Semi-analytical algorithms to study longitudinal beam instabilities in double rf systems

TL;DR

This paper introduces semi-analytical algorithms and an open-source Python tool for predicting and optimizing longitudinal beam instabilities in double rf systems, crucial for advanced light sources.

Contribution

It presents novel semi-analytical algorithms and an open-source package for analyzing and optimizing beam stability in double rf systems, improving accuracy and computational efficiency.

Findings

Algorithms effectively predict Robinson and PTBL instabilities.

Application to SOLEIL II demonstrates optimization of rf parameters.

Open-source ALBuMS tool facilitates stability analysis.

Abstract

Double rf systems are critical for achieving the parameters of 4th-generation light sources. These systems, comprising both main and harmonic rf cavities, relax statistical collective effects but also introduce instabilities, such as Robinson and periodic transient beam loading (PTBL) instabilities. In this paper, we provide semi-analytical algorithms designed to predict and analyze these instabilities with improved accuracy and robustness. The algorithms leverage recent advancements in the field, offering a computationally efficient and accurate complement to multibunch tracking simulations. Using the SOLEIL II project as a case study, we demonstrate how these algorithms can optimize rf cavity parameters in high-dimensional parameter spaces, thereby maximizing the Touschek lifetime. An open-source Python package, ALBuMS (Algorithms for Longitudinal Multibunch Beam Stability), is provided as an accessible tool for double rf system stability analysis.