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Evolution of magnetic field in a weakly relativistic counterstreaming inhomogeneous e/e+ plasmas

Published online by Cambridge University Press:  24 July 2020

Sandeep Kumar
Affiliation:
Department of Physics, Manav Rachna University (MRU), Faridabad, Haryana, India
Y. K. Kim
Affiliation:
Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, South Korea
T. Kang
Affiliation:
Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, South Korea
Min Sup Hur*
Affiliation:
Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, South Korea
Moses Chung*
Affiliation:
Department of Physics, Ulsan National Institute of Science and Technology, Ulsan, South Korea
*
Author for correspondence: M. Chung and M. S. Hur, Department of Physics, Ulsan National Institute of Science Technology, Ulsan, South Korea. E-mail: mchung@unist.ac.kr; mshur@unist.ac.kr
Author for correspondence: M. Chung and M. S. Hur, Department of Physics, Ulsan National Institute of Science Technology, Ulsan, South Korea. E-mail: mchung@unist.ac.kr; mshur@unist.ac.kr

Abstract

The nonlinear evolution of electron Weibel instability in a symmetric, counterstream, unmagnetized electron–positron e/e+ plasmas is studied by a 2D particle-in-cell (PIC) method. The magnetic field is produced and amplified by the Weibel instability, which extracts energy from the plasma anisotropy. A weakly relativistic drift velocity of 0.5c is considered for two counterstreaming e/e+ plasma flows. Simulations show that in a homogeneous e/e+ plasma distribution, the magnetic field amplifies exponentially in the linear regime and rapidly decays after saturation. However, in the case of inhomogeneous e/e+ plasma distribution, the magnetic field re-amplifies at post-saturation. We also find that the amount of magnetic field amplification at post-saturation depends on the strength of the density inhomogeneity of the upstream plasma distribution. The temperature calculation shows that the finite thermal anisotropy exists in the case of an inhomogeneous plasma distribution which leads to the second-stage magnetic field amplification after the first saturation. Such density inhomogeneities are present in a variety of astrophysical sources: for example, in supernova remnants and gamma-ray bursts. Therefore, the present analysis is very useful in understanding these astrophysical sources, where anisotropic density fluctuations are very common in the downstream region of the relativistic shocks and the widely distributed magnetic field.

Type
Research Article
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press

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References

Arber, TD, Bennett, K, Brady, CS, Lawrence-Douglas, A, Ramsay, MG, Sircombe, NJ, Gillies, P, Evans, RG, Schmitz, H, Bell, AR and Ridgers, CP (2015) Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Physics and Controlled Fusion 57, 113001.CrossRefGoogle Scholar
Ardaneh, K, Cai, D, Nishikawa, KI and Lembege, B (2015) Collisionless Weibel shocks and electron acceleration in gamma-ray bursts. The Astrophysical Journal 811, 57.CrossRefGoogle Scholar
Armstrong, JW, Cordes, JM and Rickett, BJ (1981) Density power spectrum in the local interstellar medium. Nature 291, 561564.CrossRefGoogle Scholar
Armstrong, JW, Rickett, BJ and Spangler, SR (1995) Electron density power spectrum in the local interstellar medium. The Astrophysical Journal 443, 209.CrossRefGoogle Scholar
Bamba, A, Yamazaki, R, Yoshida, T, Terasawa, T and Koyama, K (2005) A spatial and spectral study of nonthermal filaments in historical supernova remnants: observational results with Chandra. The Astrophysical Journal 621, 793.CrossRefGoogle Scholar
Bell, AR (2004) Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Monthly Notices of the Royal Astronomical Society 353, 550.CrossRefGoogle Scholar
Berezhko, EG, Puhlhofer, G and Volk, HJ (2003 a) Gamma-ray emission from Cassiopeia A produced by accelerated cosmic rays. Astronomy and Astrophysics 400, 971.CrossRefGoogle Scholar
Berezhko, EG, Ksenofontov, LT and Volk, HJ (2003 b) Confirmation of strong magnetic field amplification and nuclear cosmic ray acceleration in SN 1006. Astronomy and Astrophysics 412, L11.CrossRefGoogle Scholar
Bret, A (2006) A simple analytical model for the Weibel instability in the non-relativistic regime. Physics Letters A 359, 52.CrossRefGoogle Scholar
Bret, A and Deutsch, C (2006) Stabilization of the filamentation instability and the anisotropy of the background plasma. Physics of Plasmas 13, 022110.CrossRefGoogle Scholar
Bret, A, Stockem, AN and Narayan, R (2016) Theory of the formation of a collisionless weibel shock: pair vs. electron/proton plasmas. Laser and Particle Beams 34, 362.CrossRefGoogle Scholar
Califano, F, Pegoraro, F, Bulanov, SV and Mangeney, A (1998) Kinetic saturation of the Weibel instability in a collisionless plasma. Physical Review E 57, 7048.CrossRefGoogle Scholar
Cho, M-H, Kim, Y-K, Suk, H, Ersfeld, B, Jaroszynski, DA and Hur, MS (2015) Strong terahertz emission from electromagnetic diffusion near cutoff in plasma. New Journal of Physics 17, 043045.CrossRefGoogle Scholar
Davidson, RC, Hammer, DA, Haber, I and Wagner, CE (1972) Nonlinear development of electromagnetic instabilities in anisotropic plasmas. Physics of Fluids 15, 317.CrossRefGoogle Scholar
Dieckmann, ME and Bret, A (2017) Simulation study of the formation of a non-relativistic pair shock. Journal of Plasma Physics 83, 905830104.CrossRefGoogle 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, 198.CrossRefGoogle Scholar
Fiuza, F, Fonseca, RA, Tonge, J, Mori, WB and Silva, LO (2012) Weibel-instability-mediated collisionless shocks in the laboratory with ultraintense lasers. Physical Review Letters 108, 235004.CrossRefGoogle ScholarPubMed
Fox, W, Fiksel, G, Bhattacharjee, A, Chang, PY, Germaschewski, K, Hu, SX and Nilson, PM (2013) Filamentation instability of counterstreaming laser-driven plasmas. Physical Review Letters 111, 225002.CrossRefGoogle ScholarPubMed
Fried, BD (1959) Mechanism for instability of transverse plasma waves. Physics of Fluids 2, 337.CrossRefGoogle Scholar
Fried, BD and Conte, SD (1961) The Plasma Dispersion Function. New York: Academic Press.Google Scholar
Grassi, A, Grech, M, Amiranoff, F, Pegoraro, F, Macchi, A and Riconda, C (2017) Electron Weibel instability in relativistic counterstreaming plasmas with flow-aligned external magnetic fields. Physical Review E 95, 023203.CrossRefGoogle ScholarPubMed
Hur, MS and Suk, H (2011) Numerical study of 1.1 GeV electron acceleration over a-few-millimeter-long plasma with a tapered density. Physics of Plasmas 18, 033102.CrossRefGoogle Scholar
Kalman, G, Montes, C and Quemada, D (1968) Anisotropic temperature plasma instabilities. Physics of Fluids 11, 1797.CrossRefGoogle Scholar
Kronberg, P (2002) Intergalactic magnetic fields. Physics Today 55, 1240.CrossRefGoogle Scholar
Lazar, M (2008) Fast magnetization in counterstreaming plasmas with temperature anisotropies. Physics Letters A 372, 2446.CrossRefGoogle Scholar
Lazar, M, Schlickeiser, R and Shukla, PK (2006) Cumulative effect of the filamentation and Weibel instabilities in counterstreaming thermal plasmas. Physics of Plasmas 13, 102107.CrossRefGoogle Scholar
Lazar, M, Schlickeiser, R and Shukla, PK (2008) Cumulative effect of the Weibel-type instabilities in symmetric counterstreaming plasmas with kappa anisotropies. Physics of Plasmas 15, 042103.CrossRefGoogle Scholar
Lazar, M, Schlickeiser, R, Wielebinski, R and Poedts, S (2009 a) Cosmological effects of Weibel-type instabilities. The Astrophysical Journal 693, 1133.CrossRefGoogle Scholar
Lazar, M, Smolyakov, A, Schlickeiser, R and Shukla, PK (2009 b) A comparative study of the filamentation and Weibel instabilities and their cumulative effect. I. Non-relativistic theory. Journal of Plasma Physics 75, 19.CrossRefGoogle Scholar
Lee, LC and Jokipii, JR (1976) The irregularity spectrum in interstellar space. The Astrophysical Journal 206, 735743.CrossRefGoogle Scholar
Lucek, SG and Bell, AR (2000) Non-linear amplification of a magnetic field driven by cosmic ray streaming. Monthly Notices of the Royal Astronomical Society 314, 65.CrossRefGoogle Scholar
Medvedev, MV and Loeb, A (1999) Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. The Astrophysical Journal 526, 697.CrossRefGoogle Scholar
Medvedev, MV, Fiore, M, Fonseca, RA, Silva, LO and Mori, WB (2005) Long-time evolution of magnetic fields in relativistic gamma-ray burst shocks. Astrophysical Journal Letters 618, L75.CrossRefGoogle Scholar
Niemiec, J, Pohl, M, Stroman, T and Nishikawa, KI (2008) Production of magnetic turbulence by cosmic rays drifting upstream of supernova remnant shocks. The Astrophysical Journal 684, 11741189.CrossRefGoogle Scholar
Nishikawa, KI, Hardee, P, Richardson, G, Preece, R, Sol, H and Fishman, GJ (2003) Particle acceleration in relativistic jets due to Weibel instability. The Astrophysical Journal 595, 555.CrossRefGoogle Scholar
Ohira, Y, Reville, B, Kirk, JG and Takahara, F (2009) Two-dimensional particle-in-cell simulations of the nonresonant, cosmic-ray driven instability in SNR shocks. The Astrophysical Journal 698, 445.CrossRefGoogle Scholar
Reville, B, Kirk, JG and Duffy, P (2006) A current-driven instability in parallel, relativistic shocks. Plasma Physics and Controlled Fusion 48, 1741.CrossRefGoogle Scholar
Reville, B, Kirk, JG, Duffy, PD and O'Sullivan, S (2007) A cosmic ray current-driven instability in partially ionised media. Astronomy and Astrophysics 475, 435439.CrossRefGoogle Scholar
Riquelme, MA and Spitkovsky, A (2008) Kinetic simulations of the current-driven instability in cosmic ray modified relativistic shocks. International Journal of Modern Physics D 17, 1803.CrossRefGoogle Scholar
Rowlands, G, Dieckmann, ME and Shukla, PK (2007) The plasma filamentation instability in one dimension: nonlinear evolution. New Journal of Physics 9, 247.CrossRefGoogle Scholar
Silva, LO, Fonseca, RA, Tonge, JW, Mori, WB and Dawson, JM (2002) On the role of the purely transverse Weibel instability in fast ignitor scenarios. Physics of Plasmas 9, 2458.CrossRefGoogle Scholar
Sironi, L and Goodman, J (2007) Production of magnetic energy by macroscopic turbulence in GRB afterglows. The Astrophysical Journal 671, 1858.CrossRefGoogle Scholar
Spitkovsky, A (2008) On the structure of relativistic collisionless shocks in electron-ion plasmas. Astrophysical Journal Letters 673, L39.CrossRefGoogle Scholar
Stockem, A and Lazar, M (2008) Revision of cumulative effect of the filamentation and Weibel instabilities in counterstreaming thermal plasmas. Physics of Plasmas 15, 014501.CrossRefGoogle Scholar
Stockem, A, Lazar, M, Shukla, PK and Smolyakov, A (2009) A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams. Journal of Plasma Physics 75, 529.CrossRefGoogle Scholar
Tomita, S and Ohira, Y (2016) Weibel instability driven by spatially anisotropic density structures. The Astrophysical Journal 825, 103.CrossRefGoogle Scholar
Uchiyama, Y, Aharonian, T, Tanaka, T, Takahashi, T and Maeda, Y (2007) Extremely fast acceleration of cosmic rays in a supernova remnant. Nature 449, 576.CrossRefGoogle Scholar
Vink, J and Laming, JM (2003) On the magnetic fields and particle acceleration in Cassiopeia A. The Astrophysical Journal 584, 758.CrossRefGoogle Scholar
Weibel, ES (1959) Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Physical Review Letters 2, 83.CrossRefGoogle Scholar