Iterative Extremum Seeking for feedforward compensation of beam loading in particle accelerator RF cavities

Particle accelerators utilize radio frequency (RF) resonant electromagnetic cavities to establish very large (mega-volt per meter) field gradients with which to accelerate particles (typically protons or electrons). The particles gain energy by draining it from the RF fields, thereby disturbing the steady state oscillations of the RF cavities. An RF feedback control system is required in order to both quickly bring cavity fields up to their required steady state set points, and also to maintain them at those set points despite disturbances such as the beam itself. If the RF field amplitude or phase moves too far from set points then subsequent particles will not be properly accelerated. The gains of RF feedback systems are bounded by large delays (several μs) and the effectiveness of model-based feed forward signals is limited by model accuracy. Therefore, the arrival of a beam creates a sudden impact on the RF fields which cannot be adequately compensated by simple PID-type controllers or model-based methods alone, resulting in lengthy transients of the RF system's amplitude and phase. In this work we demonstrate the use of an iterative Extremum Seeking method for automatic control of RF fields to compensate for beam loading, which is being designed to handle the exotic beam loading conditions that we expect to have in the MaRIE free electron laser (FEL) [24].