High gain proportional rf control stability at TESLA cavities

Fast proportional rf control is used as the basis for rf field regulation in actual linear accelerator projects like the international linear collider (ILC) and the European x-ray free electron laser (XFEL) based on TESLA technology. Additional control loops improve the field regulation by treating repetitive effects and compensating the beam loading. Nevertheless, the ability for high gain operation of the fast loops is desirable for the strong suppression of nonpredictive and nonrepetitive disturbances. TESLA cavities host nine fundamental modes (FMs) where only one is used for beam acceleration. The unwanted FMs have a significant influence on the proportional rf control loop stability at high gains. Within this paper, the stability of proportional rf control loops taking the FMs and digitalization effects into account will be discussed in detail together with measures enabling a significant increase of the gain values.