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Nonlinear collisionless damping of Weibel turbulence in relativistic blast waves

Part of: Focus on Plasma Astrophysics Laboratory Astrophysics

Published online by Cambridge University Press:  30 October 2014

Martin Lemoine
Martin Lemoine*
Affiliation:
Institut d'Astrophysique de Paris, CNRS - UPMC, 98 bis boulevard Arago, F-75014 Paris, France
*
†Email address for correspondence: lemoine@iap.fr
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Abstract

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The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order nonlinear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic shock wave of a gamma-ray burst.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 455810101
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Copyright
Copyright © Cambridge University Press 2014 

References

REFERENCES

Achterberg, A., Gallant, Y. A., Kirk, J. G. and Guthmann, A. W. 2001 Particle acceleration by ultrarelativistic shocks: theory and simulations. Month. Not. Roy. Astron. Soc. 328, 393–408.CrossRefGoogle Scholar
Achterberg, A. and Wiersma, J. 2007 The Weibel instability in relativistic plasmas. I. Linear theory. Astron. Astrophys. 475, 1–18.CrossRefGoogle Scholar
Achterberg, A., Wiersma, J. and Norman, C. A. 2007 The Weibel instability in relativistic plasmas. II. Nonlinear theory and stabilization mechanism. Astron. Astrophys. 475, 19–36.CrossRefGoogle Scholar
Bednarz, J. and Ostrowski, M. 1998 Energy spectra of cosmic rays accelerated at ultrarelativistic shock waves. Phys. Rev. Lett. 80, 3911–3914.CrossRefGoogle Scholar
Ben-Israel, I., Piran, T., Eviatar, A. and Weinstock, J. 1975 A statistical theory of electromagnetic waves in turbulent plasmas. Astrophys. Space Sci. 38, 125–155.CrossRefGoogle Scholar
Bergman, J. and Eliasson, B. 2001 Linear wave dispersion laws in unmagnetized relativistic plasma: analytical and numerical results. Phys. Plasmas 8, 1482–1492.CrossRefGoogle Scholar
Bezzerides, B. and Weinstock, J. 1972 Nonlinear saturation of parametric instabilities. Phys. Rev. Lett. 28, 481–484.CrossRefGoogle Scholar
Birmingham, T. J. and Bornatici, M. 1971 Propagators in strong plasma turbulence. Phys. Fluids 14, 2239–2241.CrossRefGoogle Scholar
Blandford, R. and Eichler, D. 1987 Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys. Rep. 154, 1–75.CrossRefGoogle Scholar
Blandford, R. D. and McKee, C. F. 1976 Fluid dynamics of relativistic blast waves. Phys. Fluids 19, 1130–1138.CrossRefGoogle Scholar
Bret, A., Gremillet, L. and Dieckmann, M. E. 2010 Multidimensional electron beam-plasma instabilities in the relativistic regime. Phys. Plasmas 17 (12), 120 501.CrossRefGoogle 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, 378–387.CrossRefGoogle Scholar
Drake, R. P. and Gregori, G. 2012 Design considerations for unmagnetized collisionless-shock measurements in homologous flows. Astrophys. J. 749, 171.CrossRefGoogle Scholar
Dum, C. T. and Dupree, T. H. 1970 Nonlinear stabilization of high-frequency instabilities in a magnetic field. Phys. Fluids 13, 2064–2081.CrossRefGoogle Scholar
Dupree, T. H. 1966 A perturbation theory for strong plasma turbulence. Phys. Fluids 9, 1773–1782.CrossRefGoogle Scholar
Felten, T. and Schlickeiser, R. 2013a Spontaneous electromagnetic fluctuations in unmagnetized plasmas. V. Relativistic form factors of weakly damped/amplified thermal modes. Phys. Plasmas 20 (8), 082 117.CrossRefGoogle Scholar
Felten, T. and Schlickeiser, R. 2013b Spontaneous electromagnetic fluctuations in unmagnetized plasmas. VI. Transverse, collective mode for arbitrary distribution functions. Phys. Plasmas 20 (10), 104 502.CrossRefGoogle Scholar
Felten, T., Schlickeiser, R., Yoon, P. H. and Lazar, M. 2013 Spontaneous electromagnetic fluctuations in unmagnetized plasmas. II. Relativistic form factors of aperiodic thermal modes. Phys. Plasmas 20 (5), 052 113.CrossRefGoogle Scholar
Ghisellini, G., Ghirlanda, G., Nava, L. and Celotti, A. 2010 GeV emission from gamma-ray bursts: a radiative fireball? Month. Not. Roy. Astron. Soc. 403, 926–937.CrossRefGoogle Scholar
Gruzinov, A. 2000 Ultra-relativistic blast wave: stability and strong non-universality. ArXiv Astrophys. e-prints.Google Scholar
Gruzinov, A. and Waxman, E. 1999 Gamma-ray burst afterglow: polarization and analytic light curves. Astrophys. J. 511, 852–861.CrossRefGoogle Scholar
Kato, T. N. and Takabe, H. 2008 Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas. Astrophys. J. Lett. 681, L93–L96.CrossRefGoogle Scholar
Katz, B., Keshet, U. and Waxman, E. 2007 Self-similar collisionless shocks. Astrophys. J. 655, 375–390.CrossRefGoogle Scholar
Kelner, S. R., Aharonian, F. A. and Khangulyan, D. 2013 On the jitter radiation. Astrophys. J. 774, 61.CrossRefGoogle Scholar
Keshet, U., Katz, B., Spitkovsky, A. and Waxman, E. 2009 Magnetic field evolution in relativistic unmagnetized collisionless shocks. Astrophys. J. Lett. 693, L127–L130.CrossRefGoogle Scholar
Keshet, U. and Waxman, E. 2005 Energy spectrum of particles accelerated in relativistic collisionless shocks. Phys. Rev. Lett. 94 (11), 111 102.CrossRefGoogle ScholarPubMed
Kirk, J. G., Guthmann, A. W., Gallant, Y. A. and Achterberg, A. 2000 Particle acceleration at ultrarelativistic shocks: an eigenfunction method. Astrophys. J. 542, 235–242.CrossRefGoogle Scholar
Kocharovsky, V. V., Kocharovsky, V. V. and Martyanov, V. J. 2010 Self-consistent current sheets and filaments in relativistic collisionless plasma with arbitrary energy distribution of particles. Phys. Rev. Lett. 104 (21), 215 002.CrossRefGoogle ScholarPubMed
Kumar, P. and Barniol, D., R. 2009 On the generation of high-energy photons detected by the Fermi Satellite from gamma-ray bursts. Month. Not. Roy. Astron. Soc. 400, L75–L79.CrossRefGoogle Scholar
Kumar, P. and Barniol, D., R. 2010 External forward shock origin of high-energy emission for three gamma-ray bursts detected by Fermi. Month. Not. Roy. Astron. Soc. 409, 226–236.CrossRefGoogle Scholar
Lemoine, M. 2013 Synchrotron signature of a relativistic blast wave with decaying microturbulence. Month. Not. Roy. Astron. Soc. 428, 845–866.CrossRefGoogle Scholar
Lemoine, M., Li, Z. and Wang, X.-Y. 2013 On the magnetization of gamma-ray burst blast waves. Month. Not. Roy. Astron. Soc. 435, 3009–3016.CrossRefGoogle Scholar
Lemoine, M. and Pelletier, G. 2003 Particle transport in tangled magnetic fields and Fermi acceleration at relativistic shocks. Astrophys. J. 589, L73–L76.CrossRefGoogle Scholar
Lemoine, M. and Pelletier, G. 2010 On electromagnetic instabilities at ultra-relativistic shock waves. Month. Not. Roy. Astron. Soc. 402, 321–334.CrossRefGoogle Scholar
Lemoine, M. and Pelletier, G. 2011 Dispersion and thermal effects on electromagnetic instabilities in the precursor of relativistic shocks. Month. Not. Roy. Astron. Soc. 417, 1148–1161.CrossRefGoogle Scholar
Lemoine, M., Pelletier, G. and Revenu, B. 2006 On the efficiency of Fermi acceleration at relativistic shocks. Astrophys. J. Lett. 645, L129–L132.CrossRefGoogle Scholar
Levinson, A. 2009 Convective instability of a relativistic ejecta decelerated by a surrounding medium: an origin of magnetic fields in gamma-ray bursts? Astrophys. J. Lett. 705, L213–L216.CrossRefGoogle Scholar
Levinson, A. 2010 Relativistic rayleigh-taylor instability of a decelerating shell and its implications for gamma-ray bursts. Geophys. Astrophys. Fluid Dyn. 104, 85–111.CrossRefGoogle Scholar
Lyubarsky, Y. and Eichler, D. 2006 Are gamma-ray burst shocks mediated by the weibel instability? Astrophys. J. 647, 1250–1254.CrossRefGoogle Scholar
Mart'yanov, V. Y., Kocharovsky, V. V. and Kocharovsky, V. V. 2008 Saturation of relativistic Weibel instability and the formation of stationary current sheets in collisionless plasma. Sov. J. Exp. Theor. Phys. 107, 1049–1060.CrossRefGoogle Scholar
Medvedev, M. V., Fiore, M., Fonseca, R. A., Silva, L. O. and Mori, W. B. 2005 Long-time evolution of magnetic fields in relativistic Gamma-Ray burst shocks. Astrophys. J. 618, L75–L78.CrossRefGoogle Scholar
Medvedev, M. V., Frederiksen, J. T., Haugbø, T. and Nordlund, A. A. 2011 Radiation signatures of sub-larmor scale magnetic fields. Astrophys. J. 737, 55.CrossRefGoogle Scholar
Medvedev, M. V. and Loeb, A. 1999 Generation of magnetic fields in the relativistic shock of Gamma-Ray burst sources. Astrophys. J. 526, 697–706.CrossRefGoogle Scholar
Medvedev, M. V. and Zakutnyaya, O. V. 2009 Magnetic fields and cosmic rays in GRBs: a self-similar collisionless foreshock. Astrophys. J. 696, 2269–2274.CrossRefGoogle Scholar
Mizuno, Y., Pohl, M., Niemiec, J., Zhang, B., Nishikawa, K.-I. and Hardee, P. E. 2014 Magnetic field amplification and saturation in turbulence behind a relativistic shock. Month. Not. Roy. Astron. Soc. 439, 3490–3503.CrossRefGoogle Scholar
Moiseev, S. S. and Sagdeev, R. Z. 1963 Collisionless shock waves in a plasma in a weak magnetic field. J. Nucl. Energy 5, 43–47.CrossRefGoogle Scholar
Niemiec, J., Ostrowski, M. and Pohl, M. 2006 Cosmic-ray acceleration at ultrarelativistic shock waves: effects of downstream short-wave Turbulence. Astrophys. J. 650, 1020–1027.CrossRefGoogle Scholar
Panaitescu, A. and Kumar, P. 2001 Fundamental physical parameters of collimated Gamma-Ray burst afterglows. Astrophys. J. Lett. 560, L49–L53.CrossRefGoogle Scholar
Pelletier, G. 1977 Renormalization method and singularities in the theory of Langmuir turbulence. J. Plasma Phys. 18, 49–76.CrossRefGoogle Scholar
Pelletier, G., Lemoine, M. and Marcowith, A. 2009 On Fermi acceleration and magnetohydrodynamic instabilities at ultra-relativistic magnetized shock waves. Month. Not. Roy. Astron. Soc. 393, 587–597.CrossRefGoogle Scholar
Piran, T. 2004 The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143–1210.CrossRefGoogle Scholar
Plotnikov, I., Pelletier, G. and Lemoine, M. 2011 Particle transport in intense small-scale magnetic turbulence with a mean field. Astron. Astrophys. 532, A68.CrossRefGoogle Scholar
Pokhotelov, O. A. and Amariutei, O. A. 2011 Quasi-linear dynamics of Weibel instability. Ann. Geophys. 29, 1997–2001.CrossRefGoogle Scholar
Rabinak, I., Katz, B. and Waxman, E. 2011 Long-wavelength unstable modes in the far upstream of relativistic collisionless shocks. Astrophys. J. 736, 157.CrossRefGoogle Scholar
Ruyer, C., Gremillet, L., Bénisti, D. and Bonnaud, G. 2013 Electromagnetic fluctuations and normal modes of a drifting relativistic plasma. Phys. Plasmas 20 (11), 112 104.CrossRefGoogle Scholar
Shaisultanov, R., Lyubarsky, Y. and Eichler, D. 2012 Stream instabilities in relativistically hot plasma. Astrophys. J. 744, 182.CrossRefGoogle Scholar
Sironi, L. and Goodman, J. 2007 Production of magnetic energy by macroscopic turbulence in GRB afterglows. Astrophys. J. 671, 1858–1867.CrossRefGoogle Scholar
Sironi, L. and Spitkovsky, A. 2009 Synthetic Spectra from particle-in-cell simulations of relativistic collisionless shocks. Astrophys. J. Lett. 707, L92–L96.CrossRefGoogle Scholar
Sironi, L., Spitkovsky, A. and Arons, J. 2013 The maximum energy of accelerated particles in relativistic collisionless shocks. Astrophys. J. 771, 54.CrossRefGoogle Scholar
Spitkovsky, A. 2008a On the structure of relativistic collisionless shocks in electron-Ion plasmas. Astrophys. J. Lett. 673, L39–L42.CrossRefGoogle Scholar
Spitkovsky, A. 2008b Particle acceleration in relativistic collisionless shocks: Fermi process at last? Astrophys. J. Lett. 682, L5–L8.CrossRefGoogle Scholar
Waxman, E. 1997 Gamma-Ray–burst afterglow: supporting the cosmological fireball model, constraining parameters, and making predictions. Astrophys. J. Lett. 485, L5–L8.CrossRefGoogle Scholar
Weinstock, J. 1969 Formulation of a statistical theory of strong plasma turbulence. Phys. Fluids 12, 1045–1058.CrossRefGoogle Scholar
Weinstock, J. 1970 Turbulent plasmas in a magnetic field-a statistical theory. Phys. Fluids 13, 2308–2316.CrossRefGoogle Scholar
Weinstock, J. 1972 Nonlinear theory of frequency shifts and broadening of plasma waves. Phys. Fluids 15, 454–459.CrossRefGoogle Scholar
Weinstock, J. and Bezzerides, B. 1973 Nonlinear saturation of parametric instabilities: spectrum of turbulence and enhanced collision frequency. Phys. Fluids 16, 2287–2303.CrossRefGoogle Scholar
Wiersma, J. and Achterberg, A. 2004 Magnetic field generation in relativistic shocks. An early end of the exponential Weibel instability in electron-proton plasmas. Astron. Astrophys. 428, 365–371.CrossRefGoogle Scholar
Wijers, R. A. M. J. and Galama, T. J. 1999 Physical parameters of GRB 970508 and GRB 971214 from their afterglow synchrotron emission. Astrophys. J. 523, 177–186.CrossRefGoogle Scholar
Yoon, P. H., Schlickeiser, R. and Kolberg, U. 2014 Thermal fluctuation levels of magnetic and electric fields in unmagnetized plasma: the rigorous relativistic kinetic theory. Phys. Plasmas 21 (3), 032 109.CrossRefGoogle Scholar