Hostname: page-component-cc8bf7c57-n7qbj Total loading time: 0 Render date: 2024-12-12T01:51:17.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  15 November 2018

Antoine Bret  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 Harvard-Smithsonian Center for Astrophysics, Harvard University, 60 Garden St., Cambridge, MA 02138, USA
Ramesh Narayan
Affiliation:
Harvard-Smithsonian Center for Astrophysics, Harvard University, 60 Garden St., Cambridge, MA 02138, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Collisionless shocks follow the Rankine–Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent particle-in-cell simulations reveal a significant departure from magnetohydrodynamics behaviour for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we present a non-relativistic model of the plasma evolution through the shock front, allowing for a derivation of the downstream anisotropy in terms of the field strength. Our scenario assumes double adiabatic evolution of a pair plasma through the shock front. As a result, the perpendicular temperature is conserved. If the resulting downstream is firehose stable, then the plasma remains in this state. If unstable, it migrates towards the firehose stability threshold. In both cases, the conservation equations, together with the relevant hypothesis made on the temperature, allows a full determination of the downstream anisotropy in terms of the field strength.

Keywords

astrophysical plasmasplasma nonlinear phenomenaspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 6 , December 2018 , 905840604
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

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.Google Scholar
Balogh, A. & Treumann, R. A. 2013 Physics of Collisionless Shocks: Space Plasma Shock Waves. Springer.Google Scholar
Bittencourt, J. A. 2013 Fundamentals of Plasma Physics. Springer.Google Scholar
Bret, A. 2016 Particle trajectories in weibel magnetic filaments with a flow-aligned magnetic field. J. Plasma Phys. 82 (4), 905820403.Google Scholar
Bret, A., Pe’er, A., Sironi, L., SaḐowski, A. & Narayan, R. 2017 Kinetic inhibition of magnetohydrodynamics shocks in the vicinity of a parallel magnetic field. J. Plasma Phys. 83 (2), 715830201.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
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.Google Scholar
Feynman, R. P., Leighton, R. B. & Sands, M. L. 1963 The Feynman Lectures on Physics, vol. 2. Pearson/Addison-Wesley.Google Scholar
Gary, S. P. 1993 Theory of Space Plasma Microinstabilities. Cambridge University Press.Google Scholar
Gary, S. P. & Karimabadi, H. 2009 Fluctuations in electron–positron plasmas: linear theory and implications for turbulence. Phys. Plasmas 16 (4), 042104.Google Scholar
Gerbig, D. & Schlickeiser, R. 2011 Jump conditions for relativistic magnetohydrodynamic shocks in a gyrotropic plasma. Astrophys. J. 733 (1), 32.Google Scholar
Guo, X., Sironi, L. & Narayan, R. 2017 Electron heating in low-Mach-number perpendicular shocks. I. Heating mechanism. Astrophys. J. 851, 134.Google 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.Google 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.Google Scholar
Kunz, M. W., Schekochihin, A. A. & Stone, J. M. 2014 Firehose and mirror instabilities in a collisionless shearing plasma. Phys. Rev. Lett. 112, 205003.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.Google Scholar
Majorana, A. & Anile, A. M. 1987 Magnetoacoustic shock waves in a relativistic gas. Phys. Fluids 30, 3045–3049.Google Scholar
Marcowith, A., Bret, A., Bykov, A., Dieckmann, M. E., Drury, L., Lembège, B., Lemoine, M., Morlino, G., Murphy, G., Pelletier, G. et al. 2016 The microphysics of collisionless shock waves. Rep. Progr. Phys. 79, 046901.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.Google Scholar
Scargle, J. D. 1968 On relativistic magnetohydrodynamics. Astrophys. J. 151, 791.Google Scholar
Schlickeiser, R. 2010 Linear theory of temperature anisotropy instabilities in magnetized thermal pair plasmas. The Open Plasma Phys. J. 3, 1–19.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.Google Scholar
Sironi, L. & Spitkovsky, A. 2011 Particle acceleration in relativistic magnetized collisionless electron–ion shocks. Astrophys. J. 726, 75.Google Scholar
Vogl, D. F., Biernat, H. K., Erkaev, N. V., Farrugia, C. J. & Mühlbachler, S. 2001 Jump conditions for pressure anisotropy and comparison with the earth’s bow shock. Nonlinear Process. Geophys. 8 (3), 167–174.Google Scholar
Weibel, E. S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83.Google Scholar