  The first supernova explosions are potentially relevant sources for the
production of the first large-scale magnetic fields. For this reason we present
a set of high resolution simulations studying the effect of supernova
explosions on magnetized, primordial halos. We focus on the evolution of an
initially small-scale magnetic field formed during the collapse of the halo. We
vary the degree of magnetization, the halo mass, and the amount of explosion
energy in order to account for expected variations as well as to infer
systematical dependencies of the results on initial conditions. Our simulations
suggest that core collapse supernovae with an explosion energy of 10^51 erg and
more violent pair instability supernovae with 10^53 erg are able to disrupt
halos with masses up to a about 10^6 and 10^7 M_sun, respectively. The peak of
the magnetic field spectra shows a continuous shift towards smaller k-values,
i.e. larger length scales, over time reaching values as low as k = 4. On small
scales the magnetic energy decreases at the cost of the energy on large scales
resulting in a well-ordered magnetic field with a strength up to ~ 10^-8 G
depending on the initial conditions. The coherence length of the magnetic field
inferred from the spectra reaches values up to 250 pc in agreement with those
obtained from autocorrelation functions. We find the coherence length to be as
large as $50\%$ of the radius of the supernova bubble. Extrapolating this
relation to later stages we suggest that significantly strong magnetic fields
with coherence lengths as large as 1.5 kpc could be created. We discuss
possible implications of our results on processes like recollapse of the halo,
first galaxy formation, and the magnetization of the intergalactic medium.
