Radiophysics and Quantum Electronics

, Volume 60, Issue 12, pp 931–941 | Cite as

Nonlinear Effects in the Weibel Instability

  • M. A. Garasev
  • E. V. Derishev

Using the particle-in-cell code, we performed numerical simulations of the Weibel instability in plasmas with a two-temperature Maxwellian distribution function. We found harmonics in the power spectrum of the Weibel-generated turbulent magnetic field, which permitted us to measure directly the magnitude of the nonlinear effects. It is shown that by the time of the instability saturation the nonlinear effects are insignificant in the case of a large initial anisotropy and are vanishing in the case of a small initial anisotropy, so that the nonlinearity is not the reason why the magnetic field stops to increase. The asymptotic form of the power spectrum of the magnetic field in the region of small scales is determined. It is demonstrated that the nonlinearity is essential for the generation of a large-scale magnetic field and therefore plays a crucial role at the stage of the magnetic field decay. Astrophysical applications of the obtained results are discussed.


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  1. 1.
    E. S. Weibel, Phys. Rev. Lett., 2, 83 (1959).ADSCrossRefGoogle Scholar
  2. 2.
    V. V. Kocharovsky, V. V. Kocharovsky, B. Yu. Martyanov, and S. V. Tarasov, Phys. Usp., 59, 165 (2016).CrossRefGoogle Scholar
  3. 3.
    W. Fox, G. Fiksel, A. Bhattacharjee, et al., Phys. Rev. Lett., 111, No. 22, 225002 (2013).Google Scholar
  4. 4.
    A. Gruzinov, Astrophys. J. Lett., 563, L15 (2001).ADSCrossRefGoogle Scholar
  5. 5.
    M. V. Medvedev and A. Loeb, Astrophys. J., 526, 697 (1999).ADSCrossRefGoogle Scholar
  6. 6.
    K. Yu. Vagin and S. A. Uryupin, Plasma Phys. Rep., 40, No. 5, 393 (2014).ADSCrossRefGoogle Scholar
  7. 7.
    L. V. Borodachev, M. A. Garasev, D. O. Kolomiets, et al., Radiophys. Quantum Electron., 59, 991 (2016).ADSCrossRefGoogle Scholar
  8. 8.
    A. Achterberg, J. Wiersma, and C. A. Norman, Astron. Astrophys., 475, No. 1, 19 (2007).ADSCrossRefGoogle Scholar
  9. 9.
    L. V. Borodachev and D. O. Kolomiets, J. Plasma Phys., 77, No. 2, 277 (2011).Google Scholar
  10. 10.
    T. Kato, Phys. Plasmas, 12, No. 8, 080705 (2005).ADSCrossRefGoogle Scholar
  11. 11.
    M. E. Dieckmann, Plasma Phys. Control. Fusion, 51, 124042 (2009).ADSCrossRefGoogle Scholar
  12. 12.
    A. Stockem, M. E. Dieckmann, and R. Schlickeiser, Plasma Phys. Control. Fusion, 51, 075014 (2009).ADSCrossRefGoogle Scholar
  13. 13.
    Y. F. Arber, K. Bennett, C. S. Brady, et al., Plasma Phys. Control. Fusion, 57, 113001 (2016).ADSCrossRefGoogle Scholar
  14. 14.
    T. Courant, K. Friedrichs, and H. Lewy, Math. Annal., 100, 32 (1928).CrossRefGoogle Scholar
  15. 15.
    J. Wiersma and A. Achterberg, Astron. Astrophys., 428, 365 (2004).ADSCrossRefGoogle Scholar
  16. 16.
    R. C. Davidson, D. A. Hammer, I. Haber, and C. E. Wagner, Phys. Fluids, 15, 317 (1972).ADSCrossRefGoogle Scholar
  17. 17.
    M. Garasev and E. Derishev, Mon. Notices Royal Astron. Soc., 461, No. 1, 641 (2016).ADSCrossRefGoogle Scholar
  18. 18.
    E. V. Derishev and T. Piran, Mon. Notices Royal Astron. Soc., 460, No. 2, 2036 (2016).ADSCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Physics, Russian Academy of SciencesNizhny NovgorodRussia
  2. 2.N. I. Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussia

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