Volume-averaged magnetic energy scaled by
as a function of density in a simulation of primordial star formation that includes magnetic fields. The various line styles denote the resolution of the Jeans length. If the magnetic flux is frozen into the flow, the magnetic energy evolves along the lower black dashed line. Depending on resolution, the turbulent dynamo amplifies the magnetic field strength well above this value. Here, at least 64 cells per Jeans length are required for significant amplification to occur. The shaded regions show the distribution of the gas in the \(J=64\) case. There is no indication that the magnetic energy converges with increasing resolution. Magnetic fields will likely become dynamically important during the initial collapse, and affect the susceptibility of the gas to fragmentation. Adapted from Turk et al. (2012).