  The intergalactic magnetic field within filaments should be less polluted by
magnetised outflows from active galaxies than magnetic fields in clusters.
Therefore, filaments may be a better laboratory to study magnetic field
amplification by structure formation than galaxy clusters which typically host
many more active galaxies. We present highly resolved cosmological AMR
simulations of magnetic fields in the cosmos and make predictions about the
evolution and structure of magnetic fields in filaments. Comparing our results
to observational evidence for magnetic fields in filaments suggests that
amplification of seed fields by gravitational collapse is not sufficient to
produce IGM fields. Finally, implications for cosmic ray transport are
discussed.
