Numerical modeling of the CERN PS booster cavity feedback loops

The Radio-Frequency (RF) system of the CERN Proton Synchrotron Booster (PSB) features Finemet-loaded cavities that cover a wide range of frequencies. This system generates a significant broad-band longitudinal impedance, which must be mitigated to maintain beam stability, particularly at higher beam intensities. To counteract the induced voltage, a direct RF feedback is employed over the entire operational frequency range. It is complemented by a multi-harmonic feedback that applies narrow-band signal processing to reduce the cavity impedance at integer multiples of the revolution frequency. Recent measurements have revealed that these long-delay cavity loops implemented in the Low-Level RF (LLRF) system have a substantial effect on beam dynamics. To validate the impedance model in the closed-loop regime, a detailed model of their behaviour is necessary. This contribution outlines the development process of the numerical model for the PSB cavity feedback loops for particle tracking simulations, which is based on dedicated measurements used to characterise the feedback performance. Comparisons between simulations and measurements are carried-out to assess the validity of the modeling.