Accelerators for Rare Processes and Physics Beyond Colliders: Report of the AF5 Topical Group to Snowmass 2021

This report summarizes the findings of the AF5 Topical Subgroup to Snowmass 2021, which investigated accelerators for rare processes and physics beyond colliders. The report focuses primarily on opportunities for dark sector searches and the need for coordinated development of the Fermilab experimental program for PIP-II and beyond. In addition, a number of other physics opportunities are cataloged and suggestions for synergistic R & D opportunities with various areas of technological development are discussed.