Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T04:17:18.079Z Has data issue: false hasContentIssue false

Conditions for the onset of the current filamentation instability in the laboratory

Published online by Cambridge University Press:  10 May 2018

N. Shukla*
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
J. Vieira
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
P. Muggli
Affiliation:
Max Planck Institute for Physics, 80805 Munich, Germany
G. Sarri
Affiliation:
Centre for Plasma Physics, School of Mathematics and Physics, Queen’s University of Belfast, Belfast BT7 1NN, UK
R. Fonseca
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal DCTI/ISCTE, Instituto Universitario de Lisboa, 1649-026 Lisbon, Portugal
L. O. Silva
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
*
Email address for correspondence: [email protected]

Abstract

The current filamentation instability (CFI) is capable of generating strong magnetic fields relevant to the explanation of radiation processes in astrophysical objects and leads to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral $e^{-}~e^{+}$ beams to explore the CFI with realistic parameters, by performing two-dimensional particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI growth rate and as long as the role of the competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma-based accelerated electron–positron fireball beams, plays a minor role in the growth of CFI in these scenarios.

Type
Research Article
Copyright
© Cambridge University Press 2018 

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

Achterberg, A., Wiersma, J. & Norman, C. A. 2007 The Weibel instability in relativistic plasmas II. Nonlinear theory and stabilization mechanism. A&A 475, 1936.Google Scholar
Allen, B., Yakimenko, V., Babzien, M., Fedurin, M., Kusche, K. & Muggli, P. 2012 Experimental study of current filamentation instability. Phys. Rev. Lett. 109, 185007.Google Scholar
Bahcall, J. N. & Ostriker, J. P. 1997 Unsolved Problems in Astrophysics. Princeton University Press.Google Scholar
Blumenfeld, I., Clayton, C. E., Decker, F. J., Hogan, M. J., Huang, C., Ischebeck, R., Iverson, R., Joshi, C., Katsouleas, T., Kirby, N. et al. 2007 Energy doubling of 42 GEV electrons in a metre-scale plasma wakefield accelerator. Nature (London) 445, 741744.CrossRefGoogle Scholar
Bret, A. 2009 Weibel, two-stream, filamentation, oblique, bell, buneman...which one grows faster? Astrophys. J. 699 (2), 9901003.Google Scholar
Bret, A. & Gremillet, L. 2006 Oblique instabilities in relativistic electron beam plasma interaction. Plasma Phys. Control. Fusion 48, B405B412.Google Scholar
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.Google Scholar
Cavallo, G. & Rees, M. J. 1978 A qualitative study of cosmic fireballs and gamma-ray bursts. Mon. Not. R. Astron. Soc. 183, 359365.Google Scholar
Chakraborti, S., Ray, A., Soderberg, A. M., Loeb, A. & Chandra, P. 2011 Ultra high energy cosmic rays from engine-driven relativistic supernovae. Nat. Commun. 2, 175.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Chang, P., Broderick, A. E., Pfrommer, C., Puchwein, E., Lamberts, A. & Shalaby, M. 2014 The effect of nonlinear landau damping on ultra relativistic beam plasma instabilities. Astrophys. J. 797 (2), 110.Google Scholar
Chang, P., Broderick, A. E., Pfrommer, C., Puchwein, E., Lamberts, A., Shalaby, M. & Vasil, G. 2016 The linear instability of dilute ultra relativistic e $\mp$ pair beams. Astrophys. J. 833 (1), 118.Google Scholar
Chen, P., Su, J. J., Katsouleas, T., Wilks, S. & Dawson, J. M. 1987 Plasma focusing for high-energy beams. IEEE Trans. Plasma Sci. 15, 218225.CrossRefGoogle Scholar
Dieckmann, M. E., Shukla, P. K. & Stenflo, L. 2009 Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas. Plasma Phys. Control. Fusion 51, 065015.Google Scholar
Fainberg, Y. B., Shapiro, V. D. & Shevchenko, V. I. 1970 Nonlinear theory of interaction between a ‘monochromatic beam of relativistic electrons and a plasmas’. J. Expl Theor. Phys. 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., Martins, S. F., Silva, L. O., Tonge, J. W., Tsung, F. S. & Mori, W. B. 2008 One-to-one direct modeling of experiments and astrophysical scenarios: pushing the envelope on kinetic plasma simulations. Plasma Phys. Control. Fusion 50, 124034.Google Scholar
Fonseca, R. A., Silva, L. O., Tonge, J., Hemker, R. G., Dawson, J. M. & Mori, W. B. 2002a Three-dimensional particle-in-cell simulations of the weibel instability in electron-positron plasmas. IEEE Trans. Plasma Sci. 30, 2829.Google Scholar
Fonseca, R. A., Silva, L. O., Tsung, F. S., Decyk, K. V., Lu, W., Ren, C., Mori, W. B., Deng, S., Lee, S., Katsouleas, T. et al. 2002b Osiris: a three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. Lect. Notes Comput. Sci. 2331, 046401.CrossRefGoogle Scholar
Fonseca, R. A., Vieira, J., Fiuza, F., Davidson, A., Tsung, F. S., Mori, W. B. & Silva, L. O. 2013 Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators. Plasma Phys. Control. Fusion 55, 124011.Google Scholar
Frederiksen, J. T., Hededal, C. B., Haugblle, T. & Nordlund, A. 1999 Magnetic field generation in collisionless shocks: pattern growth and transport. Astrophys. J. 608, L13.Google Scholar
Goodman, J. 1986 Are gamma-ray bursts optically thick? Astrophys. J. Lett. 308, L47.Google Scholar
Gould, R. J. & Schréder, G. P. 1967 Pair production in photon-photon collisions. Phys. Rev. 155, 14041407.CrossRefGoogle Scholar
Hantao, J. & Zweibel, E. 2015 Understanding particle acceleration in astrophysical plasmas. Science 347, 944945.Google Scholar
Hogan, M. J., Raubenheimer, T. O., Seryi, A., Muggli, P., Katsouleas, T., Huang, C., Lu, W., An, W., Marsh, K. A., Mori, W. B. et al. 2010 Plasma wakefield acceleration experiments at facet. New J. Phys. 12, 055030.Google Scholar
Inglebert, A., Ghizzo, A., Reveille, T., Sarto, D. D., Bertrand, P. & Califano, F. 2012 Multi-stream vlasov model for the study of relativistic weibel-type instabilities. Plasma Phys. Control. Fusion 54, 085004.Google Scholar
Kronberg, P. 2002 Intergalactic magnetic fields. Phys. Today 55, 1240.Google Scholar
Medvedev, M. V. & Leob, A. 1999 Generation of magnetic fields in the relativistic shock of gamma-ray-burst sources. Astrophys. J. 526, 697.Google Scholar
Medvedev, M. V., Massimiliano, F., Fonseca, R. A., Silva, L. O. & Mori, W. B. 2005 Long-time evolution of magnetic fields in relativistic gamma-ray burst shocks. Astrophys. J. 618, L75.CrossRefGoogle Scholar
Muggli, P., Martins, S. F., Vieira, J. & Silva, L. O.2013 Interaction of ultra relativistic $e-e+$ fireball beam with plasma. ArXiv e-prints, Preprint arXiv:1306.4380.Google Scholar
Neronov, A. & Semikoz, D. V. 2009 Sensitivity of $\unicode[STIX]{x1D6FE}$ -ray telescopes for detection of magnetic fields in the intergalactic medium. Phys. Rev. D 80, 123012.Google Scholar
Nishikawa, K. I., Niemiec, J., Hardee, P. E., Medvedev, M., Sol, H., Mizuno, Y., Zhang, B., Pohl, M., Oka, M. & Hartmann, D. H. 2009 Weibel instability and associated strong fields in a fully three-dimensional simulation of a relativistic shock. Astrophys. J. 698, L10.Google Scholar
Paczynski, B. 1986 Gamma-ray bursters at cosmological distance. Astrophys. J. Lett. 308, L43.Google Scholar
Pegoraro, F., Bulanov, S. V., Califano, F. & Lontano, M. 1996 Nonlinear development of the weibel instability and magnetic field generation in collisionless plasmas. Phys. Scr. T63, 262.Google Scholar
Piran, T. 1996 Relativity at action or gamma-ray bursts. General Relativity and Gravitation 28, 14211426.Google Scholar
Piran, T. 2002 The physics of gamma-ray bursts. Rev. Mod. Phys. 76, 1143.Google Scholar
Piran, T. 2005 Magnetic fields in gamma?ray bursts: a short overview. AIP Conference Proceedings 784, 164174.CrossRefGoogle Scholar
Rees, M. J. & Meszaros, P. 1992 Relativistic fireballs: energy conversion and time-scales. Astrophys. J. Lett. 308, L47.Google Scholar
Roswell, L. & Martin, L. 1973 Electromagnetic instabilities, filamentation, and focusing of relativistic electron beams. Phys. Rev. Lett. 31, 13901393.Google Scholar
Salamon, M. H. & Stecker, F. W. 1998 Absorption of high-energy gamma rays by interactions with extragalactic starlight photons at high redshifts and the high-energy gamma-ray background. Astrophys. J. 493, 547.Google Scholar
Sarri, G., Poder, K., Cole, J. M., Schumaker, W. et al. 2015 Generation of neutral and high-density electron-positron pair plasmas in the laboratory. Nat. Commun. 6, 6747.CrossRefGoogle ScholarPubMed
Schlickeiser, R. 2005 On the origin of cosmological magnetic fields by plasma instabilities. Plasma Phys. Control. Fusion 47, 122109.Google Scholar
Schlickeiser, R., Elyiv, A., Ibscher, D. & Miniati, F. 2012 The pair beam production spectrum from photon-photon annihilation in cosmic voids. Astrophys. J. 758, 101.Google Scholar
Schlickeiser, R., Krakau, S. & Supsar, M. 2013 Plasma effects on fast pair beams. II. Reactive versus kinetic instability of parallel electrostatic waves. Astrophys. J. 777, 49.CrossRefGoogle Scholar
Schroeder, C. B. & Benedetti, C. E. A. 2011 Growth and phase velocity of self-modulated beam-driven plasma waves. Phys. Rev. Lett. 107, 145002.Google Scholar
Sentoku, Y., Mima, K., Kaw, P. & Nishikawa, K. 2003 Anomalous resistivity resulting from mev-electron transport in overdense plasma. Phys. Rev. Lett. 90, 155001.Google Scholar
Shalaby, M., Broderick, A. E., Chang, P., Pfrommer, C., Lamberts, A. & Puchwein, E. 2017 Importance of resolving the spectral support of beam-plasma instabilities in simulations. Astrophys. J. 848, 81.Google Scholar
Shukla, N. & Shukla, P. 2010 Proton-temperature-anisotropy-driven magnetic fields in plasmas with cold and relativistically hot electrons. J. Plasma Phys. 76, 15.Google Scholar
Shukla, N., Stockem, A., Fiuza, F. & Silva, L. O. 2012 Enhancement in the electromagnetic beam-plasma instability due to ion streaming. J. Plasma Phys. 78, 181187.Google Scholar
Silva, L. O., Fonseca, R. A., Tonge, J. W., Dawson, J. M., Mori, W. B. & Medvedev, M. V. 2003 Interpenetrating plasma shells: near-equipartition magnetic field generation and nonthermal particle acceleration. Astrophys. J. 596, L121.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, 24582461.Google Scholar
Sironi, L. & Giannios, D. 2014 Relativistic pair beams from tev blazars: a source of reprocessed gev emission rather than intergalactic heating. Astrophys. J. 787 (1), 49.Google Scholar
Stockem, A., Bret, A., Fonseca, R. A. & Silva, L. O. 2015 Physics of collisionless shocks: theory and simulation. Plasma Phys. Control. Fusion 58, 014005.Google Scholar
Su, J. J., Katsouleas, T., Dawson, J. M., Chen, P., Jones, M. & Keinigs, R. 1987 Stability of the driving bunch in the plasma wakefield accelerator. IEEE Trans. Plasma Sci. 15 (2), 192198.CrossRefGoogle Scholar
Tzoufras, M., Ren, C., Tsung, F. S., Tonge, J. W., Mori, W. B., Fiore, M., Fonseca, R. A. & Silva, L. O. 2006 Space-charge effects in the current-filamentation or weibel instability. Phys. Rev. Lett. 96, 105002.Google Scholar
Uzdensky, A. & Rightley, S. 2014 Plasma physics of extreme astrophysical environments. Rep. Prog. Phys. 77, 036902.Google Scholar
Waxman, E. & Loeb, A. 2009 Constraints on the local sources of ultra high-energy cosmic rays. J. Cosmol. Astropart. Phys 08, 026.Google Scholar
Weibel, E. S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 8384.Google Scholar
Widrow, L. 2002 Origin of galactic and extragalactic magnetic fields. Rev. Mod. Phys. 74, 775.Google Scholar
Yang, T. B., Arons, J. & Langdo, A. B. 1994 Evolution of the Weibel instability in relativistically hot electron-positron plasmas. Phys. Plasmas 1, 30593077.Google Scholar