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Microphysics of Cosmic Ray Driven Plasma Instabilities

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Part of the book series: Space Sciences Series of ISSI ((SSSI,volume 47))

Abstract

Energetic nonthermal particles (cosmic rays, CRs) are accelerated in supernova remnants, relativistic jets and other astrophysical objects. The CR energy density is typically comparable with that of the thermal components and magnetic fields. In this review we discuss mechanisms of magnetic field amplification due to instabilities induced by CRs. We derive CR kinetic and magnetohydrodynamic equations that govern cosmic plasma systems comprising the thermal background plasma, comic rays and fluctuating magnetic fields to study CR-driven instabilities. Both resonant and non-resonant instabilities are reviewed, including the Bell short-wavelength instability, and the firehose instability. Special attention is paid to the longwavelength instabilities driven by the CR current and pressure gradient. The helicity production by the CR current-driven instabilities is discussed in connection with the dynamo mechanisms of cosmic magnetic field amplification.

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References

  • A. Achterberg, The energy spectrum of electrons accelerated by weak magnetohydrodynamic turbulence. Astron. Astrophys. 76, 276–286 (1979)

    ADS  Google Scholar 

  • A. Achterberg, Modification of scattering waves and its importance for shock acceleration. Astron. Astrophys. 119, 274–278 (1983)

    ADS  MATH  Google Scholar 

  • A. Achterberg, R.D. Blandford, Transmission and damping of hydromagnetic waves behind a strong shock front—implications for cosmic ray acceleration. Mon. Not. R. Astron. Soc. 218, 551–575 (1986)

    ADS  MATH  Google Scholar 

  • F.A. Aharonian, A.M. Atoyan, On the emissivity of π^0^-decay gamma radiation in the vicinity of accelerators of galactic cosmic rays. Astron. Astrophys. 309, 917–928 (1996)

    ADS  Google Scholar 

  • E. Amato, The streaming instability: a review. Mem. Soc. Astron. Ital. 82, 806 (2011)

    ADS  Google Scholar 

  • E. Amato, P. Blasi, A kinetic approach to cosmic-ray-induced streaming instability at supernova shocks. Mon. Not. R. Astron. Soc. 392, 1591–1600 (2009). arXiv:0806.1223

    Article  ADS  Google Scholar 

  • A.R. Bell, The acceleration of cosmic rays in shock fronts. I. Mon. Not. R. Astron. Soc. 182, 147–156 (1978)

    ADS  Google Scholar 

  • A.R. Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Mon. Not. R. Astron. Soc. 353, 550–558 (2004)

    Article  ADS  Google Scholar 

  • A.R. Bell, The interaction of cosmic rays and magnetized plasma. Mon. Not. R. Astron. Soc. 358, 181–187 (2005)

    Article  ADS  Google Scholar 

  • A.R. Bell, S.G. Lucek, Cosmic ray acceleration to very high energy through the non-linear amplification by cosmic rays of the seed magnetic field. Mon. Not. R. Astron. Soc. 321, 433–438 (2001)

    Article  ADS  Google Scholar 

  • A. Beresnyak, T.W. Jones, A. Lazarian, Turbulence-induced magnetic fields and structure of cosmic ray modified shocks. Astrophys. J. 707, 1541–1549 (2009). arXiv:0908.2806

    Article  ADS  Google Scholar 

  • A. Beresnyak, A. Lazarian, Wave decay in magnetohydrodynamic turbulence. Astrophys. J. 678, 961–967 (2008). arXiv:0805.0630

    Article  ADS  Google Scholar 

  • E.G. Berezhko, Instability in a shock propagating through gas with a cosmic-ray component. Sov. Astron. Lett. 12, 352–354 (1986)

    ADS  Google Scholar 

  • E.G. Berezhko, G.F. Krymskiĭ, REVIEWS OF TOPICAL PROBLEMS: Acceleration of cosmic rays by shock waves. Sov. Phys. Usp. 31, 27–51 (1988)

    Article  ADS  Google Scholar 

  • V.S. Berezinskii, S.V. Bulanov, V.A. Dogiel, V.L. Ginzburg et al., Astrophysics of Cosmic Rays (North-Holland, Amsterdam, 1990)

    Google Scholar 

  • E.G. Blackman, G.B. Field, New dynamical mean-field dynamo theory and closure approach. Phys. Rev. Lett. 89(26), 265007–265010 (2002). arXiv:astro-ph/0207435

    Article  ADS  Google Scholar 

  • R. Blandford, D. Eichler, Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys. Rep. 154, 1–75 (1987)

    Article  ADS  Google Scholar 

  • A. Brandenburg, Turbulence and its parameterization in accretion discs. Astron. Nachr. 326, 787–797 (2005). arXiv:astro-ph/0510015

    Article  ADS  MATH  Google Scholar 

  • A. Brandenburg, Advances in theory and simulations of large-scale dynamos. Space Sci. Rev. 144, 87–104 (2009a). arXiv:0901.0329

    Article  ADS  Google Scholar 

  • A. Brandenburg, Large-scale dynamos at low magnetic Prandtl numbers. Astrophys. J. 697, 1206–1213 (2009b). arXiv:0808.0961

    Article  ADS  Google Scholar 

  • A. Brandenburg, K.H. Rädler, K. Kemel, Mean-field transport in stratified and/or rotating turbulence. Astron. Astrophys. 539, A35 (2012). arXiv:1108.2264

    Article  ADS  Google Scholar 

  • A.M. Bykov, Interstellar turbulence and shock waves. Sov. Astron. Lett. 8, 320 (1982)

    ADS  Google Scholar 

  • A.M. Bykov, A model for the generation of interstellar turbulence. Sov. Astron. Lett. 14, 60 (1988)

    ADS  Google Scholar 

  • A.M. Bykov, D.C. Ellison, S.M. Osipov, G.G. Pavlov et al., X-ray stripes in Tycho’s supernova remnant: synchrotron footprints of a nonlinear cosmic-ray-driven instability. Astrophys. J. 735, L40 (2011). arXiv:1106.3441

    Article  ADS  Google Scholar 

  • A.M. Bykov, D.C. Ellison, M. Renaud, Magnetic fields in cosmic particle acceleration sources. Space Sci. Rev. 166, 71–95 (2012). arXiv:1105.0130

    Article  ADS  Google Scholar 

  • A.M. Bykov, P.E. Gladilin, S.M. Osipov, Particle acceleration at supernova shocks in young stellar clusters. Mem. Soc. Astron. Ital. 82, 800 (2011a). arXiv:1111.2587

    ADS  Google Scholar 

  • A.M. Bykov, S.M. Osipov, D.C. Ellison, Cosmic ray current driven turbulence in shocks with efficient particle acceleration: the oblique, long-wavelength mode instability. Mon. Not. R. Astron. Soc. 410, 39–52 (2011b). arXiv:1010.0408

    Article  ADS  Google Scholar 

  • A.M. Bykov, I.N. Toptyghin, Particle acceleration by astrophysical supersonic turbulence, in 16th International Cosmic Ray Conference, vol. 2 Kyoto, Japan, (1979), p. 66

    Google Scholar 

  • A.M. Bykov, Y.A. Uvarov, D.C. Ellison, Dots, clumps, and filaments: the intermittent images of synchrotron emission in random magnetic fields of young supernova remnants. Astrophys. J. 689, L133–L136 (2008). arXiv:0811.2498

    Article  ADS  Google Scholar 

  • D. Caprioli, P. Blasi, E. Amato, M. Vietri, Dynamical effects of self-generated magnetic fields in cosmic-ray-modified shocks. Astrophys. J. 679, L139–L142 (2008). arXiv:0804.2884

    Article  ADS  Google Scholar 

  • G. Cassam-Chenaï, J.P. Hughes, J. Ballet, A. Decourchelle, The blast wave of Tycho’s supernova remnant. Astrophys. J. 665, 315–340 (2007). arXiv:astro-ph/0703239

    Article  ADS  Google Scholar 

  • S.V. Chalov, Diffusive shock instability in plasma modified by cosmic-rays. Sov. Astron. Lett. 14, 114 (1988a)

    ADS  Google Scholar 

  • S.V. Chalov, Instability of the structure of strong oblique MHD cosmic-ray shocks. Astrophys. Space Sci. 148, 175–187 (1988b)

    Article  ADS  MATH  Google Scholar 

  • P.H. Diamond, M.A. Malkov, Dynamics of mesoscale magnetic field in diffusive shock acceleration. Astrophys. J. 654, 252–266 (2007). arXiv:astro-ph/0605374

    Article  ADS  Google Scholar 

  • E.A. Dorfi, L.O. Drury, A cosmic ray driven instability, in International Cosmic Ray Conference, vol. 3, ed. by F.C. Jones International Cosmic Ray Conference, (1985), pp. 121–123

    Google Scholar 

  • L.O. Drury, An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep. Prog. Phys. 46, 973–1027 (1983)

    Article  ADS  Google Scholar 

  • L.O. Drury, Reaction effects in diffusive shock acceleration. Adv. Space Res. 4, 185–191 (1984)

    Article  ADS  Google Scholar 

  • L.O. Drury, Escaping the accelerator: how, when and in what numbers do cosmic rays get out of supernova remnants? Mon. Not. R. Astron. Soc. 415, 1807–1814 (2011). arXiv:1009.4799

    Article  ADS  Google Scholar 

  • L.O. Drury, T.P. Downes, Turbulent magnetic field amplification driven by cosmic ray pressure gradients. Mon. Not. R. Astron. Soc. 427, 2308–2313 (2012). arXiv:1205.6823

    Article  ADS  Google Scholar 

  • L.O. Drury, S.A.E.G. Falle, On the stability of shocks modified by particle acceleration. Mon. Not. R. Astron. Soc. 223, 353 (1986)

    ADS  MATH  Google Scholar 

  • L.O. Drury, W.J. Markiewicz, H.J. Voelk, Simplified models for the evolution of supernova remnants including particle acceleration. Astron. Astrophys. 225, 179–191 (1989)

    ADS  Google Scholar 

  • R. Durrer, C. Caprini, Primordial magnetic fields and causality J. Cosmol. Astropart. Phys. 11, 010 (2003). arXiv:astro-ph/0305059

    Article  ADS  Google Scholar 

  • D.C. Ellison, A.M. Bykov, Gamma-ray emission of accelerated particles escaping a supernova remnant in a molecular cloud. Astrophys. J. 731, 87 (2011). arXiv:1102.3885

    Article  ADS  Google Scholar 

  • K.A. Eriksen, J.P. Hughes, C. Badenes, R. Fesen et al., Evidence for particle acceleration to the knee of the cosmic ray spectrum in Tycho’s supernova remnant. Astrophys. J. 728, L28 (2011). arXiv:1101.1454

    Article  ADS  Google Scholar 

  • A.J. Farmer, P. Goldreich, Wave damping by magnetohydrodynamic turbulence and its effect on cosmic-ray propagation in the interstellar medium. Astrophys. J. 604, 671–674 (2004). arXiv:astro-ph/0311400

    Article  ADS  Google Scholar 

  • F. Fraschetti, Turbulent amplification of magnetic field driven by dynamo effect at rippled shocks. (2013). arXiv:1304.4956

  • Y. Fujita, F. Takahara, Y. Ohira, K. Iwasaki, Alfvén wave amplification and self-containment of cosmic rays escaping from a supernova remnant. Mon. Not. R. Astron. Soc. 415, 3434–3438 (2011). arXiv:1105.0683

    Article  ADS  Google Scholar 

  • S. Gabici, Cosmic ray escape from supernova remnants. Mem. Soc. Astron. Ital. 82, 760 (2011). arXiv:1108.4844

    ADS  Google Scholar 

  • S. Gabici, F.A. Aharonian, S. Casanova, Broad-band non-thermal emission from molecular clouds illuminated by cosmic rays from nearby supernova remnants. Mon. Not. R. Astron. Soc. 396, 1629–1639 (2009). arXiv:0901.4549

    Article  ADS  Google Scholar 

  • J. Giacalone, J.R. Jokipii, Magnetic field amplification by shocks in turbulent fluids. Astrophys. J. 663, L41–L44 (2007)

    Article  ADS  Google Scholar 

  • P. Goldreich, S. Sridhar, Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680 (1997). arXiv:astro-ph/9612243

    Article  ADS  Google Scholar 

  • M. Hanasz, K. Otmianowska-Mazur, G. Kowal, H. Lesch, Cosmic-ray-driven dynamo in galactic disks. a parameter study. Astron. Astrophys. 498, 335–346 (2009). arXiv:0812.3906

    Article  ADS  Google Scholar 

  • E.A. Helder, J. Vink, A.M. Bykov, Y. Ohira et al., Observational signatures of particle acceleration in supernova remnants. Space Sci. Rev. 173, 369–431 (2012). arXiv:1206.1593

    Article  ADS  Google Scholar 

  • F.C. Jones, D.C. Ellison, The plasma physics of shock acceleration. Space Sci. Rev. 58, 259–346 (1991)

    Article  ADS  Google Scholar 

  • N.K.R. Kevlahan, The vorticity jump across a shock in a non-uniform flow. J. Fluid Mech. 341, 371–384 (1997)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • G.F. Krymskii, A regular mechanism for the acceleration of charged particles on the front of a shock wave, in Akademiia Nauk SSSR Doklady, vol. 234, (1977), pp. 1306–1308

    Google Scholar 

  • R.M. Kulsrud, R. Cen, J.P. Ostriker, D. Ryu, The protogalactic origin for cosmic magnetic fields. Astrophys. J. 480, 481 (1997). arXiv:astro-ph/9607141

    Article  ADS  Google Scholar 

  • M.A. Malkov, P.H. Diamond, Nonlinear shock acceleration beyond the bohm limit. Astrophys. J. 642, 244–259 (2006). arXiv:astro-ph/0509235

    Article  ADS  Google Scholar 

  • M.A. Malkov, P.H. Diamond, Nonlinear dynamics of acoustic instability in a cosmic ray shock precursor and its impact on particle acceleration. Astrophys. J. 692, 1571–1581 (2009)

    Article  ADS  Google Scholar 

  • M.A. Malkov, P.H. Diamond, R.Z. Sagdeev, F.A. Aharonian, I.V. Moskalenko, Analytic Solution for Self-regulated Collective Escape of Cosmic Rays from their Acceleration Sites. Astrophys. J. 768(1), 13 (2013). doi:10.1088/0004-637X/768/1/73

    Article  Google Scholar 

  • M.A. Malkov, L.O. Drury, Nonlinear theory of diffusive acceleration of particles by shock waves. Rep. Prog. Phys. 64, 429–481 (2001)

    Article  ADS  Google Scholar 

  • M.A. Malkov, R.Z. Sagdeev, P.H. Diamond, Magnetic and density spikes in cosmic-ray shock precursors. Astrophys. J. 748, L32 (2012). arXiv:1110.0257

    Article  ADS  Google Scholar 

  • A. Marcowith, M. Lemoine, G. Pelletier, Turbulence and particle acceleration in collisionless supernovae remnant shocks. II. cosmic-ray transport. Astron. Astrophys. 453, 193–202 (2006). arXiv:astro-ph/0603462

    Article  ADS  MATH  Google Scholar 

  • J.F. McKenzie, H.J. Voelk, Non-linear theory of cosmic ray shocks including self-generated Alfvén waves. Astron. Astrophys. 116, 191–200 (1982)

    ADS  MATH  Google Scholar 

  • J.F. McKenzie, K.O. Westphal, Interaction of hydromagnetic waves with hydromagnetic shocks. Phys. Fluids 13, 630–640 (1970)

    Article  ADS  MATH  Google Scholar 

  • L. Nava, S. Gabici, Anisotropic cosmic ray diffusion and gamma-ray production close to supernova remnants, with an application to W28. Mon. Not. R. Astron. Soc. 429, 1643–1651 (2013). arXiv:1211.1668

    Article  ADS  Google Scholar 

  • P.D. Noerdlinger, A.K.M. Yui, Persistence of the firehouse instability in highly relativistic plasmas. Astrophys. J. 151, 901 (1968)

    Article  ADS  Google Scholar 

  • Y. Ohira, K. Murase, R. Yamazaki, Gamma-rays from molecular clouds illuminated by cosmic rays escaping from interacting supernova remnants. Mon. Not. R. Astron. Soc. 410, 1577–1582 (2011). arXiv:1007.4869

    ADS  Google Scholar 

  • E.N. Parker, The dynamical state of the interstellar gas and field. Astrophys. J. 145, 811 (1966)

    Article  ADS  Google Scholar 

  • E.N. Parker, The dynamical state of the interstellar gas and field. III. Turbulence and enhanced diffusion. Astrophys. J. 149, 535 (1967)

    Article  ADS  Google Scholar 

  • G. Pelletier, M. Lemoine, A. Marcowith, Turbulence and particle acceleration in collisionless supernovae remnant shocks. I. Anisotropic spectra solutions. Astron. Astrophys. 453, 181–191 (2006). arXiv:astro-ph/0603461

    Article  ADS  MATH  Google Scholar 

  • V. Ptuskin, Propagation of galactic cosmic rays. Astropart. Phys. 39, 44–51 (2012)

    Article  ADS  Google Scholar 

  • V.S. Ptuskin, Influence of cosmic rays on propagation of long magneto hydrodynamic waves. Astrophys. Space Sci. 76, 265–278 (1981)

    Article  ADS  MATH  Google Scholar 

  • V.S. Ptuskin, V.N. Zirakashvili, A.A. Plesser, Non-linear diffusion of cosmic rays. Adv. Space Res. 42, 486–490 (2008)

    Article  ADS  Google Scholar 

  • B. Reville, S. O’Sullivan, P. Duffy, J.G. Kirk, The transport of cosmic rays in self-excited magnetic turbulence. Mon. Not. R. Astron. Soc. 386, 509–515 (2008). arXiv:0802.0109

    Article  ADS  Google Scholar 

  • S.P. Reynolds, Supernova remnants at high energy. Annu. Rev. Astron. Astrophys. 46, 89–126 (2008)

    Article  ADS  Google Scholar 

  • M.A. Riquelme, A. Spitkovsky, Nonlinear study of Bell’s cosmic ray current-driven instability. Astrophys. J. 694, 626–642 (2009). arXiv:0810.4565

    Article  ADS  Google Scholar 

  • M.A. Riquelme, A. Spitkovsky, Magnetic amplification by magnetized cosmic rays in supernova remnant shocks. Astrophys. J. 717, 1054–1066 (2010). arXiv:0912.4990

    Article  ADS  Google Scholar 

  • I. Rogachevskii, N. Kleeorin, A. Brandenburg, D. Eichler, Cosmic-ray current-driven turbulence and mean-field dynamo effect. Astrophys. J. 753, 6 (2012). arXiv:1204.4246

    Article  ADS  Google Scholar 

  • R. Rosner, G. Bodo, The origin of filaments in the interstellar medium. Astrophys. J. 470, L49 (1996)

    Article  ADS  Google Scholar 

  • D. Ryu, H. Kang, T.W. Jones, The stability of cosmic-ray-dominated shocks—a secondary instability. Astrophys. J. 405, 199–206 (1993)

    Article  ADS  Google Scholar 

  • D. Ryu, J. Kim, S.S. Hong, T.W. Jones, The effect of cosmic-ray diffusion on the Parker instability. Astrophys. J. 589, 338–346 (2003). arXiv:astro-ph/0301625

    Article  ADS  Google Scholar 

  • R.Z. Sagdeev, V.D. Shafranov, On the instability of a plasma with anisotropic distribution of velocities in magnetic field. Sov. Phys. JETP 12(1), 130–132 (1961)

    Google Scholar 

  • R. Schlickeiser, Cosmic Ray Astrophysics (Springer, Berlin, 2002)

    Book  Google Scholar 

  • M. Schrinner, K.H. Rädler, D. Schmitt, M. Rheinhardt et al., Mean-field view on rotating magnetoconvection and a geodynamo model. Astron. Nachr. 326, 245–249 (2005)

    Article  ADS  Google Scholar 

  • K.M. Schure, A.R. Bell, A long-wavelength instability involving the stress tensor. Mon. Not. R. Astron. Soc. 418, 782–788 (2011). arXiv:1107.5817

    Article  ADS  Google Scholar 

  • K.M. Schure, A.R. Bell, L.O’C. Drury, A.M. Bykov, Diffusive shock acceleration and magnetic field amplification. Space Sci. Rev. 173, 491–519 (2012). arXiv:1203.1637

    Article  ADS  Google Scholar 

  • V.D. Shapiro, K.B. Quest, M. Okolicsanyi, Non-resonant firehose instability: consequences for the theory of cosmic ray acceleration. Geophys. Res. Lett. 25, 845–848 (1998)

    Article  ADS  Google Scholar 

  • F.H. Shu, The Parker instability in differentially-rotating disks. Astron. Astrophys. 33, 55 (1974)

    ADS  Google Scholar 

  • J. Skilling, Cosmic ray streaming. I. Effect of Alfvén waves on particles. Mon. Not. R. Astron. Soc. 172, 557–566 (1975)

    ADS  Google Scholar 

  • I.N. Toptygin, Cosmic rays in interplanetary magnetic fields (1983)

    Google Scholar 

  • R.A. Treumann, W. Baumjohann, Advanced Space Plasma Physics (1997)

    Book  MATH  Google Scholar 

  • Y. Uchiyama, F.A. Aharonian, T. Tanaka et al., Extremely fast acceleration of cosmic rays in a supernova remnant. Nature 449, 576–578 (2007)

    Article  ADS  Google Scholar 

  • J. Vink, Supernova remnants: the X-ray perspective. Astron. Astrophys. Rev. 20, 49 (2012). arXiv:1112.0576

    Article  ADS  Google Scholar 

  • A.E. Vladimirov, A.M. Bykov, D.C. Ellison, Spectra of magnetic fluctuations and relativistic particles produced by a nonresonant wave instability in supernova remnant shocks. Astrophys. J. 703, L29–L32 (2009). arXiv:0908.2602

    Article  ADS  Google Scholar 

  • H. Yan, A. Lazarian, R. Schlickeiser, Cosmic-ray streaming from supernova remnants and gamma-ray emission from nearby molecular clouds. Astrophys. J. 745, 140 (2012). arXiv:1111.2410

    Article  ADS  Google Scholar 

  • V.N. Zirakashvili, V.S. Ptuskin, Diffusive shock acceleration with magnetic amplification by nonresonant streaming instability in supernova remnants. Astrophys. J. 678, 939–949 (2008). arXiv:0801.4488

    Article  ADS  Google Scholar 

  • V.N. Zirakashvili, V.S. Ptuskin, H.J. Völk, Modeling Bell’s nonresonant cosmic-ray instability. Astrophys. J. 678, 255–261 (2008). arXiv:0801.4486

    Article  ADS  Google Scholar 

  • E.G. Zweibel, Energetic particle trapping by Alfvén wave instabilities, in Particle Acceleration Mechanisms in Astrophysics, ed. by J. Arons, C. McKee, C. Max. American Institute of Physics Conference Series, vol. 56, (1979), pp. 319–328

    Google Scholar 

  • E.G. Zweibel, Cosmic-ray history and its implications for galactic magnetic fields. Astrophys. J. 587, 625–637 (2003). arXiv:astro-ph/0212559

    Article  ADS  Google Scholar 

  • E.G. Zweibel, J.E. Everett, Environments for magnetic field amplification by cosmic rays. Astrophys. J. 709, 1412–1419 (2010). arXiv:0912.3511

    Article  ADS  Google Scholar 

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Bykov, A.M., Brandenburg, A., Malkov, M.A., Osipov, S.M. (2013). Microphysics of Cosmic Ray Driven Plasma Instabilities. In: Balogh, A., Bykov, A., Cargill, P., Dendy, R., Dudok de Wit, T., Raymond, J. (eds) Microphysics of Cosmic Plasmas. Space Sciences Series of ISSI, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7413-6_6

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