Impact of Simplified Stationary Cavity Beam Loading on the Longitudinal Feedback System for SIS100

The main synchrotron SIS100 of the Facility for Antiproton and Ion Research (FAIR) will be equipped with a bunch-by-bunch feedback system to damp longitudinal beam oscillations. In the basic layout, one three-tap finite impulse response (FIR) filter will be used for each single bunch and oscillation mode. The detected oscillations are used to generate a correction voltage in dedicated broadband radio frequency (RF) cavities. The digital filter is completely described by two parameters, the feedback gain and the passband center frequency, which have to be defined depending on the longitudinal beam dynamics. In earlier works, the performance of the closed loop control with such an FIR-filter was analyzed and compared to simulations and measurements with respect to the damping of coherent dipole and quadrupole modes, the first modes of oscillation. This contribution analyzes the influence of cavity beam loading on the closed loop performance and the choice of the feedback gain and passband center frequency to verify future high current operation at FAIR.