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Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas

Published online by Cambridge University Press:  25 April 2016

A. Bret ,
A. Stockem Novo ,
R. Narayan ,
C. Ruyer ,
M. E. Dieckmann  and
L. O. Silva
A. 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
A. Stockem Novo
Affiliation:
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- and Astrophysik, Ruhr-Universität, 44801 Bochum, Germany
R. Narayan
Affiliation:
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, MS-51 Cambridge, MA 02138, USA
C. Ruyer
Affiliation:
High Energy Density Science Division, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
M. E. Dieckmann
Affiliation:
Department of Science and Technology, Linköping University, SE-60174 Norrköping, Sweden
L. O. Silva
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear – Laboratório Associado, Instituto Superior Técnico, Lisboa, Portugal
*
Address correspondence and reprint requests to: A. Bret, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain. E-mail: [email protected]
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Abstract

Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.

Keywords

Collisionless shocksWeibel instability
Type
Research Article
Information
Laser and Particle Beams , Volume 34 , Issue 2 , June 2016 , pp. 362 - 367
Copyright
Copyright © Cambridge University Press 2016 

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References

REFERENCES

Bale, S.D., Mozer, F.S. & Horbury, T.S. (2003). Density-transition scale at quasiperpendicular collisionless shocks. Phys. Rev. Lett. 91, 265004.CrossRefGoogle ScholarPubMed
Bell, A.R. (1978). The acceleration of cosmic rays in shock fronts. I. Mon. Not. R. Astron. Soc. 182, 147.CrossRefGoogle Scholar
Blandford, R.D. & McKee, C.F. (1976). Fluid dynamics of relativistic blast waves. Phys. Fluids 19, 1130.CrossRefGoogle Scholar
Blandford, R. & Ostriker, J. (1978). Particle acceleration by astrophysical shocks. Astrophys. J. 221, L29.Google Scholar
Bludman, S.A., Watson, K.M. & Rosenbluth, M.N. (1960). Statistical mechanics of relativistic streams. Ii. Phys. Fluids 3, 747.CrossRefGoogle Scholar
Bret, A. (2015). Particles trajectories in magnetic filaments. Phys. Plasmas 22, 072116.Google Scholar
Bret, A. & Deutsch, C. (2006). A fluid approach to linear beam plasma electromagnetic instabilities. Phys. Plasmas 13, 042106.CrossRefGoogle Scholar
Bret, A., Firpo, M.-C. & Deutsch, C. (2005). Bridging the gap between two stream and filamentation instabilities. Laser Part. Beams 23, 375–383.Google Scholar
Bret, A., Gremillet, L., Bénisti, D. & Lefebvre, E. (2008). Exact relativistic kinetic theory of an electron-beamplasma system: hierarchy of the competing modes in the system-parameter space. Phys. Rev. Lett. 100, 205008.Google Scholar
Bret, A., Gremillet, L. & Dieckmann, M.E. (2010 a). Multidimensional electron beam-plasma instabilities in the relativistic regime. Phys. Plasmas 17, 120501.Google Scholar
Bret, A., Gremillet, L. & Dieckmann, M.E. (2010 b). Multidimensional electron beam-plasma instabilities in the relativistic regime. Phys. Plasmas 17, 120501.Google Scholar
Bret, A., Stockem, A., Fiúza, F., Ruyer, C., Gremillet, L., Narayan, R. & Silva, L.O. (2013). Collisionless shock formation, spontaneous electro-magnetic fluctuations, and streaming instabilities. Phys. Plasmas 20, 042102.CrossRefGoogle Scholar
Bret, A., Stockem, A., Narayan, R. & Silva, L.O. (2014). Collisionless Weibel shocks: Full formation mechanism and timing. Phys. Plasmas 21, 072301.Google Scholar
Caprioli, D. & Spitkovsky, A. (2014). Simulations of ion acceleration at non-relativistic shocks. i. acceleration efficiency. Astrophys. J. 783, 91.CrossRefGoogle Scholar
Chen, H., Nakai, M., Sentoku, Y., Arikawa, Y., Azechi, H., Fujioka, S., Keane, C., Kojima, S., Goldstein, W., Maddox, B.R., Miyanaga, N., Morita, T., Nagai, T., Nishimura, H., Ozaki, T., Park, J., Sakawa, Y., Takabe, H., Williams, G. & Zhang, Z. (2013). New insights into the laser produced electron–positron pairs. New J. Phys. 15, 065010.Google Scholar
Davidson, R.C., Hammer, D.A., Haber, I. & Wagner, C.E. (1972). Nonlinear development of electromagnetic instabilities in anisotropic plasmas. Phys. Fluids 15, 317.CrossRefGoogle Scholar
Faĭnberg, Y.B., Shapiro, V.D. & Shevchenko, V. (1970). Nonlinear theory of interaction between a monochromatic beam of relativistic electrons and a plasma. Sov. Phys. — JETP 30, 528.Google Scholar
Fiuza, F., Fonseca, R.A., Tonge, J., Mori, W.B. & Silva, L.O. (2012). Weibel-instability-mediated collisionless shocks in the laboratory with ultraintense lasers. Phys. Rev. Lett. 108, 235004.Google Scholar
Fonseca, R.A., Silva, L.O., Tsung, F.S., Decyk, V.K., Lu, W., Ren, C., Mori, W.B., Deng, S., Lee, S., Katsouleas, T. & Adam, J.C. (2002). Osiris: a three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. In Computational Science ICCS 2002’, Vol. 2331 of Lecture Notes in Computer Science, (Sloot, P., Hoekstra, A., Tan, C. and Dongarra, J., Eds), pp. 342–351. Heidelberg: Springer-Verlag.Google Scholar
Huntington, C.M., Fiúza, F., Ross, J.S., Zylstra, A.B., Drake, R.P., Froula, D.H., Gregori, G., Kugland, N.L., Kuranz, C.C., Levy, M.C., Li, C.K., Meinecke, J., Morita, T., Petrasso, R., Plechaty, C., Remington, B.A., Ryutov, D.D., Sakawa, Y., Spitkovsky, A., Takabe, H. & Park, H.-S. (2015). Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows. Nat. Phys. 11, 173.CrossRefGoogle Scholar
Kasper, J.C., Lazarus, A.J. & Gary, S.P. (2008). Hot solar-wind helium: direct evidence for local heating by alfvén-cyclotron dissipation. Phys. Rev. Lett. 101, 261103.Google Scholar
Krymskii, G. (1977). A regular mechanism for the acceleration of charged particles on the front of a shock wave. Dokl. Akad. Nauk SSSR 234, 1306.Google Scholar
Lyubarsky, Y. & Eichler, D. (2006). Are gamma-ray bursts mediated by the Weibel instability? Astrophys. J. 647, 1250.Google Scholar
Marcowith, A., Bret, A., Bykov, A., Dieckman, M.E., Drury, L., Lembège, B., Lemoine, M., Morlino, G., Murphy, G., Pelletier, G., Plotnikov, I., Reville, B., Riquelme, M., Sironi, L. & Stockem Novo, A. (2016). The microphysics of collisionless shock waves. Rep. Progr. Phys. 79, 046901.Google Scholar
Medvedev, M., Fiore, M., Fonseca, R., Silva, L. & Mori, W. (2005). Long-time evolution of magnetic fields in relativistic gamma-ray burst shocks. Astrophys. J. 618, L75.CrossRefGoogle Scholar
Piran, T. (2005). The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143.Google Scholar
Poisson, S. (1808). Mémoire sur la théorie du son. J. École Polytech. 7, 319.Google Scholar
Sagdeev, R.Z. (1966). Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23.Google Scholar
Salas, M.D. (2007). The curious events leading to the theory of shock waves. Shock Waves 16, 477–487.Google Scholar
Sarri, G., Poder, K., Cole, J., Schumaker, W., Di Piazza, A., Reville, B., Doria, D., Dromey, B., Gizzi, L., Green, A., Grittani, G., Kar, S., Keitel, C.H., Krushelnick, K., Kushel, S., Mangles, S., Najmudin, Z., Thomas, A.G.R., Vargas, M. & Zepf, M. (2015). Generation of a neutral, high-density electron-positron plasma in the laboratory. Nat. Commun. 6, 6747.Google Scholar
Schwartz, S.J., Henley, E., Mitchell, J. & Krasnoselskikh, V. (2011). Electron temperature gradient scale at collisionless shocks. Phys. Rev. Lett. 107, 215002.Google Scholar
Shaisultanov, R., Lyubarsky, Y. & Eichler, D. (2012). Stream instabilities in relativistically hot plasma. Astrophys. J. 744, 182.Google Scholar
Sironi, L., Spitkovsky, A. & Arons, J. (2013). The maximum energy of accelerated particles in relativistic collisionless shocks. Astrophys. J. 771, 54.Google Scholar
Spitkovsky, A. (2008). Particle acceleration in relativistic collisionless shocks: Fermi process at last? Astrophys. J. Lett. 682, L5–L8.Google Scholar
Stockem, A., Fiuza, F., Bret, A., Fonseca, R. & Silva, L. (2014). Exploring the nature of collisionless shocks under laboratory conditions. Sci. Rep. 4, 3934.CrossRefGoogle ScholarPubMed
Stockem, A., Fiúza, F., Fonseca, R.A. & Silva, L.O. (2012). The impact of kinetic effects on the properties of relativistic electron-positron shocks. Plasma Phys. Control. Fusion 54, 125004.Google Scholar
Stockem Novo, A., Bret, A., Fonseca, R.A. & Silva, L.O. (2015). Shock formation in electron-ion plasmas: Mechanism and timing. Astrophys. J. Lett. 803, L29.Google Scholar
Stokes, G. (1848). On a dificulty in the theory of sound. Phil. Mag. Ser. 3 33, 349–356.Google Scholar
Treumann, R.A. (2009). Fundamentals of collisionless shocks for astrophysical application, 1. Non-relativistic shocks. Astron. Astrophys. Rev. 17, 409–535.Google Scholar
Vietri, M., De Marco, D. & Guetta, D. (2003). On the generation of ultra-high-energy cosmic rays in gamma-ray bursts: A reappraisal. Astrophys. J. 592, 378–389.CrossRefGoogle Scholar
Zel'dovich, I. & Raizer, Y. (2002). Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Mineola, NY: Dover Books on Physics, Dover Publications.Google Scholar