We present an ongoing work in which a surrogate model is being developed to reproduce the response dynamics of the third-integer resonant extraction process in the Delivery Ring (DR) at Fermilab. This is in pursuit of smoothly extracting circulating beam to the Mu2e Experiment’s production target, whereby the goal is to extract a uniform slice of the circulating 1e12 protons in the DR over 25,000 turns (43 ms). The DR contains 3 harmonic sextupoles that excite a third-integer resonance and three fast, tune-ramping quadrupole magnets that drive the horizontal tune towards the 29/3 resonance. In our initial work, the surrogate model trains on a semi-analytical simulation provided in the same format as live data. Using Reinforcement Learning (and other potential ML methods), the trained surrogate acts as the “environment” in which a simple ML control agent could learn to dynamically adjust the quadrupole ramp at 430 break points within the 43 microsecond spill window. The controller will be hosted on a dedicated Arria 10 FPGA. In this work, we report the accuracy and fidelity of the surrogate model in comparison to the response dynamics of the physics simulator.

We present the development of a machine learning (ML) regulation system for third-order resonant beam extraction in the Mu2e experiment at Fermilab. Classical and ML-based controllers have been optimized using semi-analytic simulations and evaluated in terms of regulation performance and training efficiency. We compare several controller architectures and discuss the integration of neural control into an adaptive framework. In addition, we report progress on implementing low-latency, edge-based inference to enable deployment in hardware-constrained environments. This work demonstrates the feasibility and potential advantages of ML-based control for regulating complex, non-stationary systems, with applications extending beyond resonant extraction.

The Muon to Electron Experiment (Mu2e) requires a uniform beam profile from the Muon Delivery Ring to meet their experimental needs. A specialized Spill Regulation System (SRS) has been developed to help achieve consistent spill uniformity. The system is based on a custom-designed carrier board featuring an Arria 10 SoC, capable of executing real-time feedback control. The FPGA processes beam pulses of approximately 200 ns every 1.695 microsecond, allowing for continuous monitoring of the extracted spill intensity through fast bunch integration. The system directly controls three quadrupole magnets, which work in conjunction with sextupole magnets to achieve third-order resonant extraction. Furthermore, the board interfaces with Fermilab’s Accelerator Control Network (ACNET), enabling operators to modify spill regulation settings in real-time via the control network while providing diagnostic waveforms. These waveforms help operators monitor the process and fine-tune the feedback mechanisms. This paper presents an overview of the board's architecture and its initial progress toward regulating beam extraction. This initial version of the regulation system aims to evaluate baseline performance to inform future system improvements.

We present an ongoing work in which a surrogate model is being developed to reproduce the response dynamics of the third-integer resonant extraction process in the Delivery Ring (DR) at Fermilab. This is in pursuit of smoothly extracting circulating beam to the Mu2e Experiment’s production target, whereby the goal is to extract a uniform slice of the circulating 1e12 protons in the DR over 25,000 turns (43 ms). The DR contains 3 harmonic sextupoles that excite a third-integer resonance and three fast, tune-ramping quadrupole magnets that drive the horizontal tune towards the 29/3 resonance. In our initial work, the surrogate model trains on a semi-analytical simulation provided in the same format as live data. Using Reinforcement Learning (and other potential ML methods), the trained surrogate acts as the “environment” in which a simple ML control agent could learn to dynamically adjust the quadrupole ramp at 430 break points within the 43 microsecond spill window. The controller will be hosted on a dedicated Arria 10 FPGA. In this work, we report the accuracy and fidelity of the surrogate model in comparison to the response dynamics of the physics simulator.