Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-25T15:05:11.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Density jump for oblique collisionless shocks in pair plasmas: physical solutions

Published online by Cambridge University Press:  16 April 2024

Antoine Bret Open the ORCID record for Antoine Bret [Opens in a new window] ,
Colby C. Haggerty  and
Ramesh Narayan
Antoine Bret*
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real, Spain Center for Astrophysics — Harvard & Smithsonian, Harvard University, 60 Garden St., Cambridge, MA 02138, USA Black Hole Initiative at Harvard University, 20 Garden St., Cambridge, MA 02138, USA
Colby C. Haggerty
Affiliation:
Institute for Astronomy, University of Hawaii, Manoa, 2680 Woodlawn Dr., Honolulu, HI 96822, USA
Ramesh Narayan
Affiliation:
Center for Astrophysics — Harvard & Smithsonian, Harvard University, 60 Garden St., Cambridge, MA 02138, USA Black Hole Initiative at Harvard University, 20 Garden St., Cambridge, MA 02138, USA
*
†Email address for correspondence: antoineclaude.bret@uclm.es
Get access Rights & Permissions [Opens in a new window]

Abstract

Collisionless shocks are frequently analysed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, the fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article (Bret & Narayan, J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615), a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in Bret & Narayan (J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615) by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: (i) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by particle-in-cell simulations. (ii) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or no downstream configuration (as in MHD). The largest departure from MHD is found for the case of a parallel shock.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 90 , Issue 2 , April 2024 , 905900213
Check for updates
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press

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

Abraham-Shrauner, B. 1967 Propagation of hydromagnetic waves through an anisotropic plasma. J. Plasma Phys. 1 (3), 361–378.CrossRefGoogle Scholar
Axford, W.I., Leer, E. & Skadron, G. 1977 The acceleration of cosmic rays by shock waves. In International Cosmic Ray Conference, vol. 11, p. 132.Google Scholar
Bale, S.D., Kasper, J.C., Howes, G.G., Quataert, E., Salem, C. & Sundkvist, D. 2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 103, 211101.CrossRefGoogle ScholarPubMed
Bale, S.D., Mozer, F.S. & Horbury, T.S. 2003 Density-transition scale at quasiperpendicular collisionless shocks. Phys. Rev. Lett. 91, 265004.CrossRefGoogle ScholarPubMed
Balogh, A. & Treumann, R.A. 2013 Physics of Collisionless Shocks: Space Plasma Shock Waves. Springer.CrossRefGoogle Scholar
Bell, A.R. 1978 a The acceleration of cosmic rays in shock fronts. I. Mon. Not. R. Astron. Soc. 182, 147.CrossRefGoogle Scholar
Bell, A.R. 1978 b The acceleration of cosmic rays in shock fronts. II. Mon. Not. R. Astron. Soc. 182, 443.CrossRefGoogle Scholar
Blandford, R & Eichler, D 1987 Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys. Rep. 154, 1.CrossRefGoogle Scholar
Blandford, R.D. & Ostriker, J.P. 1978 Particle acceleration by astrophysical shocks. Astrophys. J. Lett. 221, L29–L32.CrossRefGoogle Scholar
Bret, A. 2020 Can we trust MHD jump conditions for collisionless shocks? Astrophys. J. 900 (2), 111.CrossRefGoogle Scholar
Bret, A. 2021 Modified jump conditions for parallel collisionless shocks. Phys. Plasmas 28 (8), 082107.CrossRefGoogle Scholar
Bret, A. 2023 a Density jump as a function of magnetic field strength for parallel collisionless shocks with anisotropic upstream pressure. Mon. Not. R. Astron. Soc. 520 (4), 6083–6090.CrossRefGoogle Scholar
Bret, A. 2023 b Density jump as a function of magnetic field strength for perpendicular collisionless shocks with anisotropic upstream pressure. Mon. Not. R. Astron. Soc. 524 (3), 4498–4505.CrossRefGoogle Scholar
Bret, A. & Narayan, R. 2018 Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas. J. Plasma Phys. 84 (6), 905840604.CrossRefGoogle Scholar
Bret, A. & Narayan, R. 2019 Density jump as a function of magnetic field for collisionless shocks in pair plasmas: the perpendicular case. Phys. Plasmas 26 (6), 062108.CrossRefGoogle Scholar
Bret, A. & Narayan, R. 2022 a Density jump as a function of magnetic field for switch-on collisionless shocks in pair plasmas. J. Plasma Phys. 88 (3), 905880320.CrossRefGoogle Scholar
Bret, A. & Narayan, R. 2022 b Density jump for oblique collisionless shocks in pair plasmas: allowed solutions. J. Plasma Phys. 88 (6), 905880615.CrossRefGoogle Scholar
Bret, A., Pe'er, A., Sironi, L., Sa̧dowski, A. & Narayan, R. 2017 Kinetic inhibition of magnetohydrodynamics shocks in the vicinity of a parallel magnetic field. J. Plasma Phys. 83 (2), 715830201.CrossRefGoogle Scholar
Brown, C.R., Juno, J., Howes, G.G., Haggerty, C.C. & Constantinou, S. 2023 Isolation and phase-space energization analysis of the instabilities in collisionless shocks. J. Plasma Phys. 89 (3), 905890308.CrossRefGoogle Scholar
Buneman, O. 1993 Computer Space Plasma Physics (ed. H. Matsumoto & Y. Omura), p. 67. Terra Scientific.Google Scholar
Caprioli, D., Haggerty, C.C. & Blasi, P. 2020 Kinetic simulations of cosmic-ray-modified shocks. II. Particle spectra. Astrophys. J. 905 (1), 2.CrossRefGoogle Scholar
Craig, A.D. & Paul, J.W.M. 1973 Observation of ‘switch-on’ shocks in a magnetized plasma. J. Plasma Phys. 9 (2), 161–186.CrossRefGoogle Scholar
Drury, L.O.C. 1983 An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep. Prog. Phys. 46, 973.CrossRefGoogle Scholar
Erkaev, N.V., Vogl, D.F. & Biernat, H.K. 2000 Solution for jump conditions at fast shocks in an anisotropic magnetized plasma. J. Plasma Phys. 64, 561–578.CrossRefGoogle Scholar
Falle, S.A.E.G. & Komissarov, S.S. 1997 On the existence of intermediate shocks. In Computational Astrophysics; 12th Kingston Meeting on Theoretical Astrophysics (ed. D.A. Clarke & M.J. West), Astronomical Society of the Pacific Conference Series, vol. 12, p. 66.Google Scholar
Falle, S.A.E.G. & Komissarov, S.S. 2001 On the inadmissibility of non-evolutionary shocks. J. Plasma Phys. 65 (1), 29–58.CrossRefGoogle Scholar
Farris, M.H., Russell, C.T., Fitzenreiter, R.J. & Ogilvie, K.W. 1994 The subcritical, quasi-parallel, switch-on shock. Geophys. Res. Lett. 21 (9), 837–840.CrossRefGoogle Scholar
Feng, H.Q., Lin, C.C., Chao, J.K., Wu, D.J., Lyu, L.H. & Lee, L.C. 2009 Observations of an interplanetary switch-on shock driven by a magnetic cloud. Geophys. Res. Lett. 36.CrossRefGoogle Scholar
Gary, S.P. 1993 Theory of Space Plasma Microinstabilities. Cambridge University Press.CrossRefGoogle Scholar
Gerbig, D. & Schlickeiser, R. 2011 Jump conditions for relativistic magnetohydrodynamic shocks in a gyrotropic plasma. Astrophys. J. 733 (1), 32.CrossRefGoogle Scholar
Goedbloed, J.P., Keppens, R. & Poedts, S. 2010 Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press.CrossRefGoogle Scholar
Guo, X., Sironi, L. & Narayan, R. 2017 Electron heating in low-Mach-number perpendicular shocks. I. Heating mechanism. Astrophys. J. 851, 134.CrossRefGoogle Scholar
Guo, X., Sironi, L. & Narayan, R. 2018 Electron heating in low Mach number perpendicular shocks. II. Dependence on the pre-shock conditions. Astrophys. J. 858, 95.CrossRefGoogle Scholar
Gurnett, D.A. & Bhattacharjee, A. 2005 Introduction to Plasma Physics: With Space and Laboratory Applications. Cambridge University Press.CrossRefGoogle Scholar
Haggerty, C.C., Bret, A. & Caprioli, D. 2022 Kinetic simulations of strongly magnetized parallel shocks: deviations from MHD jump conditions. Mon. Not. R. Astron. Soc. 509 (2), 2084–2090.CrossRefGoogle Scholar
Haggerty, C.C. & Caprioli, D. 2020 Kinetic simulations of cosmic-ray-modified shocks. I. Hydrodynamics. Astrophys. J. 905 (1), 1.CrossRefGoogle Scholar
Hasegawa, A. 1975 Plasma Instabilities and Nonlinear Effects, Springer Series on Physics Chemistry Space, vol. 8. Springer.CrossRefGoogle Scholar
Hellinger, P., Trávníček, P., Kasper, J.C. & Lazarus, A. J. 2006 Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations. Geophys. Res. Lett. 33 (9), L09101.CrossRefGoogle Scholar
Hudson, P.D. 1970 Discontinuities in an anisotropic plasma and their identification in the solar wind. Planet. Space Sci. 18 (11), 1611–1622.CrossRefGoogle Scholar
Karimabadi, H., Krauss-Varban, D. & Omidi, N. 1995 Temperature anisotropy effects and the generation of anomalous slow shocks. Geophys. Res. Lett. 22 (20), 2689–2692.CrossRefGoogle Scholar
Kennel, C.F., Blandford, R.D. & Wu, C.C. 1990 Structure and evolution of small-amplitude intermediate shock waves. Phys. Fluids B 2 (2), 253–269.CrossRefGoogle Scholar
Kulsrud, R. M 2005 Plasma Physics for Astrophysics. Princeton University Press.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1981 Course of Theoretical Physics, Physical Kinetics, vol. 10. Elsevier.Google Scholar
Maruca, B.A., Kasper, J.C. & Bale, S.D. 2011 What are the relative roles of heating and cooling in generating solar wind temperature anisotropies? Phys. Rev. Lett. 107, 201101.CrossRefGoogle ScholarPubMed
Niemiec, J., Pohl, M., Bret, A. & Wieland, V. 2012 Nonrelativistic parallel shocks in unmagnetized and weakly magnetized plasmas. Astrophys. J. 759 (1), 73.CrossRefGoogle Scholar
Russell, C.T. & Farris, M.H. 1995 Ultra low frequency waves at the earth's bow shock. Adv. Space Res. 15 (8–9), 285–296.CrossRefGoogle Scholar
Sa̧dowski, A., Narayan, R., McKinney, J.C. & Tchekhovskoy, A. 2014 Numerical simulations of super-critical black hole accretion flows in general relativity. Mon. Not. R. Astron. Soc. 439 (1), 503–520.CrossRefGoogle Scholar
Sa̧dowski, A., Narayan, R., Tchekhovskoy, A. & Zhu, Y. 2013 Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes. Mon. Not. R. Astron. Soc. 429 (4), 3533–3550.CrossRefGoogle Scholar
Sagdeev, R.Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23.Google Scholar
Salas, M.D. 2007 The curious events leading to the theory of shock waves. Shock Waves 16 (6), 477–487.CrossRefGoogle Scholar
Schwartz, S.J., Henley, E., Mitchell, J. & Krasnoselskikh, V. 2011 Electron temperature gradient scale at collisionless shocks. Phys. Rev. Lett. 107, 215002.CrossRefGoogle ScholarPubMed
Shalaby, M. 2024 In preparation.Google Scholar
Silva, T., Afeyan, B. & Silva, L.O. 2021 Weibel instability beyond bi-Maxwellian anisotropy. Phys. Rev. E 104 (3), 035201.CrossRefGoogle ScholarPubMed
Sironi, L., Spitkovsky, A. & Arons, J. 2013 The maximum energy of accelerated particles in relativistic collisionless shocks. Astrophys. J. 771 (1), 54.CrossRefGoogle Scholar
Spitkovsky, A. 2005 Simulations of relativistic collisionless shocks: shock structure and particle acceleration. In Astrophysical Sources of High Energy Particles and Radiation (ed. T. Bulik, B. Rudak & G. Madejski), American Institute of Physics Conference Series, vol. 801, pp. 345–350.Google Scholar
Thorne, K.S. & Blandford, R.D. 2017 Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press.Google Scholar
Weibel, E.S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83.CrossRefGoogle Scholar
Zeković, V. 2019 Resonant micro-instabilities at quasi-parallel collisionless shocks: cause or consequence of shock (re)formation. Phys. Plasmas 26 (3), 032106.CrossRefGoogle Scholar
Zel'dovich, Y.B. & Raizer, Y.P. 2002 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Publications.Google Scholar