X-ray observations have demonstrated that the intergalactic medium in many clusters (cf. Coma, Perseus) contains a thin, hot plasma that may be produced by the accretion process in the gravitational potential of clusters with radiative cooling; this is usually called “cooling flows” (Fabian, Nulsen, and Canizares 1984; Sarazin 1986). On the other hand, the existence of radio halos in some clusters has been reported (Coma: Jaffe, Perola, and Valentijn 1976; A401: Roland et al. 1981). In addition, many elliptical galaxies in the center of clusters are also strong synchrotron radio sources. These radio emissions provide evidence for large amounts of relativistic electrons associated with the active phenomena in or around these galaxies and clusters. We can estimate the values or limits on the magnetic field in the cluster from the limits on the inverse Compton X-ray emission with the synchrotron radio emission (cf. Jaffe 1980). The intracluster field strength Bo is roughly 1 μG. It has been suggested that the influence of cosmic rays and magnetic fields is important for the properties and dynamics of the intercluster medium (Böhringer and Morfill 1988; Soker and Sarazin 1989). If cooling flows are real, this inward flow can impede the escape of the cosmic rays from the central galaxies in clusters and enhance the magnetic field. The confinement of the cosmic rays and the magnetic field in the center of clusters affects the gas of the intracluster medium.