This model naturally explains the rarity of radio halos, their presence in dynamically young clusters, and the anticorrelation with the presence of a cooling flow. It also explains the rapid fall in the spectrum at high frequencies, and the extent of the halo, as it does not require the electrons to diffuse from a central region but rather accelerates electrons everywhere.
Magnetic fields are also amplified by the turbulence in a cluster merger, but decay only slowly and so are gradually built up in successive merger events to their present strengths. Thus all clusters today should contain fields of strength ~1, with obviously some variation about this depending on the history of the cluster.
At this point a brief digression to consider the ultimate origin of the magnetic fields and relativistic electrons in galaxy clusters is in order. Cluster mergers and the ensuing turbulence should be able to reaccelerate existing relativistic electrons and amplify existing fields, but will find it difficult to accelerate thermal electrons to the required energies, or to generate the observed fields from a weak primordial field. An ultimate origin for both particles and fields must be found. Obvious and promising candidates are normal radio sources. Many clusters of galaxies are observed to contain radio galaxies today. At high and intermediate redshifts, radio sources are commonly found in cluster environments (Hintzen, Ulvestad & Owen 1983; Yee & Green 1987; Yates, Miller & Peacock 1989; Hill & Lilly 1991). Harris et al. (1992) note that the number of relativistic electrons (of all energies) is similar for the Coma halo, relic radio galaxies, and FR II radio galaxies. A consistent picture is therefore that the magnetic fields and relativistic electrons in cluster radio halos originated in radio sources that were then spread throughout the whole cluster by a merger event.
The magnetic field strength in cooling flows increases strongly towards the cluster centre. Thus if there are relativistic electrons in the cluster, either as a remnant of an earlier halo or diffusing out of a central active galaxy, then the radio emission will also be centrally concentrated. Second order Fermi acceleration by turbulence and collisions with clouds in the cooling flow may be able to keep electrons energetic enough to radiate at 90 cm as observed in the Perseus cluster, a possibility worth further investigation. Electrons may also be accelerated as small gas clouds contract, collapse, and cool out of the flow, or by shocks or magnetic reconnection in the cooling blobs.
If observations are made at sufficiently low frequencies then radio halos should be present in all galaxy clusters. The required frequencies are very low, however, as a 10^9 yr old halo has a break frequency of only 10 MHz. Given the current rate of cluster evolution, we might expect to see a small number of cluster halos at 38 MHz that are of order 5x10^8 yr old.