Identification of magnetic field errors in synchrotrons based on deep Lie map networks

Abstract

Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite nonsystematic resonances, reduce dynamic aperture, and may result in beam loss. Their effect can be compensated by assuming knowledge of their location and strength. Established identification procedures are based on orbit response matrices or resonance driving terms. While they sequentially build a field error model for subsequent accelerator sections, a method detecting field errors in parallel could save valuable beam time. We introduce deep Lie map networks, which enable the construction of an accelerator model including multipole components for the magnetic field errors by linking charged particle dynamics with machine learning methodology in a data-driven approach. Based on simulated beam position monitor readings for the example case of SIS18 at GSI, we demonstrate inference of location and strengths of gradient and sextupole errors for all accelerator sections in parallel. The obtained refined accelerator model may support setup of corrector magnets in operation to allow more precise control over tunes, chromaticities, and resonance compensation.