Electrostatic Bender Optics

TL;DR

This paper derives the relativistically-correct Hamiltonian and transfer matrix for electrostatic benders with curved electrodes, providing a comprehensive framework for analyzing their optical properties in particle accelerators.

Contribution

It introduces a general derivation of the Hamiltonian and transfer matrix for electrostatic benders with electrode curvature in the non-bend direction, extending previous models.

Findings

Derived the relativistically-correct Hamiltonian for curved electrostatic benders.

Established the transfer matrix for these benders.

Provides a foundation for more accurate beam optics modeling.

Abstract

The relativistically-correct Hamiltonian and transfer matrix of electrostatic benders is derived. This is the general case where the bender electrodes have curvature in the non-bend direction.