Title: Synchronization and Phase Locking of Resonant Magnet Power Supplies For Mu2e Experiment at Fermilab

Abstract: The Muon-to-Electron Conversion (Mu2e) Experiment demands a highly precise magnet and collimator system to achieve a stringent extinction level of $1\times 10^{-10}$ for out-of-time beam particles. Extinction is ensured by an AC Dipole system consisting of two magnet components: a 295 kHz system to allow for the passage of a 590 kHz beam at the nodes, and a 4.42 MHz system to minimize in-time beam slewing. Both components must be accurately phase-locked to the Delivery Ring's bunch rate as well as be synchronized with beam transfers from the Recycler.
In this paper, we present the design, implementation, and results of a control system for the Mu2e magnet system based on an Intel Arria 10 FPGA. This system handles the phase-locking of the magnets to the Delivery Ring, as well as the phase jumps required for synchronization with transfers from the Recycler.