EuroCirCol is a conceptual design study of a post-LHC, Future Circular Hadron Collider (FCC-hh) which aims to expand the current energy and luminosity frontiers. The vacuum chamber of this 100 TeV, 100 km collider, will have to cope with unprecedented levels of synchrotron radiation linear power for proton colliders, 160 times higher than in the LHC for baseline parameters, releasing consequently much larger amounts of gas into the system. At the same time, it will be dealing with a tighter magnet aperture. In order to reach a good vacuum level, it has been necessary to find solutions beyond the particle colliders' state of art. This paper proposes a design of a novel beam screen, the element responsible for absorbing the emitted power. It is intended to overcome the drawbacks derived from the stronger synchrotron radiation while allowing at the same time a good beam quality.