič, P., Jian, L. K. & Luhmann, J. G. 2012 Whistler waves associated with weak interplanetary shocks. J. Geophys. Res. 117, A11103.Google Scholar
Riquelme, M. A. & Spitkovsky, A. 2011 Electron injection by whistler waves in non-relativistic shocks. Astrophys. J. 733, 63.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
Sagdeev, R. Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23.Google Scholar
Scholer, M. & Burgess, D. 2007 Whistler waves, core ion heating, and nonstationarity in oblique collisionless shocks. Phys. Plasmas 14, 072103.Google Scholar
Sulaiman, A. H., Masters, A., Dougherty, M. K., Burgess, D., Fujimoto, M. & Hospodarsky, G. B. 2015 Quasiperpendicular high Mach number shocks. Phys. Rev. Lett. 115, 125001.Google Scholar
Walker, S. N., Balikhin, M. A. & Nozdrachev, M. N. 1999 Ramp nonstationarity and the generation of whistler waves upstream of a strong quasiperpendicular shock. Geophys. Res. Lett. 26, 1357–1360.Google Scholar
Wilson, L. B., Cattell, C., Kellogg, P. J., Goetz, K., Kersten, K., Hanson, L., MacGregor, R. & Kasper, J. C. 2007 Waves in interplanetary shocks: a Wind/WAVES study. Phys. Rev. Lett. 99, 041101-4.Google Scholar
Wilson, L. B., Sibeck, D. G., Breneman, A. W., Contel, O. L., Cully, C., Turner, D. L., Angelopoulos, V. & Malaspina, D. M. 2014 Quantified energy dissipation rates in the terrestrial bow shock: 2. Waves and dissipation. J. Geophys. Res. 119, 6475–6495.Google Scholar
Wilson, L. B. I., Cattell, C. A., Kellogg, P. J., Goetz, K., Kersten, K., Kasper, J. C., Szabo, A. & Meziane, K. 2009 Low-frequency whistler waves and shocklets observed at quasi-perpendicular interplanetary shocks. J. Geophys. Res. 114, A10106.Google Scholar
Wilson III, L. B., Koval, A., Szabo, A., Stevens, M. L., Kasper, J. C., Cattell, C. A. & Krasnoselskikh, V. V. 2017 Revisiting the structure of low-Mach number, low-beta, quasi-perpendicular shocks. J. Geophys. Res. 81, 2097.Google Scholar
Wilson, L. B. I., Koval, A., Szabo, A., Breneman, A., Cattell, C. A., Goetz, K., Kellogg, P. J., Kersten, K., Kasper, J. C., Maruca, B. A. et al. 2012 Observations of electromagnetic whistler precursors at supercritical interplanetary shocks. Geophys. Res. Lett. 39, L08109.Google Scholar
Supplementary material: File

Granit and Gedalin supplementary material

Granit and Gedalin supplementary material 1

Download Granit and Gedalin supplementary material(File)
File 3.1 MB