Transverse-Longitudinal Emittance Transfer in Circular Accelerators Revised

TL;DR

This paper revises a method for transferring emittance between transverse and longitudinal planes in circular accelerators, emphasizing the importance of including end fields for conservation and demonstrating the process via resonance tuning.

Contribution

It corrects previous models by including end fields, clarifies the emittance transfer mechanism, and shows how resonance tuning enables emittance flow between planes.

Findings

Including end fields conserves 6D emittance.

Resonance tuning facilitates emittance transfer.

Coupling exists even without dedicated devices.

Abstract

We revise a previous version of this paper proposing a method to transfer emittances from the transverse planes to the longitudinal. It turned out the system showed non-Hamiltonian behavior because the longitudinal component of the transverse electric field at ends of the transverse resonator were not included in the model. Including those fields the 6D emittance is conserved. We review the mechanism behind the emittance conservation. It is still possible to produce an emittance transfer with the RF quadrupole field setting the tunes on synchro-betatron resonance for a short period of time then reducing the transverse RF field to zero. We found some coupling between the transverse and the longitudinal planes is always present, even there in no special device in the accelerator to provoke it. The role of the transverse RF field is to modify the transverse tunes quickly putting the system to synchro-betatron resonance for a short time. The emittance tends to flow from the plane with bigger emittance to the smaller one.