Abstract

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 $\{${\tilde} 10$^{7}$$\}$ M\_{\sun}, 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 {\tilde} 10$^{-5}$ G can be expected at number densities of {\tilde} 5 cm$^{-3}$.