Mass-weighted spherically binned radial profiles of magnetic field strength, magnetic field amplification B/ρ^2/3, and the magnetic-to-kinetic energy density ratio E_B/E_K for halo 1 when reaching a peak density of 3 × 10⁻¹³ g cm⁻³. The first, second, and third column of this multiple plot shows the magnetic properties of the runs with a proper initial magnetic field strength of B₀ = 10⁻¹⁴ [G], B₀ = 10⁻¹⁰ [G], and B₀ = 10⁻⁸ [G], respectively. The light blue lines represent the simulations with J₂₁ = 10³ where the cooling is driven via molecular hydrogen, and the red lines are for simulations with J₂₁ = 10⁵ where the cooling is driven by atomic hydrogen. The different line styles represent different Jeans resolutions: dash-dotted for 32 cells, dashed for 64 cells, solid for 128 cells, and dotted for 256 cells per Jeans length. Independently of the value of J₂₁, the magnetic field strength, as well as the other magnetic properties, increases with increasing Jeans resolution for the runs with B₀ = 10⁻¹⁴ [G]. When increasing the initial magnetic field the simulations with J₂₁ = 10³ start to present a dependency loss on the Jeans resolution at lower B₀ in comparison with the atomic cooling runs, which suggest that potentially the saturation occurs first in these simulations.