Dissertationsubmitted to theCombined Faculties of the Natural Sciences and Mathematicsof the Ruperto-Carola-University of Heidelberg, Germanyfor the degree ofDoctor of Natural SciencesPut forward byGiulia Vannoniborn in: Florence, ItalythOral examination: 27 November, 2008Diffusive Shock Acceleration in RadiationDominated EnvironmentsReferees: Prof. Dr. Werner HofmannProf. Dr. Felix AharonianAbstractInthisworkIdescribeanumericalmethoddeveloped, forthefirsttime, forthestudyofDiffu-siveShockAccelerationinastrophysicalenvironmentswheretheradiationpressuredominatesoverthe magnetic pressure. This work is motivated by the overwhelming evidence of the accelerationof particles to high energy in astrophysical objects, traced by the non–thermal radiation they emitdue to interactions with the gas, radiation fields and magnetic fields. The main objective of thiswork is to create a generic framework to study self–consistently the interaction of acceleration atshocks and radiative energy losses and the effect such an interplay has on the particle spectrumand on the radiation they emit, in the case when energy losses determine the maximum achievableenergy. I apply the developed method to electrons accelerated in three different types of sources:a Supernova Remnant in the Galactic Centre region, a microquasar, and a galaxy cluster. Inall three cases the energy losses due to the interaction of electrons with radiation dominate oversynchrotron cooling.