It has become quite clear that dynamically significant magnetic fields of order 10−6 Gauss are present in galactic halos (Perry, these Proceedings) at redshifts up to
z≥ 2. Comparable fields have been detected on cluster and even on supercluster scales (Giovannini, these Proceedings). The existence of such high fields is surprising because it is highly unlikely that primeval magnetic fields could have been much stronger than 10–18 Gauss. These observations require that there be an epoch of very vigorous dynamo action that can amplify this seed primordial field up to the observed values. Since strong fields are already in place by redshifts of z≃ 2, this amplification process must operate very quickly. This argues against the idea that such fields could be generated on huge intercluster scales since the dynamical times are far too long. A much more promising site for the dynamo process is in the dark matter halos of young galaxies during the epoch of galaxy formation. The fundamental point is that vigorous dynamo action can take place in shocks that are expected to occur throughout the dark matter potential wells of protogalaxies (Pudritz and Silk 1989 (≡ PS), Pudritz 1989).