The European X-ray Free Electron Laser (EuXFEL) is an X-ray laser facility driven by a superconducting linear accelerator. It is currently the brightest X-ray source of its kind, enabling unprecedented discoveries in the physical and life sciences. The EuXFEL High Duty-Cycle (HDC) upgrade will enable operation with long RF pulses (duty cycle above 10%) up to continuous wave (100% duty cycle), effectively increasing the number of produced X-ray pulses per second by an order of magnitude. This upgrade introduces first-of-its-kind challenges in controlling superconducting radio-frequency (SRF) cavities, specifically their RF field and frequency stability.

Building on previous achievements, the goal of this PhD project is to explore advanced control strategies to achieve the specified SRF cavity field stability (0.01% in amplitude and 0.01° in phase), despite their extremely narrow bandwidth (in the order of 10 Hz). In particular, the resonance controller for multiple cavities driven by a single source (MCAV) can be improved by introducing narrow-bandwidth active noise compensation. RF field feedback can be further enhanced by investigating variable-gain controllers that adapt to cavity detuning, or exploring other feedback algorithms. In addition, the MCAV approach can be optimized by leveraging information from all individual cavities, rather than relying solely on their vector sum, thereby enabling the development of a MIMO (multiple-input, multiple-output) controller. Furthermore, the limitations and potential benefits of increasing the RF pulse repetition rate beyond the currently proposed 1 Hz will be studied.

Beyond advancing state-of-the-art control techniques for particle accelerators, this PhD project has a clear practical objective: to define the optimal SRF cavity control approach for the HDC upgrade of EuXFEL, currently planned for the next decade