  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. 
Supernova explosions in magnetized, primordial dark matter halos