Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T13:29:35.178Z Has data issue: false hasContentIssue false
  • English
  • Français

The formation of a collisionless shock

Published online by Cambridge University Press:  08 July 2013

Antoine Bret ,
Anne Stockem ,
Frederico Fiúza ,
Erica Pérez Álvaro ,
Charles Ruyer ,
Ramesh Narayan  and
Luís O. Silva
Antoine Bret*
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, Ciudad Real, Spain
Anne Stockem
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear – Laboratório Associado, Instituto Superior Técnico, Lisboa, Portugal
Frederico Fiúza
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear – Laboratório Associado, Instituto Superior Técnico, Lisboa, Portugal
Erica Pérez Álvaro
Affiliation:
ETSI Industriales, Universidad de Castilla-La Mancha, Ciudad Real, Spain Instituto de Investigaciones Energéticas y Aplicaciones Industriales, Campus Universitario de Ciudad Real, Ciudad Real, Spain
Charles Ruyer
Affiliation:
CEA, DAM, DIF F-91297 Arpajon, France
Ramesh Narayan
Affiliation:
Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts
Luís O. Silva
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear – Laboratório Associado, Instituto Superior Técnico, Lisboa, Portugal
*
Address correspondence and reprint requests to: Antoine Bret, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain. E-mail: antoineclaude.bret@uclm.es
Get access Rights & Permissions [Opens in a new window]

Abstract

Collisionless shocks are key processes in astrophysics where the energy dissipation at the shock front is provided by collective plasma effects rather than particle collisions. While numerous simulations and laser-plasma experiments have shown they can result from the encounter of two plasma shells, a first principle theory of the shock formation is still lacking. In this respect, a series of 2D Particle-In-Cells simulations have been performed of two identical cold colliding pair plasmas. The simplicity of this system allows for an accurate analytical tracking of the physics. To start with, the Weibel-filamentation instability is triggered in the overlapping region, which generates a turbulent region after a saturation time τs. The incoming flow then piles-up in this region, building-up the shock density region according to some nonlinear processes, which will be the subject of future works. By evaluating the seed field giving rise to the instability, we derive an analytical expression for τs in good agreement with simulations. In view of the importance of the filamentation instability, we show a static magnetic field can cancel it if and only if it is perfectly aligned with the flow.

Keywords

Collisionless shocksWeibel instabilityPlasma fluctuations
Type
Research Article
Information
Laser and Particle Beams , Volume 31 , Issue 3 , September 2013 , pp. 487 - 491
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Betti, R., Zhou, C. D., Anderson, K. S., Perkins, L. J., Theobald, W. & Solodov, A. A. (2007). Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001.CrossRefGoogle ScholarPubMed
Blandford, R. & Eichler, D. (1987). Particle acceleration at astrophysical shocks: A theory of cosmic ray orgin. Phys. Rep. 154, 1.CrossRefGoogle Scholar
Boyd, T. & Sanderson, J. (2003). The Physics of Plasmas. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
Bret, A. (2009). Weibel, two-stream, filamentation, oblique, bell, bune-man… which one grows faster? Astrophys. J. 699, 990.CrossRefGoogle Scholar
Bret, A. & Alvaro, E. P. (2011). Robustness of the filamentation instability as shock mediator in arbitrarily oriented magnetic field. Phys. Plasma 18, 080706.CrossRefGoogle Scholar
Bret, A. & Deutsch, C. (2006). Stabilization of the filamentation instability and the anisotropy of the background plasma. Phys. Plasmas 13, 022110.CrossRefGoogle Scholar
Bert, A., Firpo, M. & Deutsch, C. (2005). Bridging the gap between two stream and filamentation instabilites. Laser Part. Beams 23, 375.Google Scholar
Bret, A., Gremillet, L., Bénisti, D. & Lefebvre, E. (2008). Exact relativistic kinetic theory of an electron-beam plasma system: Hierarchy of the competing modes in the system-parameter space. Phys. Rev. Lett. 100, 205008.CrossRefGoogle ScholarPubMed
Bret, A., Gremillet, L. & Dieckmann, M. E. (2010). Multidimensional electron beam-plasma instabilities in the relativistic regime. Phys. Plasmas 17, 120501.CrossRefGoogle Scholar
Canaud, B., Laffite, S., Brandon, V. & Temporal, M. (2012). 2d analysis of direct-drive shock-ignited hiper-like target implosions with the full laser megajoule. Laser Part. Beams 30, 183.CrossRefGoogle Scholar
Davidson, R. C., Hammer, D. A., Haber, I. & Wagner, C. E. (1972). Nonlinear development of electromagnetic instabilities in anisotropic plasma. Phys. Fluids 15, 317.CrossRefGoogle Scholar
Drury, L. O. C. (1983). An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rpt. Prog. Phys. 46, 973.Google Scholar
Fonseca, R., Silva, L., Tsung, F., Decyk, V., Lu, W., Ren, C., Mori, W., Deng, S., Lee, S., Katsouleas, T. & Adam, J. (2002). Osiris: A three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. Lecture Notes in Comput. Sci. 2331, 342.CrossRefGoogle Scholar
Fried, B. D. (1959). Mechanism for instability of transverse plasma waves. Phys. Fluids 2, 337.CrossRefGoogle Scholar
Godfrey, B. B., Shanahan, W. R. & Thode, L. E. (1975). Linear theory of a cold relativistic beam propagating along an external magnetic field. Phys. Fluids 18, 346.CrossRefGoogle Scholar
Letessier-Selvon, A. & Stanev, T. (2011). Ultrahigh energy cosmic rays. Rev. Mod. Phys. 83, 907.CrossRefGoogle Scholar
Liu, M.-P., Xie, B.-S., Huang, Y.-S., Liu, J. & Yu, M. (2009). Enhanced ion acceleration by collisionless electrostatic shock in thin foils irradiated by ultraintense laser pulse. Laser Part. Beams 27, 327.CrossRefGoogle Scholar
Liu, X., Li, Y. T., Zhang, Y., Zhong, J. Y., Zheng, W. D., Dong, Q. L., Chen, M., Zhao, G., Sakawa, Y., Morita, T., Kuramitsu, Y., Kato, T. N., Chen, L. M., Lu, X., Ma, J. L., Wang, W. M., Sheng, Z. M., Takabe, H., Rhee, Y.-J., Ding, Y. K., Jiang, S. E., Liu, S. Y., Zhu, J. Q. & Zhang, J. (2011). Collisionless shockwaves formed by counter-streaming laser-produced plasmas. N. J. Phys. 13, 093001.CrossRefGoogle Scholar
Medvedev, M. V. & Loeb, A. (1999). Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. Astrophys. J. 526, 697.CrossRefGoogle Scholar
Nakar, E., Bret, A. & Milosavljević, M. (2011). Two-stream-like instability in dilute hot relativistic beams and astrophysical relativistic shocks. Astrophysic. J. 738, 93.CrossRefGoogle Scholar
Oohara, W. & Hatakeyama, R. (2003). Pair-ion plasma generation using fullerenes. Phys. Rev. Lett. 91, 205005.CrossRefGoogle ScholarPubMed
Piran, T. (2004). The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143.Google Scholar
Romagnani, L., Bulanov, S., Borghesi, M., Audebert, P., Gauthier, J., Lwenbrck, K., Mackinnon, A., Patel, P., Pretzler, G., Toncian, T. & et al. (2008). Observation of collisionless shocks in laser-plasma experiments. Phys. Rev. Lett. 101, 025004.CrossRefGoogle ScholarPubMed
Ross, J. S., Glenzer, S. H., Amendt, P., Bergner, R., Divol, L., Kugland, N. L., Landen, O. L., Plechaty, C., Remington, B., Ryutov, D., Rozmus, W., Froula, D. H., Fiksel, G., Sorce, C., Kuramitsu, Y., Morita, T., Sakawa, Y., Takabe, H., Drake, R. P., Grosskopf, M., Kuranz, C., Gregori, G., Meinecke, J., Murphy, C. D., Koenig, M., Pelka, A., Ravasio, A., Vinci, T., Liang, E., Presura, R., Spitkovsky, A., Miniati, F. & Park, H.-S. (2012). Characterizing counter-streaming interpenetrating plasma relevant to astrophysical collisionless shocks. Phys. Plasmas 19, 056501.CrossRefGoogle Scholar
Ruyer, C. & Gremillet, L. (2012), In Preparation.Google Scholar
Sagdeev, R. Z. (1966). Cooperative phenomena and shock waves in collisionless plasmas. Rev. Plasma Phys. 4, 23.Google Scholar
Sarri, G., Dieckmann, M., Kourakis, I. & Borghesi, M. (2011). Generation of a purely electrostatic collisionless shock during the expansion of a dense plasma through a rarefied medium. Phys. Rev. Lett. 107, 025003.CrossRefGoogle ScholarPubMed
Schwartz, S. J., Henley, E., Mitchell, J. & Krasnoselskikh, V. (2011). Electron temperature gradient scale at collisionless shocks. Phys. Rev. Lett. 107, 215002.CrossRefGoogle ScholarPubMed
Silva, L. O., Fonseca, R. A., Tonge, J. W., Dawson, J. M., Mori, W. B., & Medvedev, M. V. (2003). Interpenetrating plasma shells: Nearequipartition magnetic field generation and nonthermal particle acceleration. Astrophys. J. 596, L121–L124.CrossRefGoogle Scholar
Silva, L. O., Fonseca, R. A., Tonge, J. W., Mori, W. B. & Dawson, J. M. (2002). On the role of the purely transverse weibel instability in fast ignitor scenarios. Phys. Plasmas 9, 2458.CrossRefGoogle Scholar
Sironi, L. & Spitkovsky, A. (2009). Particle acceleration in relativistic magnetized collisionless pair shocks: Dependence of shock acceleration on magnetic obliquity. Astrophys. J. 698, 1523.CrossRefGoogle Scholar
Warren, J. S., Hughes, J. P., Badenes, C., Ghavamian, P., McKee, C. F., Moffett, D., Plucinsky, P. P., Rakowski, C., Reynoso, E. & Slane, P. (2005). Cosmic-ray acceleration at the forward shock in Tycho's supernova remnant: Evidence from chandra X-ray observations. Astrophys. J. 634, 376.CrossRefGoogle Scholar
Yoon, P. H. (2007). Spontaneous thermal magnetic field fluctuation. Phys. Plasmas 14, 064504.CrossRefGoogle Scholar