Some notes on beam dynamics due to vertical oscillations in an all-electric storage ring

TL;DR

This paper rederives and generalizes key formulas related to beam dynamics caused by vertical oscillations in an all-electric storage ring, providing clearer theoretical foundations and correcting previous inaccuracies.

Contribution

It introduces a Hamiltonian formalism to rederive and extend Orlov's formulas, improving the theoretical understanding of vertical oscillations in electric storage rings.

Findings

Corrected and generalized formulas for beam dynamics

Clarified theoretical framework for vertical oscillations

Enhanced accuracy of particle tracking simulations

Abstract

A document has recently been posted on the arXiv [1], describing analytical formulas and results of particle tracking simulations, for precision tests of numerical integration algorithms for an EDM (electric dipole moment) storage ring. In the context of an all-electric storage ring, the authors cite theoretical formulas by Orlov [2]. However, the reference to Orlov is to a talk at a workshop in 2012, and is unpublished and difficult for independent researchers to access and validate. This note rederives and generalizes some of Orlov's principal results, using a Hamiltonian formalism, and also corrects some details in both Orlov's note [2] and the arXiv post [1].