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While present standard model of cosmology yields no clear prediction for theinitial magnetic field strength, efficient dynamo action may compensate forinitially weak seed fields via rapid amplification. In particular, thesmall-scale dynamo is expected to exponentially amplify any weak magnetic fieldin the presence of turbulence. We explore whether this scenario is viable usingcosmological magneto-hydrodynamics simulations modeling the formation of thefirst galaxies, which are expected to form in so-called atomic cooling haloswith virial temperatures $\rm T_{vir} \geq 10^{4}$ K. As previous calculationshave shown that a high Jeans resolution is needed to resolve turbulentstructures and dynamo effects, our calculations employ resolutions of up to 128cells per Jeans length. The presence of the dynamo can be clearly confirmed forresolutions of at least 64 cells per Jeans length, while saturation occurs atapproximate equipartition with turbulent energy. As a result of the largeReynolds numbers in primordial galaxies, we expect saturation to occur at earlystages, implying magnetic field strengths of \sim0.1 $\mu$G at densities of10^4 cm^{-3}.

The small scale dynamo and the amplification of magnetic fields in massive primordial haloes