Comprehensive studies with the MARS15(2016) Monte-Carlo code are described on evaluation of prompt and residual radiation levels induced by nominal and accidental beam losses in the 5-MW, 2-GeV European Spallation Source (ESS) Linac. These are to provide a basis for radiation shielding design verification through the accelerator complex. The calculation model is based on the latest engineering design and includes a sophisticated algorithm for particle tracking in the machine RF cavities as well as a well-established model of the beam loss. Substantial efforts were put in solving the deep-penetration problem for the thick shielding around the tunnel with numerous complex penetrations. It allowed us to study in detail not only the prompt dose, but also component and air activation, radiation loads on the soil outside the tunnel, and skyshine studies for the complicated 3-D surface above the machine. Among the other things, the newest features in MARS15 (2016), such as a ROOT-based beamline builder and a TENDL-based event generator for nuclear interactions below 100 MeV, were very useful in this challenging application.
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