Abstract
The origin of cosmic magnetic fields outside of galaxies remains controversial. In the intracluster medium field strengths of the order of muG have been reported. Possibly the outflows of AGN have magnetised the ICM. 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, since they host less active galaxies. Moreover, filaments are thought to contain the Warm-Hot Intergalactic Medium which represents a large fraction of the baryonic matter in the universe. Diffuse synchrotron emission by cosmic rays in these filaments will reveal the presence of this medium. We present highly resolved cosmological adaptive mesh refinement simulations of magnetic fields in the cosmos and make predictions about the evolution and structure of magnetic fields in filaments. Magnetic fields in clusters may also have their origin in AGN, whose evolution, in turn, is strongly affected by magnetic fields. We show how the dynamics of AGN-blown bubbles, that are vital for feedback mechanisms in clusters and galaxies, is governed by ambient magnetic fields that are effective at suppressing hydrodynamic instabilities.