In response to recommendations in the 2013 update of the European Strategy for Particle Physics, a conceptual design effort for an energy upgrade of the Large Hadron Collider (LHC) at CERN, the so-called high-energy LHC (HE-LHC), was launched as part of the Future Circular Collider study. The HE-LHC machine, which is meant to use 16 T magnet technologies in the existing LHC tunnel, would provide proton collisions at a center-of-mass energy of 27 TeV ($\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}\mathrm{LHC}$) with a total stored energy of 1.34 GJ ($\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}\mathrm{LHC}$) per beam. By adapting the LHC collimation system, a first layout of the HE-LHC's betatron cleaning insertion was conceived, with the requirement to sustain---for at least 10 seconds---the impact of about 1.86 MW, corresponding to a beam lifetime of 12 minutes, without inducing any magnet quench nor any damage to other accelerator components. In this article, we evaluate the power deposition on the collimation insertion for proton beam operation in the HE-LHC machine at top energy, by means of particle tracking and interaction calculations. The beam loss effects on the warm elements as well as on the superconducting dispersion suppressor magnets are assessed through a three-step simulation approach. In particular, for the proposed future high-energy LHC, we demonstrate the necessity of adding local collimators in the dispersion suppressor, and we uncover the harmful consequences of a potential removal of the beam line ``dogleg'' in the collimation insertion.
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