  Random motions can occur in the intergalactic gas of galaxy clusters at all
stages of their evolution. Depending on the poorly known value of the Reynolds
number, these motions can or cannot become turbulent, but in any case they can
generate random magnetic fields via dynamo action. We argue that magnetic
fields inferred observationally for the intracluster medium require dynamo
action, and then estimate parameters of random flows and magnetic fields at
various stages of the cluster evolution. Polarization in cluster radio halos
predicted by the model would be detectable with the SKA.
