  Cooling flows are regions where the importance of non-thermal intra-cluster
medium components such as magnetic fields and cosmic rays may be strongest
within a galaxy cluster. They are also regions where such components are best
detectable due to the high gas density which influences Faraday rotation
measurements of magnetic fields and secondary particle production in hadronic
interactions of cosmic ray nuclei with the ambient thermal gas. New estimates
of magnetic fields in cooling flow and non-cooling flow clusters are presented,
which are based on a newly developed Fourier analysis of extended Faraday
rotation maps. We further present new constraints on the cluster cosmic ray
proton population using radio and gamma-ray observations measurements of
cluster cooling flows, which are especially suited for this purpose due to
their high gas and magnetic energy densities. We argue that radio synchrotron
emission of cosmic ray electrons generated hadronically by cosmic ray protons
is a very plausible explanation for the radio mini-halos observed in some
cooling flows.
