Machine learning for orbit steering in the presence of nonlinearities

Circular particle accelerators require precise beam orbit correction to maintain the beam's trajectory close to the ideal `golden orbit', which is centered within all magnetic elements of the ring, except for slight deviations due to installed experiments. Traditionally, this correction is achieved using methodologies based on the response matrix (RM). The RM elements remain constant when the accelerator's lattice includes solely linear elements or when a linear approximation is valid for small perturbations, allowing for the calculation of corrector strengths to steer the beam. However, most circular accelerators contain nonlinear magnets, leading to variations in RM elements when the beam experiences large perturbations, rendering traditional methods less effective and necessitating multiple iterations for convergence. To address these challenges, a machine learning (ML)-based approach is explored for beam orbit correction. This approach, applied to synchrotron SLS 2.0 under construction at the Paul Scherrer Institut, is evaluated against and in combination with the standard RM-based method under various conditions. A possible limitation of ML for this application is the potential change in the dimensionality of the ML model after optimization, which could affect performance. A solution to this issue is proposed, improving the robustness and appeal of the ML-based method for efficient beam orbit steering.