Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T15:01:21.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

Published online by Cambridge University Press:  10 February 2012

L. HAIM ,
M. GEDALIN ,
A. SPITKOVSKY ,
V. KRASNOSELSKIKH  and
M. BALIKHIN
L. HAIM
Affiliation:
Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel ([email protected])
M. GEDALIN
Affiliation:
Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel ([email protected])
A. SPITKOVSKY
Affiliation:
Princeton University, Princeton, NJ, USA
V. KRASNOSELSKIKH
Affiliation:
LPCE/CNRS, Orleans, France
M. BALIKHIN
Affiliation:
ACSE, University of Sheffield, Sheffield, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ≪1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron–ion shock front. This potential is responsible for electron energization.

Type
Papers
Information
Journal of Plasma Physics , Volume 78 , Issue 3 , June 2012 , pp. 295 - 302
Copyright
Copyright © Cambridge University Press 2012

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

Achterberg, A., Gallant, Y. A., Kirk, J. G. and Guthmann, A. W. 2001 Particle acceleration by ultrarelativistic shocks: theory and simulations. MNRAS 328, 393–408.CrossRefGoogle Scholar
Alsop, D. and Arons, J. 1988 Relativistic magnetosonic solitons with reflected particles in electron-positron plasmas. Phys. Fluids 31, 839–847.CrossRefGoogle Scholar
Arons, J., Backer, D. C., Spitkovsky, A. and Kaspi, V. M. 2005 Probing relativistic winds: the case of PSR J0737-3039 A and B. In: Binary Radio Pulsars (ed. Rasio, F. A. and Stairs, I. H.). Astronomical Society of the Pacific Conference Series, Vol. 328. San Francisco, CA: Astronomical Society of the Pacific, pp. 95.Google Scholar
Bogovalov, S. and Tsinganos, K. 2005 Shock formation at the magnetic collimation of relativistic jets. MNRAS 357, 918–928.CrossRefGoogle Scholar
Boillat, G. and Ruggeri, T. 1989 Wave and shock velocities in relativistic magnetohydrodynamics compared with the speed of light. Contin. Mech. Thermodyn. 1, 47–52.CrossRefGoogle Scholar
Burgess, D. 2006 Interpreting multipoint observations of substructure at the quasi-perpendicular bow shock: simulations. J. Geophys. Res. 111, 10210, American Geophysical Union.Google Scholar
Chang, P., Spitkovsky, A. and Arons, J. 2008 Long-term evolution of magnetic turbulence in relativistic collisionless shocks: electron-positron plasmas. Astrophys. J. 674, 378.CrossRefGoogle Scholar
Chiueh, T. 1989 Relativistic solitons and shocks in magnetized e(-)-e(+)-p(+) fluids. Phys. Rev. Lett. 63, 113–116.CrossRefGoogle ScholarPubMed
Chiueh, T. and Lai, T.-C. 1991 Magnetosonic soliton in a relativistically hot plasma. Phys. Rev. A 44, 6944–6947.CrossRefGoogle Scholar
Daigne, F. and Mochkovitch, R. 2000 Gamma-ray bursts from internal shocks in a relativistic wind: a hydrodynamical study. Astron. Astrophys. 358, 1157–1166.Google Scholar
Gallant, Y. A., Achterberg, A. and Kirk, J. G. 1999 Particle acceleration at ultra-relativistic shocks. Gamma-ray burst afterglow spectra and UHECRs. Astron. Astrophys. Suppl. Ser. 138, 549–550.CrossRefGoogle Scholar
Gallant, Y. A. and Arons, J. 1994 Structure of relativistic shocks in pulsar winds: a model of the wisps in the Crab Nebula. Astrophys. J. 435, 230–260.CrossRefGoogle Scholar
Gallant, Y. A., Hoshino, M., Langdon, A. B., Arons, J. and Max, C. E. 1992 Relativistic, perpendicular shocks in electron–positron plasmas. Astrophys. J. 391, 73–101.CrossRefGoogle Scholar
Gedalin, M. 1993 Linear waves in relativistic anisotropic magnetohydrodynamics. Phys. Rev. E 47, 4354–4357.CrossRefGoogle ScholarPubMed
Gedalin, M. 1998 Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description. Phys. Plasmas 5, 127–132.CrossRefGoogle Scholar
Gedalin, M., Balikhin, M. A. and Eichler, D. 2008 Efficient electron heating in relativistic shocks and gamma-ray-burst afterglow. Phys. Rev. E 77 (2), 026403.CrossRefGoogle ScholarPubMed
Hoshino, M., Arons, J., Gallant, Y. A. and Langdon, A. B. 1992 Relativistic magnetosonic shock waves in synchrotron sources – shock structure and non-thermal acceleration of positrons. Astrophys. J. 390, 454–479.CrossRefGoogle Scholar
Katz, B., Keshet, U. and Waxman, E. 2007 Self-similar collisionless shocks. Astrophys. J. 655, 375–390.CrossRefGoogle Scholar
Kennel, C. F., Edmiston, J. P. and Hada, T. 1985 A Quarter Century of Collisionless Shock Research. Washington DC American Geophysical Union Geophysical Monograph Series Vol. 34. Washington, DC: AGU, pp. 1–36.Google Scholar
Kennel, C. F. and Pellat, R. 1976 Relativistic nonlinear plasma waves in a magnetic field. J. Plasma Phys. 15, 335–355.CrossRefGoogle Scholar
Kennel, C. F. and Sagdeev, R. Z. 1967 Collisionless shock waves in high plasmas, 1. J. Geophys. Res. 72 (13), 3303–3326.CrossRefGoogle Scholar
Keshet, U., Katz, B. and Spitkovsky, A. 2009 Magnetic field evolution in relativistic unmagnetized collisionless shocks. Astrophys. J. 693, L127–L130.CrossRefGoogle Scholar
Komissarov, S. S. 2003 Limit shocks of relativistic magnetohydrodynamics. MNRAS 341, 717–720.CrossRefGoogle Scholar
Kong, X.-Y., Xu, Y.-H. and Zhong, Z.-X. 1982 Relativistic shock waves in double radio sources. Acta Astrophys. Sin. 2, 81–90.Google Scholar
Krasnosel'skikh, V. V. 1985 The nonlinear motion of a plasma across a magnetic field. Zhurnal Eksperimental noi i Teoreticheskoi Fiziki 89, 498–510.Google Scholar
Krasnosel'Skikh, V. V., Vinogradova, T., Balikhin, M. A., Alleyne, H. S. C., Pardaens, A. K., Woolliscroft, L. J. C., Klimov, S. I., Petrukovich, A., Mier-Jedrzejowicz, W. A. C. and Southwood, D. J. 1991 On the nature of low frequency turbulence in the foot of strong quasi-perpendicular shocks. Adv. Space Res. 11, 15–18.CrossRefGoogle Scholar
Lakhina, G. S. and Verheest, F. 1997 Alfvnic solitons in ultrarelativistic electron–positron plasmas. Astrophys. Space Sci. 253, 97–106.CrossRefGoogle Scholar
Langdon, A. B., Arons, J. and Max, C. E. 1988 Structure of relativistic magnetosonic shocks in electron-positron plasmas. Phys. Rev. Lett. 61, 779–782.CrossRefGoogle ScholarPubMed
Lessen, M. and Deshpande, N. V. 1967 Stability of relativistic magnetohydrodynamic shock waves. Phys. Fluids 10, 782–785.CrossRefGoogle Scholar
Lichnerowicz, A. 1967 Relativistic Hydrodynamics and Magnetohydrodynamics. New York: Benjamin.Google Scholar
Lichnerowicz, A. 1970 Shock waves in relativistic magnetohydrodynamics. Phys. Scr. 2, 221–225.CrossRefGoogle Scholar
Lobzin, V. V., Krasnoselskikh, V. V., Bosqued, J.-M., Pinon, J.-L., Schwartz, S. J. and Dunlop, M. 2007 Non-stationarity and reformation of high-Mach-number quasiperpendicular shocks: cluster observations. Geophys. Res. Lett. 340, 5107.Google Scholar
Medvedev, M. V. and Loeb, A. 1999 Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. Astrophys. J. 526 (2), 697–706.CrossRefGoogle Scholar
Mimica, P., Aloy, M. A. and Mller, E. 2007 Internal shocks in relativistic outflows: collisions of magnetized shells. Astron. Astrophys. 466, 93–106.CrossRefGoogle Scholar
Mochkovitch, R., Maitia, V. and Marques, R. 1995 Internal shocks in a relativistic wind as a source for gamma-ray bursts? Astrophys. Space Sci. 231, 441–444.CrossRefGoogle Scholar
Mszros, P. 2000 Gamma-ray bursts and bursters. Nucl. Phys. B. 80, 63–77.CrossRefGoogle Scholar
Nishikawa, K.-I., Hardee, P., Hededal, C. B., Richardson, G., Preece, R., Sol, H. and Fishman, G. J. 2006 Particle acceleration, magnetic field generation, and emission in relativistic shocks. Adv. Space Res. 38, 1316–1319.CrossRefGoogle Scholar
Piran, T. 2004 The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143–1210.CrossRefGoogle Scholar
Sagdeev, R. Z. 1966 Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23.Google Scholar
Spitkovsky, A. 2005 Simulations of relativistic collisionless shocks: shock structure and particle acceleration. In: Astrophysical Sources of High Energy Particles and Radiation (ed. Bulik, T., Rudak, B., and Madejski, G.). American Institute of Physics Conference Series, Vol. 801. College Park, MD: AIP, pp. 345–350.Google Scholar
Spitkovsky, A. 2008 On the structure of relativistic collisionless shocks in electron-ion plasmas. Astrophys. J. 673 (1), L39–L42.CrossRefGoogle Scholar
Treumann, R. A. 2009 Fundamentals of collisionless shocks for astrophysical application. 1. Non-relativistic shocks. Astron. Astrophys. Rev. 17 (4), 409–535.CrossRefGoogle Scholar
Ulrich, M.-H., Maraschi, L. and Urry, C. M. 1997 Variability of active galactic nuclei. Annu. Rev. Astron. Astrophys. 35, 445–502.CrossRefGoogle Scholar
Wardle, J. F. C., Homan, D. C., Ojha, R. and Roberts, D. H. 1998 Electron-positron jets associated with the quasar 3C279. Nature 395, 457–461.CrossRefGoogle Scholar
Waxman, E. 2006 Gamma-ray bursts and collisionless shocks. Plasma Phys. Control. Fusion 48, B137–B151.CrossRefGoogle Scholar
Webb, G. M., Zank, G. P. and McKenzie, J. F. 1987 Relativistic oblique magnetohydrodynamic shocks. J. Plasma Phys. 37, 117–141.CrossRefGoogle Scholar
Wiersma, J. and Achterberg, A. 2005 Magnetic field generation in relativistic shocks. Nuovo Cimento C Geophys. Space Phys. C 28, 459.Google Scholar