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

Published online by Cambridge University Press:  22 December 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:
Center for Astrophysics – Harvard and Smithsonian, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
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Abstract

Shock waves in plasma are usually dealt with using magnetohydrodynamics (MHD). Yet, MHD entails the assumption of a short mean free path, which is not fulfilled in a collisionless plasma. Recently, for pair plasmas, we devised a model allowing one to account for kinetic effects within a MHD-like formalism. Its relies on an estimate of the anisotropy generated when crossing the front, with a subsequent assessment of the stability of this anisotropy in the downstream. We solved our model for parallel, perpendicular and switch-on shocks. Here we bridge between all these cases by treating the problem of an arbitrarily, but coplanar, oriented magnetic field. Even though the formalism presented is valid for anisotropic upstream temperatures, only the case of a cold upstream is solved. We find extra solutions which are not part of the MHD catalogue, and a density jump that is notably less in the quasi-parallel, highly magnetized, regime. Given the complexity of the calculations, this work is mainly devoted to the presentation of the mathematical aspect of our model. A forthcoming article will be devoted to the physics of the shocks here defined.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 6 , December 2022 , 905880615
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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
Berezhko, E.G. & Ellison, D. C. 1999 A simple model of nonlinear diffusive shock acceleration. Astrophys. J. 526 (1), 385–399.CrossRefGoogle Scholar
Bret, A. 2010 Transferring a symbolic polynomial expression from Mathematica to Matlab. arXiv:1002.4725.Google 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.Google Scholar
Bret, A. & Narayan, R. 2022 Density jump as a function of magnetic field for switch-on collisionless shocks in pair plasmas. J. Plasma Phys. 88 (3), 905880320.CrossRefGoogle 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
David, L., Fraschetti, F., Giacalone, J., Wimmer-Schweingruber, R.F., Berger, L. & Lario, D. 2022 In situ measurement of the energy fraction in suprathermal and energetic particles at ACE, wind, and PSP interplanetary shocks. Astrophys. J. 928 (1), 66.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
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
Feldman, W.C., Bame, S.J., Gary, S.P., Gosling, J.T., McComas, D., Thomsen, M.F., Paschmann, G., Sckopke, N., Hoppe, M.M. & Russell, C.T. 1982 Electron heating within the earth's bow shock. Phys. Rev. Lett. 49 (3), 199–201.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
Génot, V. 2009 Analytical solutions for anisotropic MHD shocks. Astrophys. Space Sci. Trans. 5 (1), 31–34.CrossRefGoogle Scholar
Goedbloed, J.P. 2008 Time reversal duality of magnetohydrodynamic shocks. Phys. Plasmas 15 (6), 062101.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
Hasegawa, A. 1975 Plasma Instabilities and Nonlinear Effects. Springer Series on Physics Chemistry Space, vol. 8. Springer.Google 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. & 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
Ryu, D. & Jones, T.W. 1995 Numerical magnetohydrodynamics in astrophysics: algorithm and tests for one-dimensional flow. Astrophys. J. 442, 228.Google 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
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
Wu, C.C. 2003 MKDVB and CKB Shock Waves. Space Sci. Rev. 107 (1), 403–421.CrossRefGoogle Scholar