A CAD Tool for Linear Optics Design: A Controls Engineer's Geometric Approach to Hill's Equation

TL;DR

This paper presents a systematic derivation of linear optics design formulae for synchrotrons from Hamiltonian dynamics, enabling software engineers to develop CAD tools similar to those used in mechanical engineering since the 1960s.

Contribution

It introduces a geometric, Hamiltonian-based approach to linear optics design, facilitating the creation of CAD tools for accelerator physics.

Findings

Derived formulae from first principles using Hamiltonian dynamics

Captured key use cases for streamlined CAD tool development

Enables software engineers to prototype linear optics design tools

Abstract

The formulae relevant for the Linear Optics design of Synchrotrons are derived systematically from first principles, a straightforward exercise in Hamiltonian Dynamics. Equipped with these, the relevant "Use Cases" are then captured for a streamlined approach. This will enable professionals -- Software Engineers -- to efficiently prototype & architect a CAD Tool for ditto; something which has been available to Mechanical Engineers since the mid-1960s.