Residual Dispersion in a Combiner Ring

TL;DR

This paper proves that no linear or nonlinear optical system can simultaneously close multiple local orbit bumps and dispersion in a single beam transport region, using the CLIC CR2 ring as an example.

Contribution

It provides a formal proof that such a system cannot exist, highlighting fundamental limitations in beam optics design.

Findings

No physical solutions exist for closing multiple orbit bumps and dispersion simultaneously.

All solutions are either unphysical or trivial.

The proof applies to both linear and nonlinear optical systems.

Abstract

In this paper we present a proof to show that there exists no system of linear or nonlinear optics which can simultaneously close multiple local orbit bumps and dispersion through a single beam transport region. The second combiner ring in the CLIC drive beam recombination system, CR2, is used as an example of where such conditions are necessary. We determine the properties of a lattice which is capable of closing the local orbit bumps and dispersion and show that all resulting solutions are either unphysical or trivial.