Magnetic energy flux as a function of time for B_IGM = 10^-5   μG measured at a radius of 4r_s (dotted line) and 9r_s (dashed line) from the halo centre. The analytical prediction of Bertone et al. (2006) is overplotted as the red solid line. We overploted the result for the direct magnetic energy injection with zero initial magnetic field (solid line) as described in Appendix A.