  An analytical model predicting the growth rates, the absolute growth times
and the saturation values of the magnetic field strength within galactic haloes
is presented. The analytical results are compared to cosmological MHD
simulations of Milky-Way like galactic halo formation performed with the N-body
/ \textsc{Spmhd} code \textsc{Gadget}. The halo has a mass of
$\approx{}3\cdot{}10^{12}$ $M_{\odot}$ and a virial radius of $\approx{}$270
kpc. The simulations in a $\Lambda$CDM cosmology also include radiative
cooling, star formation, supernova feedback and the description of non-ideal
MHD. A primordial magnetic seed field ranging from $10^{-10}$ to $10^{-34}$ G
in strength agglomerates together with the gas within filaments and
protohaloes. There, it is amplified within a couple of hundred million years up
to equipartition with the corresponding turbulent energy. The magnetic field
strength increases by turbulent small-scale dynamo action. The turbulence is
generated by the gravitational collapse and by supernova feedback.
Subsequently, a series of halo mergers leads to shock waves and amplification
processes magnetizing the surrounding gas within a few billion years. At first,
the magnetic energy grows on small scales and then self-organizes to larger
scales. Magnetic field strengths of $\approx{}10^{-6}$ G are reached in the
center of the halo and drop to $\approx{}10^{-9}$ G in the IGM. Analyzing the
saturation levels and growth rates, the model is able to describe the process
of magnetic amplification notably well and confirms the results of the
simulations.
