  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.
