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The growth of the longitudinal beam–plasma instability in the presence of an inhomogeneous background

  • Mohamad Shalaby (a1), Avery E. Broderick (a2) (a3), Philip Chang (a4), Christoph Pfrommer (a1), Ewald Puchwein (a1) and Astrid Lamberts (a5)...

Abstract

We study the longitudinal stability of beam–plasma systems in the presence of a density inhomogeneity in the background plasma. Previous works have focused on the non-relativistic regime where hydrodynamical models are used to evolve pre-existing Langmuir waves within inhomogeneous background plasmas. Here, for the first time we study the problem with kinetic equations in a fully relativistic way. We do not assume the existence of Langmuir waves, and we focus on the rate and the mechanism by which waves are excited in such systems from an initial perturbation. We derive the structure of the unstable modes and compute an analytical approximation for their growth rates. Our computation is limited to dilute and cold beams, and shows an excellent agreement with particle-in-cell simulations performed using the SHARP code. We show that, due to such an inhomogeneity, the virulent beam–plasma instabilities in the intergalactic medium are not suppressed but their counterparts in the solar wind can be suppressed as evidenced by propagating type-III solar radio bursts.

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Copyright

Corresponding author

Email address for correspondence: mshalaby@live.ca

References

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Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth dover printing, tenth gpo printing edn.Dover.
Ackermann, M., Ajello, M., Baldini, L., Ballet, J., Barbiellini, G., Bastieri, D., Bellazzini, R., Bissaldi, E., Blandford, R. D., Bloom, E. D. et al. & Fermi-LAT Collaboration 2018 The search for spatial extension in high-latitude sources detected by the Fermi large area telescope. Astrophys. J. Suppl. 237 (2), 32.
Ardaneh, K., Cai, D. & Nishikawa, K.-I. 2016 Collisionless electron–ion shocks in relativistic unmagnetized jet–ambient interactions: non-thermal electron injection by double layer. Astrophys. J. 827, 124.
Ardaneh, K., Cai, D., Nishikawa, K.-I. & Lembége, B. 2015 Collisionless Weibel shocks and electron acceleration in gamma-ray bursts. Astrophys. J. 811, 57.
Birdsall, C. K. & Maron, N. 1980 Plasma self-heating and saturation due to numerical instabilities. J. Comput. Phys. 36, 119.
Boyd, T. J. M. & Sanderson, J. J. 2003 The Physics of Plasmas. Cambridge University Press.
Breǐzman, B. N. & Ruytov, D. D. 1969 Quasilinear relaxation of an electron beam in an inhomogeneous bounded plasma. Sov. J. Expl Theor. Phys. 30, 759.
Breǐzman, B. N. & Ryutov, D. D. 1971 Quasilinear relaxation of an ultrarelativistic electron beam in a plasma. Sov. J. Expl Theor. Phys. 33, 220.
Breǐzman, B. N., Ryutov, D. D. & Chebotaev, P. Z. 1972 Nonlinear effects in the interaction between an ultrarelativistic electron beam and a plasma. Sov. J. Expl Theor. Phys. 35, 741.
Bret, A., Gremillet, L. & Dieckmann, M. E. 2010 Multidimensional electron beam–plasma instabilities in the relativistic regime. Phys. Plasmas 17 (12), 120501.
Broderick, A. E., Chang, P. & Pfrommer, C. 2012 The cosmological impact of luminous TeV blazars. I. Implications of plasma instabilities for the intergalactic magnetic field and extragalactic gamma-ray background. Astrophys. J. 752, 22.
Broderick, A. E., Pfrommer, C., Puchwein, E. & Chang, P. 2014 Implications of plasma beam instabilities for the statistics of the Fermi hard gamma-ray blazars and the origin of the extragalactic gamma-ray background. Astrophys. J. 790, 137.
Broderick, A. E., Tiede, P., Chang, P., Lamberts, A., Pfrommer, C., Puchwein, E., Shalaby, M. & Werhahn, M. 2018 Missing gamma-ray halos and the need for new physics in the gamma-ray sky. Astrophys. J. 868, 87.
Broderick, A. E., Tiede, P., Shalaby, M., Pfrommer, C., Puchwein, E., Chang, P. & Lamberts, A. 2016 Bow ties in the sky. I: the angular structure of inverse compton gamma-ray halos in the Fermi sky. Astrophys. J. 832, 109.
Chang, P., Broderick, A. E. & Pfrommer, C. 2012 The cosmological impact of luminous TeV blazars. II. Rewriting the thermal history of the intergalactic medium. Astrophys. J. 752, 23.
Chang, P., Broderick, A. E., Pfrommer, C., Puchwein, E., Lamberts, A. & Shalaby, M. 2014 The effect of nonlinear Landau damping on ultrarelativistic beam plasma instabilities. Astrophys. J. 797, 110.
Chang, P., Broderick, A. E., Pfrommer, C., Puchwein, E., Lamberts, A., Shalaby, M. & Vasil, G. 2016 The linear instability of dilute ultrarelativistic $\text{e}^{\pm }$ pair beams. Astrophys. J. 833, 118.
Ergun, R. E., Larson, D., Lin, R. P., McFadden, J. P., Carlson, C. W., Anderson, K. A., Muschietti, L., McCarthy, M., Parks, G. K., Reme, H. et al. 1998 Wind spacecraft observations of solar impulsive electron events associated with solar type III radio bursts. Astrophys. J. 503, 435445.
Ergun, R. E. et al. 2008 Eigenmode structure in solar–wind Langmuir waves. Phys. Rev. Lett. 101 (5), 051101.
Ferch, R. L. & Sudan, R. N. 1975 Linear two-stream instability of warm relativistic electron beams. Plasma Phys. 17, 905915.
Ginzburg, V. L. & Zhelezniakov, V. V. 1958 On the possible mechanisms of sporadic solar radio emission (radiation in an isotropic plasma). Sov. Astron. 2, 653.
Griffiths, D. J. 2016 Introduction to Quantum Mechanics, 2nd edn.Cambridge University Press.
Kempf, A., Kilian, P. & Spanier, F. 2016 Energy loss in intergalactic pair beams: particle-in-cell simulation. Astron. Astrophys. 585, A132.
Krafft, C., Volokitin, A. S. & Krasnoselskikh, V. V. 2013 Interaction of energetic particles with waves in strongly inhomogeneous solar wind plasmas. Astrophys. J. 778, 111.
Lin, R. P., Potter, D. W., Gurnett, D. A. & Scarf, F. L. 1981 Energetic electrons and plasma waves associated with a solar type III radio burst. Astrophys. J. 251, 364373.
Melrose, D. B. 2009 Coherent emission. In Universal Heliophysical Processes (ed. Gopalswamy, N. & Webb, D. F.), IAU Symposium, vol. 257, pp. 305315. Cambridge University Press.
Miniati, F. & Elyiv, A. 2013 Relaxation of blazar-induced pair beams in cosmic voids. Astrophys. J. 770, 54.
Nishikawa, K. & Ryutov, D. 1976 Relaxation of relativistic electron beam in a plasma with random density inhomogeneities. J. Phys. Soc. Japan 41 (5), 17571765.
Nishikawa, K.-I., Frederiksen, J. T., Nordlund, Å., Mizuno, Y., Hardee, P. E., Niemiec, J., Gómez, J. L., Pe’er, A., Duţan, I., Meli, A. et al. 2016 Evolution of global relativistic jets: collimations and expansion with kKHI and the Weibel instability. Astrophys. J. 820, 94.
Pfrommer, C., Chang, P. & Broderick, A. E. 2012 The cosmological impact of luminous TeV blazars. III. Implications for galaxy clusters and the formation of dwarf galaxies. Astrophys. J. 752, 24.
Puchwein, E., Pfrommer, C., Springel, V., Broderick, A. E. & Chang, P. 2012 The Lyman $\unicode[STIX]{x1D6FC}$ forest in a blazar-heated Universe. Mon. Not. R. Astron. Soc. 423, 149164.
Ramirez-Ruiz, E., Nishikawa, K.-I. & Hededal, C. B. 2007 $\text{e}^{+/-}$ pair loading and the origin of the upstream magnetic field in GRB shocks. Astrophys. J. 671, 18771885.
Reid, H. A. S. & Ratcliffe, H. 2014 A review of solar type III radio bursts. Res. Astron. Astrophys. 14 (7), 773804.
Riquelme, M. A., Quataert, E. & Verscharen, D. 2016 PIC simulations of the effect of velocity space instabilities on electron viscosity and thermal conduction. Astrophys. J. 824, 123.
Shalaby, M.2017 Cosmological beam plasma instabilities. PhD thesis.
Shalaby, M., Broderick, A. E., Chang, P., Pfrommer, C., Lamberts, A. & Puchwein, E. 2017a Importance of resolving the spectral support of beam-plasma instabilities in simulations. Astrophys. J. 848, 81.
Shalaby, M., Broderick, A. E., Chang, P., Pfrommer, C., Lamberts, A. & Puchwein, E. 2017b SHARP: a spatially higher-order, relativistic particle-in-cell code. Astrophys. J. 841, 52.
Shalaby, M., Broderick, A. E., Chang, P., Pfrommer, C., Lamberts, A. & Puchwein, E. 2018 Growth of beam–plasma instabilities in the presence of background inhomogeneity. Astrophys. J. 859, 45.
Shankar, R. 2012 Principles of Quantum Mechanics. Springer.
Sironi, L. & Giannios, D. 2014 Relativistic pair beams from TeV blazars: a source of reprocessed GeV emission rather than intergalactic heating. Astrophys. J. 787, 49.
Tiede, P., Broderick, A. E., Shalaby, M., Pfrommer, C., Puchwein, E., Chang, P. & Lamberts, A. 2017a Bow ties in the sky. II. Searching for gamma-ray halos in the Fermi sky using anisotropy. Astrophys. J., 157. doi:10.3847/1538-4357/aa9375.
Tiede, P., Broderick, A. E., Shalaby, M., Pfrommer, C., Puchwein, E., Chang, P. & Lamberts, A.2017b Constraints on the intergalactic magnetic field from bow ties in the gamma-ray sky. arXiv:1702.02586.
Vafin, S., Deka, P. J., Pohl, M. & Bohdan, A. 2019 Revisit of nonlinear Landau damping for electrostatic instability driven by blazar-induced pair beams. Astrophys. J. 873, 10.
Vafin, S., Rafighi, I., Pohl, M. & Niemiec, J. 2018 The electrostatic instability for realistic pair distributions in blazar/EBL cascades. Astrophys. J. 857, 43.
Vedenov, A. A. 1967 Theory of a weakly turbulent plasma. Rev. Plasma Phys. 3, 229.
Weiler, K. W. & Panagia, N. 1978 Are crab-type supernova remnants (plerions) short-lived? Astron. Astrophys. 70, 419.
Zakharov, V. E. 1972 Collapse of Langmuir waves. Sov. J. Expl Theor. Phys. 35, 908.
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The growth of the longitudinal beam–plasma instability in the presence of an inhomogeneous background

  • Mohamad Shalaby (a1), Avery E. Broderick (a2) (a3), Philip Chang (a4), Christoph Pfrommer (a1), Ewald Puchwein (a1) and Astrid Lamberts (a5)...

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