Monte Carlo simulation of air shower development for the study of cosmic ray composition

There is compelling evidence that at least some clusters of galaxies are powerful sources of non-thermal radiation. In all cases where this radiation has been detected, a general trend is that high energy densities of cosmic rays and correspondingly low values of the average magnetic field are required in order to have a self-consistent picture of the multiwavelength observations. Mergers of clusters of galaxies might provide large enough cosmic ray injection rates and at the same time provide the mechanism for the heating of the intracluster medium to the observed temperatures. In this paper we analyze critically all the components that play a role in the non-thermal emission of clusters during a merger, with special attention to mergers occurred in the past of the cluster. We outline the consequences of this model for high energy gamma ray observations and for Faraday rotation measurements of the intracluster magnetic field.