Effect of the Sextupole Finite Length on Dynamic Aperture in the Collider Final Focus

TL;DR

This paper investigates how the finite length of sextupoles affects the dynamic aperture in collider final focus systems, especially for future colliders with low beta and large chromatic effects, proposing methods to recover aperture loss.

Contribution

It introduces an analytic approach to study high-order aberrations caused by thick sextupoles and proposes a method to recover the dynamic aperture.

Findings

Quadratic aberrations are canceled, but higher order terms degrade the aperture.

Analytic power series method effectively models aberrations.

Proposed recovery method improves dynamic aperture in realistic sextupole configurations.

Abstract

In a collider final focus (FF) system chromaticity generated by FF quadrupoles is compensated by sextupole pairs with -I map in between to cancel geometrical aberrations. However, it works perfectly only for zero-length sextupole kicks; for realistic thick magnets only quadratic aberrations are cancelled exactly while higher order terms appear and may deteriorate the transverse dynamic aperture. The latter is particularly important for prospective projects of the future circular colliders based on the Crab-Waist collision approach where extremely low beta at IP generates very large chromatic effects. In the present paper, we study these high aberrations by the power series technique and propose the method of the dynamic aperture recover. Results of analytic study are compared with those obtained by tracking.