Design and studying physical properties of cavity beam position monitors for electron accelerators

The INFN project named EuPRAXIA@SPARC_LAB is a proposal to upgrade the SPARC_LAB test facility (in Frascati, Italy) to a soft X-ray user facility based on plasma acceleration and high-gradient X-band accelerating structures. Furthermore, the European project CompactLight aims to design a compact FEL for users in the hard X-ray range. Its main pillars are a new concept high-brightness photoinjector, high-gradient X-band accelerating sections, and innovative short-period undulators. The control of the charge and the trajectory at a few pC and few um is mandatory in this machine, especially in the plasma interaction region. Great importance has the beam trajectory at the entrance of every RF module, particularly the part of the machine in the X-band and inside the plasma accelerator. Conventional stripline BPM (Beam position monitor), similar to those already in use at SPARC_LAB, can be considered for such a task. They can offer a good signal to noise ratio down to a few pC charge and a resolution in the order of several tens of $mu$m. However, this kind of device can be used only at the beginning of the accelerator, where the beam pipe is 40 mm. However, starting from X band structures, the pipe size decreases. Since one of the most crucial parameters is the device's length, it will be convenient for such a system that length to be as short as possible. As a possible solution, a cavity beam position monitor (cBPM) is proposed. A prototype cavity BPM in the C-band frequency range has been designed. This thesis presents the strategy and the process to specify the parameters that are decisive for achieving the required specifications. The simulations were performed to study RF properties and the electromagnetic response of the device. The developed RF design fits the EuPRAXIA project requirements. Other design ideas, such as a single cavity BPM, where both dipole mode and reference signals are received from one cavity, are also discussed. The resonance modes of the cavity are simulated using eigenmode solvers. By the simulations performed in frequency-domain, the coupling and isolation characteristics are obtained. The beam coupling is studied through time-domain simulations. The possible manufacturing errors were studied by simulation reconstruction. Finally, the performance of the whole system for 5.1 GHz is discussed, and theoretical resolution is approximated.