Beam breakup instability studies of powerful energy recovery linac for experiments

The maximum achievable beam current in an Energy Recovery Linac (ERL) is often constrained by Beam Breakup (BBU) instability. Our previous research highlighted that filling patterns have a substantial impact on BBU instabilities in multi-pass ERLs. In this study, we extend our investigation to the 8-cavity model of the Powerful ERL for Experiment (PERLE). We evaluate its requirements for damping cavity Higher Order Modes (HOMs) and propose optimal filling patterns and bunch timing strategies. Our findings reveal a significant new insight: while filling patterns are crucial, the timing of bunches also plays a critical role in mitigating HOM beam loading and BBU instability. This previously underestimated factor is essential for effective BBU control. We estimated the PERLE threshold current using both analytical and numerical models, incorporating the designed PERLE HOM dampers. During manufacturing, HOM frequencies are expected to vary slightly, with an assumed RMS frequency jitter of 0.001 between cavities for the same HOM. Introducing this jitter into our models, we found that the dampers effectively suppressed BBU instability, achieving a threshold current an order of magnitude higher than the design requirement. Our results offer new insights into ERL BBU beam dynamics and have important implications for the design of future ERLs.