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Density jump as a function of magnetic field for switch-on collisionless shocks in pair plasmas

Published online by Cambridge University Press:  06 July 2022

Antoine Bret Open the ORCID record for Antoine Bret [Opens in a new window]  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
Ramesh Narayan*
Affiliation:
Harvard-Smithsonian Center for Astrophysics, Harvard University, 60 Garden St., Cambridge, MA 02138, USA Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA
*
†Email address for correspondence: antoineclaude.bret@uclm.es
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Abstract

The properties of collisionless shocks, like the density jump, are usually derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed. Yet, in a collisionless plasma, an external magnetic field can sustain a stable anisotropy. We have already devised a model for the kinetic history of the plasma through the shock front (J. Plasma Phys., vol. 84, issue 6, 2018, 905840604), allowing to self-consistently compute the downstream anisotropy, and hence the density jump, in terms of the upstream parameters. This model deals with the case of a parallel shock, where the magnetic field is normal to the front both in the upstream and the downstream. Yet, MHD also allows for shock solutions, the so-called switch-on solutions, where the field is normal to the front only in the upstream. This article consists in applying our model to these switch-on shocks. While MHD offers only one switch-on solution within a limited range of Alfvén Mach numbers, our model offers two kinds of solutions within a slightly different range of Alfvén Mach numbers. These two solutions are most likely the outcome of the intermediate and fast MHD shocks under our model. While the intermediate and fast shocks merge in MHD for the parallel case, they do not within our model. For simplicity, the formalism is restricted to non-relativistic shocks in pair plasmas where the upstream is cold.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 3 , June 2022 , 905880320
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

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
Balogh, A. & Treumann, R.A. 2013 Physics of Collisionless Shocks: Space Plasma Shock Waves. Springer.CrossRefGoogle Scholar
Bret, A. 2020 Can we trust MHD jump conditions for collisionless shocks? Astrophys. J. 900 (2), 111.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. 2020 Density jump for parallel and perpendicular collisionless shocks. Laser Part. Beams 38 (2), 114–120.CrossRefGoogle Scholar
Carter, T., Dorfman, S., Gekelman, W., Tripathi, S., van Compernolle, B., Vincena, S., Rossi, G. & Jenko, F. 2015 Studies of the linear and nonlinear properties of Alfvén waves in LAPD. In APS Division of Plasma Physics Meeting Abstracts, APS Meeting Abstracts, vol. 2015, p. GM9.006.Google Scholar
Chew, G.F., Goldberger, M.L. & Low, F.E. 1956 The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions. Proc. R. Soc. Lond. A 236 (1204), 112–118.Google 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
Delmont, P. & Keppens, R. 2011 Parameter regimes for slow, intermediate and fast MHD shocks. J. Plasma Phys. 77 (2), 207–229.CrossRefGoogle Scholar
Double, G.P., Baring, M.G., Jones, F.C. & Ellison, D.C. 2004 Magnetohydrodynamic jump conditions for oblique relativistic shocks with gyrotropic pressure. Astrophys. J. 600, 485.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
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, L07106.CrossRefGoogle Scholar
Fitzpatrick, R. 2014 Plasma Physics: An Introduction. Taylor & Francis.CrossRefGoogle Scholar
Gary, S.P. 1993 Theory of Space Plasma Microinstabilities. Cambridge University Press.CrossRefGoogle Scholar
Gary, S.P. & Karimabadi, H. 2009 Fluctuations in electron-positron plasmas: linear theory and implications for turbulence. Phys. Plasmas 16 (4), 042104.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
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
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
Kennel, C.F., Blandford, R.D. & Coppi, P. 1989 MHD intermediate shock discontinuities. Part 1. Rankine–Hugoniot conditions. J. Plasma Phys. 42 (2), 299–319.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
Landau, L.D. & Lifshitz, E.M. 2013 Fluid Mechanics. Elsevier Science.Google Scholar
Lichnerowicz, A. 1976 Shock waves in relativistic magnetohydrodynamics under general assumptions. J. Math. Phys. 17 (12), 2135–2142.CrossRefGoogle Scholar
Majorana, A. & Anile, A.M. 1987 Magnetoacoustic shock waves in a relativistic gas. Phys. Fluids 30, 3045–3049.CrossRefGoogle 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
Ogilvie, K.W., Rosenvinge, T.V. & Durney, A.C. 1977 International sun-earth explorer – 3-spacecraft program. Science 198 (4313), 131–138.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
Schlickeiser, R., Michno, M.J., Ibscher, D., Lazar, M. & Skoda, T. 2011 Modified temperature-anisotropy instability thresholds in the solar wind. Phys. Rev. Lett. 107, 201102.CrossRefGoogle ScholarPubMed
Silva, T., Afeyan, B. & Silva, L.O. 2021 Weibel instability beyond bi-Maxwellian anisotropy. Phys. Rev. E 104 (3), 035201.CrossRefGoogle ScholarPubMed
Sironi, L. & Lembège, B. 2022 private communication.Google Scholar
Sironi, L. & Spitkovsky, A. 2011 Particle acceleration in relativistic magnetized collisionless electron-ion shocks. Astrophys. J. 726, 75.CrossRefGoogle Scholar
de Sterck, H. & Poedts, S. 1999 Field-aligned magnetohydrodynamic bow shock flows in the switch-on regime. Parameter study of the flow around a cylinder and results for the axi-symmetrical flow over a sphere. Astron. Astrophys. 343, 641–649.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