Safe Extremum Seeking Applications in Particle Accelerators

Particle accelerators, complex machines crucial for various scientific endeavors, require regular tuning due to time-varying beams and components. Extremum seeking control proves to be an ideal strategy for this tuning process. Fine-tuning the beam involves modifying electric and magnetic fields within the beampipe to alter the shape or trajectory of the particle bunch. Yet, safety remains paramount, considering the substantial costs associated with particle collisions with components resulting in damage. Like the cost function, the safety of the system with respect to the tuning parameters is analytically unknown. In this study, we showcase the efficacy of our Safe Extremum Seeking (Safe ES) algorithm in particle accelerator applications. Our initial demonstration involves employing the Kapchinsky Vladimirsky (KV) equations to model a beam dominated by so called "space-charge" forces. We formulate a beam loss model and conduct a simulation illustrating the capability of Safe ES on the KV equations to tune the beam spot size while ensuring that beam loss remains below a specified threshold. In a second example, we present data obtained from an experimental implementation of Safe ES on the ion beam at the Los Alamos Neutron Science Center.