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Three criteria for particle acceleration in collisionless shocks

Published online by Cambridge University Press:  18 December 2018

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
Asaf Pe'er
Affiliation:
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
*
Author for correspondence: Antoine Bret, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain andInstituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, 13071 Ciudad Real, Spain, E-mail: [email protected]

Abstract

Collisionless shocks have been the subject on many studies in recent years, due to their ability to accelerate particles. In order to do so, a shock must fulfill three criteria. First, it must be strong enough to accelerate particles efficiently. Second, both the upstream and the downstream must be collisionless. Third, the shock front must be surrounded by electromagnetic turbulence capable of scattering particles back and forth. We here consider the encounter of two identical plasma shells with initial density, temperature, and velocity n0, T0, v0, respectively. We translate the three criteria to the corresponding requirements on these parameters. A non-trivial map of the allowed region for particle acceleration emerges in the (n0, T0, v0) phase space, especially at low velocities or high densities. We first assess the case of pair plasma shells, before we turn to electrons/protons.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2018 

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References

Bale, SD, Mozer, FS and Horbury, TS (2003) Density-transition scale at quasiperpendicular collisionless shocks. Physical Review Letters 91, 265004.Google Scholar
Blandford, R and Eichler, D (1987) Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Physics Reports 154, 1.Google Scholar
Blandford, R and Ostriker, J (1978) Particle acceleration by astrophysical shocks. Astrophysical Journal 221, L29.Google Scholar
Bohm, D and Gross, EP (1949 a) Theory of plasma oscillations. a. Origin of medium-like behavior. The Physical Review 75, 1851.Google Scholar
Bohm, D and Gross, EP (1949 b) Theory of plasma oscillations. b. Excitation and damping of oscillations. The Physical Review 75, 1864.Google Scholar
Bouquet, S, Romain, T and Chieze, JP (2000) Analytical study and structure of a stationary radiative shock. The Astrophysical Journal Supplement Series 127, 245252.Google Scholar
Bouquet, S, Stéhlé, C, Koenig, M, Chièze, J-P, Benuzzi-Mounaix, A, Batani, D, Leygnac, S, Fleury, X, Merdji, H, Michaut, C, Thais, F, Grandjouan, N, Hall, T, Henry, E, Malka, V and Lafon, J-PJ (2004) Observation of laser driven supercritical radiative shock precursors. Physical Review Letters 92, 225001.Google Scholar
Bret, A, Firpo, M-C and Deutsch, C (2005) Bridging the gap between two stream and filamentation instabilities. Laser and Particle Beams 23, 375383.Google Scholar
Bret, A, Firpo, M-C and Deutsch, C (2006) Between two stream and filamentation instabilities: temperature and collisions effects. Laser and Particle Beams 24, 2733.Google Scholar
Bret, A, Gremillet, L, Bénisti, D and Lefebvre, E (2008) Exact relativistic kinetic theory of an electron-beam–plasma system: hierarchy of the competing modes in the system-parameter space. Physical Review Letters 100, 205008.Google Scholar
Bret, A, Gremillet, L and Dieckmann, ME (2010) Multidimensional electron beam-plasma instabilities in the relativistic regime. Physics of Plasmas 17, 120501.Google Scholar
Bret, A, Stockem, A, Fiúza, F, Pérez Álvaro, E, Ruyer, C, Narayan, R and Silva, LO (2013 a) The formation of a collisionless shock. Laser and Particle Beams 31, 487491.Google Scholar
Bret, A, Stockem, A, Fiuza, F, Ruyer, C, Gremillet, L, Narayan, R and Silva, LO (2013 b) Collisionless shock formation, spontaneous electromagnetic fluctuations, and streaming instabilities. Physics of Plasmas 20, 042102.Google Scholar
Bret, A, Stockem, A, Narayan, R and Silva, LO (2014) Collisionless Weibel shocks: full formation mechanism and timing. Physics of Plasmas 21, 072301.Google Scholar
Dieckmann, ME (2005) Particle simulation of an ultrarelativistic two-stream instability. Physical Review Letters 94, 155001.Google Scholar
Dieckmann, ME and Bret, A (2017) Simulation study of the formation of a non-relativistic pair shock. Journal of Plasma Physics 83, 905830104.Google Scholar
Dieckmann, ME and Bret, A (2018) Electrostatic and magnetic instabilities in the transition layer of a collisionless weakly relativistic pair shock. Monthly Notices of the Royal Astronomical Society 473, 198209.Google Scholar
Faĭnberg, YB, Shapiro, VD and Shevchenko, V (1970) Nonlinear theory of interaction between a monochromatic beam of relativistic electrons and a plasma. Journal of Experimental and Theoretical Physics 30, 528.Google Scholar
Fried, BD (1959) Mechanism for instability of transverse plasma waves. Physics of Fluids 2, 337.Google Scholar
Ichimaru, S (1973) Basic Principles of Plasma Physics. Reading, MA: W. A. Benjamin, Inc.Google Scholar
Jackson, J (1998) Classical Electrodynamics. Hoboken, NJ: Wiley.Google Scholar
Kirk, JG and Duffy, P (1999) Particle acceleration and relativistic shocks. Journal of Physics G: Nuclear and Particle Physics 25, R163.Google Scholar
Landau, L and Lifshitz, E (2013 a) Course of Theoretical Physics, Statistical Physics. Number v. 5. Amsterdam, Netherlands: Elsevier Science.Google Scholar
Landau, L and Lifshitz, E (2013 b) Fluid Mechanics. Number v. 6. Amsterdam, Netherlands: Elsevier Science.Google Scholar
Lemoine, M, Pelletier, G, Gremillet, L and Plotnikov, I (2014) A fast current-driven instability in relativistic collisionless shocks. EPL (Europhysics Letters) 106, 55001.Google Scholar
Marcowith, A, Bret, A, Bykov, A, Dieckman, ME, Drury, L, Lembège, B, Lemoine, M, Morlino, G, Murphy, G, Pelletier, G, Plotnikov, I, Reville, B, Riquelme, M, Sironi, L and Stockem Novo, A (2016) The microphysics of collisionless shock waves. Reports on Progress in Physics 79, 046901.Google Scholar
Nakar, E, Bret, A and Milosavljević, M (2011) Two-stream-like Instability in dilute hot relativistic beams and astrophysical relativistic shocks. Astrophysical Journal 738, 93.Google Scholar
Niemiec, J, Pohl, M, Bret, A and Wieland, V (2012) Nonrelativistic parallel shocks in unmagnetized and weakly magnetized plasmas. Astrophysical Journal 759, 73.Google Scholar
Ruyer, C, Gremillet, L, Bonnaud, G and Riconda, C (2017) A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks. Physics of Plasmas 24, 041409.Google Scholar
Sagdeev, RZ (1966) Cooperative phenomena and shock waves in collisionless plasmas. Reviews of Plasma Physics 4, 23.Google Scholar
Schwartz, SJ, Henley, E, Mitchell, J and Krasnoselskikh, V (2011) Electron temperature gradient scale at collisionless shocks. Physical Review Letters 107, 215002.Google Scholar
Stockem Novo, A, Bret, A, Fonseca, RA and Silva, LO (2015) Shock formation in electron-ion plasmas: mechanism and timing. Astrophysical Journal Letters 803, L29.Google Scholar
Thorne, K and Blandford, R (2017) Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton, NJ: Princeton University Press.Google Scholar
Yuan, D, Li, Y, Liu, M, Zhong, J, Zhu, B, Li, Y, Wei, H, Han, B, Pei, X, Zhao, J, Li, F, Zhang, Z, Liang, G, Wang, F, Weng, S, Li, Y, Jiang, S, Du, K, Ding, Y, Zhu, B, Zhu, J, Zhao, G and Zhang, J (2017) Formation and evolution of a pair of collisionless shocks in counter-streaming flows. Scientific Reports 7, 42915.Google Scholar
Zel'dovich, I and Raizer, Y (2002) Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Dover Books on Physics. Mineola, NY: Dover Publications.Google Scholar