The Magnetic Field in Galaxies, Galaxy Clusters, and the InterGalactic   Space
  Magnetic fields of debated origin appear to permeate the Universe on all large scales. There is mounting evidence that supernovae produce not only roughly spherical ejecta and winds, but also highly relativistic jets of ordinary matter. These jets, which travel long distances, slow down by accelerating the matter encountered on their path to cosmic-ray energies. We show that, if the turbulent motions induced by the winds and the cosmic rays generate magnetic fields in rough energy equipartition, the predicted magnetic-field strengths coincide with the ones observed not only in galaxies (5 $\mu$G in the Milky Way) but also in galaxy clusters (6 $\mu$G in Coma). The prediction for the intergalactic (or inter-cluster) field is 50 nG. 
Arnon Dar and A. De Rujula