Bachelor Thesis from the year 2005 in the subject Astronomy, grade: 1,0, University of Bremen, language: English, abstract: An adaptive mesh refinement simulation of galaxy cluster formation was performed that included the passive evolution of a magnetic field. It was found that structure formation plays an important role in amplifying large-scale magnetic fields and that the magnetic properties of the obtained cluster were in good agreement with recent observations. The initial field was amplified by a factor of up to 1000 during the formation of the cluster, and the field strength was seen to be well correlated with the gas density. We further found a magnetic energy power spectrum that is well described by -5/3 Kolmogorov-type turbulence. Near the accretion shocks on the outskirts of the cluster, the magnetic field is amplified well beyond the value expected from mere compression of gas. Here, shear flows lead to a substantial increase in field strength. Realistic Faraday rotation measures were obtained from the simulation data, which was however not resolved well-enough to allow for a more quantitative analysis.