  We explore the amplification of magnetic fields in the high-redshift
Universe. For this purpose, we perform high-resolution cosmological simulations
following the formation of primordial halos with \sim10^7 M_solar, revealing
the presence of turbulent structures and complex morphologies at resolutions of
at least 32 cells per Jeans length. Employing a turbulence subgrid-scale model,
we quantify the amount of unresolved turbulence and show that the resulting
turbulent viscosity has a significant impact on the gas morphology, suppressing
the formation of low-mass clumps. We further demonstrate that such turbulence
implies the efficient amplification of magnetic fields via the small-scale
dynamo. We discuss the properties of the dynamo in the kinematic and non-linear
regime, and explore the resulting magnetic field amplification during
primordial star formation. We show that field strengths of \sim10^{-5} G can be
expected at number densities of \sim5 cm^{-3}.
