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Galaxy clusters represent the largest gravitationally bound objects in the universe. Detailed morphological studies of galaxy clusters indicate that they are relatively young objects, currently in the formation process. Observations toward these objects reveal that the major components of the clusters are the galaxies, the diffuse, thermal cluster gas, and the dark matter. There is, however, evidence that the intracluster medium also contains magnetic fields distributed through the intracluster gas.

The presence of magnetic fields within the intracluster medium can lead to significant effects on the dynamics, and energy transport throughout the cluster. Embedded magnetic fields can modify the pressure of the intracluster medium, suppress thermal conduction, which may lead to the onset of cooling instabilities, and magnetic fields may even bias the initial mass function of star formation. Therefore, in order to understand the overall picture of the evolution of galaxy clusters, it is necessary to understand the role magnetic fields have played in this evolution.

The most direct method of probing intracluster magnetic fields relies on the Faraday rotation effect. As linearly polarized radiation passes through a magneto-ionic region, the rotation of the plane of polarization displays a characteristic wavelength dependence.

This thesis combines radio and X-ray observations, in a statistical study of Faraday rotation toward a sample of nearby galaxy clusters. A comparison of the Faraday rotation measures of sources viewed through the intracluster medium, to the rotation measures of sources falling beyond the edge of the X-ray emitting gas, reveals the presence of excess Faraday rotation in the former sample. This excess rotation is interpreted as originating in the diffuse intracluster medium.

A detailed investigation of the Faraday rotating medium indicates that the Faraday screen is well represented by a model of Faraday cells distributed through the intracluster medium. An analysis of the cluster impact parameter distribution over the rotation measure sample indicates that the Faraday cell scales vary from < 1 kpc in the central regions of the clusters, to over 100 kpc at large impact parameter. Further, the rotation measure distribution indicates the widespread existence of intracluster magnetic fields out to the edges of the X-ray emitting gas. The overall distribution of magnetic field strengths inferred from the data suggests that the fields may play a dynamically important role in the evolution of galaxy clusters.