  Recirculating energy recovery linacs are a promising technology for
delivering high power particle beams ($\sim$GW) while only requiring low power
($\sim$kW) RF sources. This is achieved by decelerating the used bunches and
using the energy they deposit in the accelerating structures to accelerate new
bunches. We present studies of the impact of the bunch packet filling pattern
on the performance of the accelerating RF system. We perform RF beam loading
simulations under various noise levels and beam loading phases with different
injection schemes. We also present a mathematical description of the RF system
during the beam loading, which can identify optimal beam filling patterns under
different conditions. The results of these studies have major implications for
design constraints for future energy recovery linacs, by providing a
quantitative metric for different machine designs and topologies.
