Quasi-isochronous storage ring colliders: Energy density enhancement as a route to high luminosity

A study is made of the single particle and collective dynamics of an electron-positron storage ring where the phase slip factor is made small in order to make the ring nearly isochronous, reduce the bunch length, and increase the peak current. 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, and makes it possible to increase the beam longitudinal brilliance by more than one order of magnitude. The shorter bunch length allows one to reduce the betatron function and the beam area at the interaction point of an electron-positron collider, leading to larger luminosity.; In this study we have extended the work of others on isochronous storage rings by quantitatively including higher-order terms in the equations of motion. Scaling laws are then derived relating the linear term with the next highest order term. We also extend the work done previously by quantitatively calculating the effects of the longitudinal microwave instability on the stability of motion including higher order terms.; As an example of a quasi-isochronous ring, a design for a 510 MeV electron positron storage ring is developed where the phase slip factor can be varied over several orders of magnitude. This 510 MeV ring is designed as a collider for use as a {dollar}phi{dollar}-factory and is compared with two other proposals for high luminosity {dollar}phi{dollar}-factories.