Second order single particle dynamics in quasi-isochronous storage rings and its application to the LNLS-UVX ring

We analyze the second order single particle longitudinal dynamics in a quasi-isochronous storage ring. We expand the momentum compaction factor to include the effects of second order terms taking sextupoles into account and of transverse betatron oscillations. The introduction of nonlinearities due to higher order terms results in a second stability region for longitudinal phase oscillations, in addition to the well known linear stable operation point. The conditions for this new solution to fall within the energy acceptance of the storage ring are presented. Inclusion of transverse motion coupling may lead to either a reduction or an enhancement of the stable longitudinal phase-space regions. The analysis is applied to the LNLS 1.15 GeV UVX electron storage ring, indicating that it should be possible to operate this ring in a quasi-isochronous mode. (orig.)