Apochromatic Beam Transport in Drift-Quadrupole Systems

TL;DR

This paper demonstrates that for any drift-quadrupole system, there exists a unique set of Twiss parameters that transport without first-order chromatic distortions, minimizing chromatic effects and second-order oscillations.

Contribution

It proves the existence and uniqueness of Twiss parameters that optimize chromatic and second-order effects in drift-quadrupole systems.

Findings

Existence of unique Twiss parameters for distortion-free transport.

Minimization of chromaticities at these Twiss parameters.

Reduction of second-order betatron oscillation effects.

Abstract

Though a straight drift-quadrupole system can not be made an achromat, there exists an example of a bend-free drift-quadrupole system which can transport certain incoming beam ellipses without introducing first-order chromatic distortions. In this paper we show that such a possibility is not a rare special case, but a general property. For every drift-quadrupole system there exists an unique set of Twiss parameters, which will be transported through that system without first order chromatic distortions. Moreover, we prove that at the same time these Twiss parameters minimize the absolute values of the system chromaticities and also bring the second order effect of the betatron oscillations on the longitudinal dynamics to the minimal possible value.