Electrostatic Bender Fields, Optics, Aberrations, with Application to the Proton EDM Ring

TL;DR

This paper derives second-order electrostatic bender optics, applies them to the proton EDM ring, and finds that fringe field shape does not affect second-order optics, with implications for electrode design.

Contribution

It provides a detailed second-order analysis of electrostatic bender optics and applies it to the proton EDM ring, clarifying the impact of fringe field shapes.

Findings

Second-order optics are insensitive to fringe field shape.

Electrode shape that linearizes vertical electric field offers no second-order advantage.

Results align with previous linear optics analyses.

Abstract

Electrostatic bender optics are derived up to second order (third order in fields and the Hamiltonian) and applied to the proposed EDM proton ring. The results for linear optics agree with those already presented by V.\ Lebedev (Nov.\ 18, 2013). Second order optics is not sensitive to the shape of the fringe fields and formulas are given. It is shown that the proposed electrode shape that linearizes the vertical electric field is no advantage to this order.