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Density jump for parallel and perpendicular collisionless shocks

Published online by Cambridge University Press:  14 April 2020

Antoine Bret Open the ORCID record for Antoine Bret [Opens in a new window]  and
Ramesh Narayan Open the ORCID record for Ramesh Narayan [Opens in a new window]
Antoine Bret*
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, 13071Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071Ciudad Real, Spain
Ramesh Narayan
Affiliation:
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA02138, USA
*
Author for correspondence: Antoine Bret, Universidad de Castilla-La Mancha, ETSI INDUSTRIALES, Avda Camilo José Cela s/n, 13071Ciudad Real, Spain. E-mail: [email protected]
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Abstract

In a collisionless shock, there are no binary collisions to isotropize the flow. It is therefore reasonable to ask to which extent the magnetohydrodynamics (MHD) jump conditions apply. Following up on recent works which found a significant departure from MHD in the case of parallel collisionless shocks, we here present a model allowing to compute the density jump for collisionless shocks. Because the departure from MHD eventually stems from a sustained downstream anisotropy that the Vlasov equation alone cannot specify, we hypothesize a kinetic history for the plasma, as it crosses the shock front. For simplicity, we deal with non-relativistic pair plasmas. We treat the cases of parallel and perpendicular shocks. Non-MHD behavior is more pronounced for the parallel case where, according to MHD, the field should not affect the shock at all.

Keywords

Collisionless shocksmagnetohydrodynamicsplasma instabilitiesRankine–Hugoniot
Type
Research Article
Information
Laser and Particle Beams , Volume 38 , Issue 2 , June 2020 , pp. 114 - 120
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Bale, SD, Mozer, FS and Horbury, TS (2003) Density-transition scale at quasiperpendicular collisionless shocks. Physical Review Letters 91, 265004.10.1103/PhysRevLett.91.265004CrossRefGoogle ScholarPubMed
Bale, SD, Kasper, JC, Howes, GG, Quataert, E, Salem, C and Sundkvist, D (2009) Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Physical Review Letters 103, 211101.10.1103/PhysRevLett.103.211101CrossRefGoogle ScholarPubMed
Bret, A (2016) Particles trajectories in Weibel magnetic filaments with a flow-aligned magnetic field. Journal of Plasma Physics 82, 905820403.CrossRefGoogle Scholar
Bret, A and Narayan, R (2018) Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas. Journal of Plasma Physics 84, 905840604.CrossRefGoogle Scholar
Bret, A, Stockem, A, Fiúza, F, Pérez Álvaro, E, Ruyer, C, Narayan, R and Silva, LO (2013 a) The formation of a collisionless shock. Laser and Particle Beams 31, 487–491.CrossRefGoogle Scholar
Bret, A, Stockem, A, Fiuza, F, Ruyer, C, Gremillet, L, Narayan, R and Silva, LO (2013 b) Collisionless shock formation, spontaneous electromagnetic fluctuations, and streaming instabilities. Physics of Plasmas 20, 042102.10.1063/1.4798541CrossRefGoogle Scholar
Bret, A, Stockem, A, Narayan, R and Silva, LO (2014) Collisionless Weibel shocks: full formation mechanism and timing. Physics of Plasmas 21, 072301.CrossRefGoogle Scholar
Bret, A, Stockem Novo, A, Narayan, R, Ruyer, C, Dieckmann, ME and Silva, LO (2016) Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas. Laser and Particle Beams 34, 362–367.CrossRefGoogle Scholar
Bret, A, Pe'er, A, Sironi, L, Dieckmann, ME and Narayan, R (2017 a) Departure from MHD prescriptions in shock formation over a guiding magnetic field. Laser and Particle Beams 35, 513–519.10.1017/S0263034617000519CrossRefGoogle Scholar
Bret, A, Pe'er, A, Sironi, L, Sa̧dowski, A and Narayan, R (2017 b) Kinetic inhibition of magnetohydrodynamics shocks in the vicinity of a parallel magnetic field. Journal of Plasma Physics 83, 715830201.CrossRefGoogle Scholar
Chew, GF, Goldberger, ML and Low, FE (1956) The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 236, 112–118.Google Scholar
Feynman, R, Leighton, R and Sands, M (1963) The Feynman Lectures on Physics. The Feynman Lectures on Physics No. 2. Reading, Massachusetts: Pearson/Addison-Wesley.Google Scholar
Gary, S (1993) Theory of Space Plasma Microinstabilities. Cambridge Atmospheric and Space Science Series. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Gary, SP and Karimabadi, H (2009) Fluctuations in electron-positron plasmas: linear theory and implications for turbulence. Physics of Plasmas 16, 042104.CrossRefGoogle Scholar
Gerbig, D and Schlickeiser, R (2011) Jump conditions for relativistic magnetohydrodynamic shocks in a gyrotropic plasma. The Astrophysical Journal 733, 32.CrossRefGoogle Scholar
Guo, X, Sironi, L and Narayan, R (2017) Electron heating in low-Mach-number perpendicular shocks. I. Heating mechanism. The Astrophysical Journal 851, 134.10.3847/1538-4357/aa9b82CrossRefGoogle Scholar
Guo, X, Sironi, L and Narayan, R (2018) Electron heating in low Mach number perpendicular shocks. II. Dependence on the pre-shock conditions. The Astrophysical Journal 858, 95.10.3847/1538-4357/aab6adCrossRefGoogle Scholar
Karimabadi, H, Krauss-Varban, D and Omidi, N (1995) Temperature anisotropy effects and the generation of anomalous slow shocks. Geophysical Research Letters 22, 2689–2692.10.1029/95GL02788CrossRefGoogle Scholar
Kulsrud, RM (2005) Plasma Physics for Astrophysics. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Landau, LD and Lifshitz, EM (1981) Course of Theoretical Physics, Physical Kinetics, vol. 10 Oxford: Elsevier.Google Scholar
Lichnerowicz, A (1976) Shock waves in relativistic magnetohydrodynamics under general assumptions. Journal of Mathematical Physics 17, 2135–2142.CrossRefGoogle Scholar
Maruca, BA, Kasper, JC and Bale, SD (2011) What are the relative roles of heating and cooling in generating solar wind temperature anisotropies? Physical Review Letters 107, 201101.CrossRefGoogle ScholarPubMed
Miceli, M, Orlando, S, Burrows, DN, Frank, KA, Argiroffi, C, Reale, F, Peres, G, Petruk, O and Bocchino, F (2019) Collisionless shock heating of heavy ions in SN 1987A. Nature Astronomy 3, 236–241.CrossRefGoogle Scholar
Niemiec, J, Pohl, M, Bret, A and Wieland, V (2012) Nonrelativistic parallel shocks in unmagnetized and weakly magnetized plasmas. The Astrophysical Journal 759, 73.CrossRefGoogle Scholar
Plotnikov, I, Grassi, A and Grech, M (2018) Perpendicular relativistic shocks in magnetized pair plasma. Monthly Notices of the Royal Astronomical Society 477, 5238–5260.10.1093/mnras/sty979CrossRefGoogle Scholar
Sagdeev, RZ (1966) Cooperative phenomena and shock waves in collisionless plasmas. Reviews of Plasma Physics 4, 23.Google Scholar
Schlickeiser, R, Michno, MJ, Ibscher, D, Lazar, M and Skoda, T (2011) Modified temperature-anisotropy instability thresholds in the solar wind. Physical Review Letters 107, 201102.CrossRefGoogle ScholarPubMed
Schwartz, SJ, Henley, E, Mitchell, J and Krasnoselskikh, V (2011) Electron temperature gradient scale at collisionless shocks. Physical Review Letters 107, 215002.CrossRefGoogle ScholarPubMed
Sironi, L and Spitkovsky, A (2009) Particle acceleration in relativistic magnetized collisionless pair shocks: dependence of shock acceleration on magnetic obliquity. The Astrophysical Journal 698, 1523–1549.CrossRefGoogle Scholar
Stockem Novo, A, Bret, A, Fonseca, RA and Silva, LO (2015) Shock formation in electron-ion plasmas: mechanism and timing. Astrophysical Journal Letters 803, L29.CrossRefGoogle Scholar
Tidman, DA (1967) Turbulent shock waves in plasmas. Physics of Fluids 10, 547–564.CrossRefGoogle Scholar
Vogl, DF, Biernat, HK, Erkaev, NV, Farrugia, CJ and Mühlbachler, S (2001) Jump conditions for pressure anisotropy and comparison with the earth's bow shock. Nonlinear Processes in Geophysics 8, 167–174.CrossRefGoogle Scholar
Zel'dovich, I and Raizer, Y (2002) Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Books on Physics. Mineola, New York: Dover Publications.Google Scholar