@article{MizunoPohlNiemiecetal.2011,
  author    = {Mizuno, Yosuke and Pohl, Martin and Niemiec, Jacek and Zhang, Bing and Nishikawa, Ken-Ichi and Hardee, Philip E.},
  title     = {Magnetic-field amplification by turbulence in a relativistic shockpropagating through an inhomogeneous medium},
  series = {The astrophysical journal : an international review of spectroscopy and astronomical physics},
  volume    = {726},
  journal   = {The astrophysical journal : an international review of spectroscopy and astronomical physics},
  number    = {2},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0004-637X},
  doi       = {10.1088/0004-637X/726/2/62},
  pages     = {11},
  year      = {2011},
  abstract  = {We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in the postshock region. We also find that the amount of magnetic-field amplification depends on the direction of the mean preshock magnetic field, and the timescale of magnetic-field growth depends on the shock strength.},
  language  = {en}
}
@article{MizunoPohlNiemiecetal.2014,
  author    = {Mizuno, Yosuke and Pohl, Martin and Niemiec, Jacek and Zhang, Bing and Nishikawa, Ken-Ichi and Hardee, Philip E.},
  title     = {Magnetic field amplification and saturation in turbulence behind a relativistic shock},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {439},
  journal   = {Monthly notices of the Royal Astronomical Society},
  number    = {4},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/stu196},
  pages     = {3490 -- 3503},
  year      = {2014},
  abstract  = {We have investigated via 2D relativistic magnetohydrodynamic simulations the long-term evolution of turbulence created by a relativistic shock propagating through an inhomogeneous medium. In the post-shock region, magnetic field is strongly amplified by turbulent motions triggered by pre-shock density inhomogeneities. Using a long-simulation box we have followed the magnetic field amplification until it is fully developed and saturated. The turbulent velocity is subrelativistic even for a strong shock. Magnetic field amplification is controlled by the turbulent motion and saturation occurs when the magnetic energy is comparable to the turbulent kinetic energy. Magnetic field amplification and saturation depend on the initial strength and direction of the magnetic field in the pre-shock medium, and on the shock strength. If the initial magnetic field is perpendicular to the shock normal, the magnetic field is first compressed at the shock and then can be amplified by turbulent motion in the post-shock region. Saturation occurs when the magnetic energy becomes comparable to the turbulent kinetic energy in the post-shock region. If the initial magnetic field in the pre-shock medium is strong, the post-shock region becomes turbulent but significant field amplification does not occur. If the magnetic energy after shock compression is larger than the turbulent kinetic energy in the post-shock region, significant field amplification does not occur. We discuss possible applications of our results to gamma-ray bursts and active galactic nuclei.},
  language  = {en}
}