  Galaxy clusters are the largest structures for which there is observational
evidence of a magnetised medium. Central cores seem to host strong magnetic
fields ranging from a few 0.1 microG up to several 10 microG in cooling flow
clusters. Numerous clusters harbor central powerful AGN which are thought to
prevent cooling flows in some clusters. The influence of such feedback on the
magnetic field remains unclear: does the AGN-induced turbulence compensate the
loss of magnetic amplification within a cool core? And how is this turbulence
sustained over several Gyr? Using high resolution magneto-hydrodynamical
simulations of the self-regulation of a radiative cooling cluster, we study for
the first time the evolution of the magnetic field within the central core in
the presence of a powerful AGN jet. It appears that the jet-induced turbulence
strongly amplifies the magnetic amplitude in the core beyond the degree to
which it would be amplified by pure compression in the gravitational field of
the cluster. The AGN produces a non-cooling core and increases the magnetic
field amplitude in good agreement with microG field observations.
