On 28 november 2013 ESA selected “The Hot and Energetic Universe” as the scientific theme for a large mission to be flown in 2028 in the second lagrangian point, and ATHENA is the mission that will address this science topic. It will carry on board the X-ray Integral Field Unit (X-IFU), a 3840 pixel array based on TES (Transition Edge Sensor) microcalorimeters providing high resolution spectroscopy (2.5 eV @ 6 keV) in the 0.3-12 keV range. Among X-IFU goals there is the detection and characterization of high redshift AGNs, Clusters of galaxies and their outskirts, and the elusive Warm Hot Intergalactic Medium (WHIM), so great care must be paid to the reduction of the background level. These scientific objectives will be reached if the particle background is kept lower than 0.05 cts cm−2 s−1, and to this aim, it is mandatory the use of a Cryogenic AC (CryoAC), as well as an optimized design of the cryostat and of the structures surrounding X-IFU. Our team, that is responsible for the ACD design, performed a detailed study to predict the rejection efficiency of the ACD as a function of its geometrical parameters and design choices. Since no experimental data on the background experienced by X-Ray microcalorimeters in the L2 orbit are available at the moment, the particle background levels have been calculated by means of Monte Carlo simulations using the Geant4 software.