We report the state of the field of High-Power Fixed-Field
Accelerators (with an emphasis on cyclotrons) as discussed by
international experts during a three-day workshop of the same name
in 2021. The workshop was part of the Snowmass'21 Community
Planning Exercise. Here, we take stock of the world inventory of
high-power fixed-field accelerators, assess available beam currents
and beam powers, and investigate limitations. Furthermore, we
evaluate the role of these machines in particle physics,
directly used or as injectors to other machines, and in industry, as
drivers for (medical) isotope production and, potentially, for
accelerator-driven systems and sub-critical reactors. Finally, we
discuss novel concepts and cutting-edge developments to push the
available current higher at several energy scales, thereby
increasing relative power. Highlights include new spiral inflector
types, direct RFQ injection, H2
+ acceleration,
utilizing vortex motion, and self-extraction schemes. We also
discuss modern computational frameworks to optimize accelerators
more efficiently, and better describe the relevant physical
processes in simulations.