  Beam breakup instability is a potential issue for all particle accelerators
and is often the limiting factor for the maximum beam current that can be
achieved. This is particularly relevant for Energy Recovery Linacs with
multiple passes where a relatively small amount of charge can result in a large
beam current. Recent studies have shown that the choice of filling pattern and
recirculation scheme for a multi-pass energy recovery linac can drastically
affect the interactions between the beam and RF system. In this paper we
further explore this topic to study how filling patterns affect the beam
breakup instability and how this can allow us to optimise the design in order
to minimise this effect. We present a theoretical model of the beam-RF
interaction as well as numerical modeling and show that the threshold current
can vary by factors of 2-4, and potentially even more depending on the machine
design parameters. Therefore a judicious choice of filling pattern can greatly
increase the onset of BBU, expanding the utility of future ERLs.
