  The electromagnetic wakefields excited by the bunches of charged particles in
the particle accelerators may cause instability in the longitudinal and
transverse motion of these bunches leading to the beam loss. These multibunch
effects need to be analyzed carefully in an accelerator design to ensure the
stability of the charged particle beams. This paper presents an analytical
method describing the multibunch transverse instabilities for ultrarelativistic
electron bunches whose energy changes linearly through the accelerating section
of interest. Fast algorithmic implementations of this analytical method are
presented for the general as well as the specific cases and this method is
demonstrated with an example. This tool can also be applied to study
single-bunch beam breakup.
