Kinetic (dashed) and magnetic (solid) power spectra of Halo3. The left panels show the power spectra in the central regions within a fixed physical radius of R₂₀₀(z = 9) = 20 kpc for four different redshifts (z = 4.5, 5.5, 7, 8.5) for both the radiative (upper) and the non-radiative (lower) simulations aimed at tracing the high-redshift dynamo in the BCG. The right panels show the ICM power spectra within 0.5R₂₀₀(z), excluding the central 20 kpc, at six different redshifts (z = 0, 1.5, 2.5, 3.5, 4.5, 6.5) focusing on dynamo activity in the ICM within the radiative and non-radiative simulations. Dotted lines illustrate different scaling behaviors (see text). The left panels show that a small-scale dynamo (with the Kazantsev scaling ∝k^3/2) driven by compressive Burgers turbulence (∝k⁻²) is only active in the central regions of the radiative simulation. By contrast, the right panels show the existence of a small-scale dynamo driven by incompressible turbulence (∝k^−5/3) throughout the entire ICM within 0.5R₂₀₀ in both simulations, albeit at a faster rate in the radiative simulation. The contribution of a Lorentzian profile, which we show for z = 4.5 in both simulations and additionally z = 0 in the radiative simulation (it scales as ∝k² on scales larger than the scale height), at lower redshifts is minimal because the sharp cutoff at the characteristic exponential scale is located at rather large scales.