On the amplification of magnetic fields in cosmic filaments and galaxy   clusters
  The amplification of primordial magnetic fields via a small-scale turbulent dynamo during structure formation might be able to explain the observed magnetic fields in galaxy clusters. The magnetisation of more tenuous large-scale structures such as cosmic filaments is more uncertain, as it is challenging for numerical simulations to achieve the required dynamical range. In this work, we present magneto-hydrodynamical cosmological simulations on large uniform grids to study the amplification of primordial seed fields in the intracluster medium (ICM) and in the warm-hot-intergalactic medium (WHIM). In the ICM, we confirm that turbulence caused by structure formation can produce a significant dynamo amplification, even if the amplification is smaller than what is reported in other papers. In the WHIM inside filaments, we do not observe significant dynamo amplification, even though we achieve Reynolds numbers of $R_{\rm e} \sim 200-300$. The maximal amplification for large filaments is of the order of $\sim 100$ for the magnetic energy, corresponding to a typical field of a few $\sim \rm nG$ starting from a primordial weak field of $10^{-10}$ G (comoving). In order to start a small-scale dynamo, we found that a minimum of $\sim 10^2$ resolution elements across the virial radius of galaxy clusters was necessary. In filaments we could not find a minimum resolution to set off a dynamo. This stems from the inefficiency of supersonic motions in the WHIM in triggering solenoidal modes and small-scale twisting of magnetic field structures. Magnetic fields this small will make it hard to detect filaments in radio observations. 
F. Vazza, M. Br\"uggen, C. Gheller, P. Wang
astro-ph.CO