  Galactic cosmic rays are believed to be mostly accelerated at supernova
shocks. However, the interstellar magnetic field is too weak to efficiently
accelerate galactic cosmic rays up to the highest energies, i.e. $10^{15}$ eV.
A stronger magnetic field in the pre-shock region could provide the efficiency
required. Bell's cosmic-ray nonresonant streaming instability has been claimed
to be responsible for the amplification of precursor magnetic fields. However,
an alternative mechanism has been proposed in which the cosmic-ray pressure
gradient forms the shock precursor and drives turbulence, amplifying the
magnetic field via the small-scale dynamo. A key ingredient for the mechanism
to operate are the inhomogeneities present in the interstellar medium (ISM).
These inhomogeneities are the consequence of turbulence. In this work we
explore the magnetic field amplification in different ISM conditions through 3D
MHD numerical simulations.

High Energy Astrophysical Phenomena