Quasi-isochronous storage rings

A study is made of the single-particle dynamics of an electron-positron storage ring where the phase-slip factor is made small in order to make the ring nearly isochronous and reduce the bunch length. What is found is that a quasi-isochronous ring makes it possible to obtain a bunch length in the millimeter range, about one order of magnitude shorter than present values. In this study we have extended the work of others on isochronous storage rings by quantitatively including higher-order terms in the longitudinal equations of motion. Scaling laws are then derived relating the linear term with the next-highest-order term. These scaling laws, which are derived from a two-dimensional Hamiltonian (one dimension of position and one of momentum), establish criteria for stability. These scaling laws are then checked with full six-dimensional tracking on one particular lattice.