Most of the magnetic energy was generated at high redshift (z>1), when radio sources were numerous. As a result, the magnetic fields in high redshift clusters will have been built up to nearly their present strength. There is considerable observational support for this scenario: Rotation Measures (Carilli, Owen & Harris 1994) and depolarization (Tribble 1992) of powerful high redshift radio galaxies and quasars indicate that these sources are in strongly magnetized environments, and observations of integrated quasar Rotation Measures show that there is a population of strongly magnetized objects with redshifts 0.5--2.
The field is dispersed throughout the cluster by turbulence following a cluster merger which mixes the thermal and relativistic plasma. This also means that the magnetic field should now be extremely well mixed into the thermal plasma, as it has had most of the age of the universe to be mixed. While the diffusion of the magnetic field into the thermal plasma necessarily involves some field dissipation, turbulence and galactic wakes will also strengthen the field through dynamo action.
The estimate of the accumulated magnetic energy density is reliable, in the sense that the source properties that are integrated over are well known. The major uncertainty is the equipartition assumption used to relate the magnetic energy to the radiated energy. The energy density could be higher if not all the particle energy is radiated before the source dies, if a significant fraction of the energy is lost to inverse Compton radiation, or if there is a new population of sources that lead to an enhancement of the luminosity function at low luminosities. The combination of these uncertainties could cause the energy density to be underestimated by a considerable factor, but is unlikely to lead to the energy density being substantially overestimated.
This paper has only dealt with the large scale, cluster wide fields. The stronger fields seen at the centres of cooling flows (Dreher, Carilli & Perley 1987; Taylor et al. 1990; Perley & Taylor 1991; Ge 1991) are due to compression of the general cluster magnetic field by the slow cooling and inflow of the dense intracluster medium (Soker & Sarazin 1990; Tribble 1993).
Other sources of magnetic fields, such as stripped interstellar media and dynamos powered by galactic wakes fall short of the energy required to explain observed intracluster fields, although they can give field strengths ~0.1. Note, though, that while galactic wakes cannot by themselves create a 1 field by acting on a smaller seed field, they may well have an important role to play in the evolution of the intracluster magnetic field.
In summary, the left over remains of radio sources are likely to be mixed into the intracluster medium and provide a more than adequate supply of magnetic energy to explain the ~ magnetic fields observed in galaxy clusters.