Transverse-Longitudinal Emittance Transfer in Circular Accelerators Revised

We revise a previous version of this paper [1] proposing a method to transfer emittances from the transverse planes to the longitudinal. It turned out the system showed non-Hamiltonian behaviour 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.