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

TL;DR

This paper introduces an exact, fast analytical method to analyze multibunch transverse instabilities caused by electromagnetic wakefields in ultrarelativistic accelerators, aiding in stability design.

Contribution

It provides a novel analytical approach and efficient algorithms for multibunch instability analysis in accelerators with linearly increasing energy.

Findings

The method accurately predicts multibunch instabilities.

Algorithms are computationally efficient for practical use.

Applicable to single-bunch beam breakup analysis.

Abstract

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.