  We present a complementary study to a new model for generating magnetic
fields of cosmological interest. The driving mechanism is the photoionisation
process by photons provided by the first luminous sources. Investigating the
transient regime at the onset of inhomogeneous reionisation, we show that
magnetic field amplitudes as high as $2 \times 10^{-16}$ Gauss can be obtained
within a source lifetime. Photons with energies above the ionisation threshold
accelerate electrons, inducing magnetic fields outside the Stroemgren spheres
which surround the ionising sources. Thanks to their mean free path, photons
with higher energies propagate further and lead to magnetic field generation
deeper in the neutral medium. We find that soft X-ray photons could contribute
to a significant premagnetisation of the intergalactic medium at a redshift of
z=15.
