Notes on orbit and spin tracking in an electrostatic storage ring

TL;DR

This paper critically examines recent claims about a numerical integration algorithm for electrostatic storage rings, questioning whether the proposed orbit tracking method is truly symplectic, especially regarding zero-length elements.

Contribution

It provides a critical analysis of the symplectic nature of the orbit tracking algorithm in recent literature, highlighting potential inaccuracies in its claims.

Findings

The orbit tracking algorithm may not be symplectic for zero-length elements.

Questions the validity of claims made in recent arXiv papers.

Highlights the importance of symplecticity in accurate beam dynamics simulations.

Abstract

Two documents have recently been posted on the arXiv describing a numerical integration algorithm: "symplectic orbit/spin tracking code for all-electric storage rings" [1] and some computational results therefrom [2]. This note comments critically on some of the claims in [1] and [2]. In particular, it is not clear that the orbit tracking algorithm described in [1] is really symplectic. Specifically, for electrostatic beamline elements, the so-called "zero length elements," which are treated as position dependent kicks in the formalism in [1], are in fact {\em not} symplectic.