Exact and fast solution of ultrarelativistic multibunch instabilities in a constant gradient accelerator

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.