Longitudinal beam dynamics studies with space charge in small isochronous ring

Studies of the longitudinal beam dynamics in the small isochronous ring (SIR) at Michigan State University revealed a fast, space-charge driven instability that did not fit the model of the negative mass instability. The observed beam behavior can be explained by the transverse horizontal component of the coherent space-charge force and its effect on the longitudinal motion. This force effectively modifies the slip factor, shifting the isochronous point and enhancing the negative mass instability. This paper presents results of numerical and experimental studies of the longitudinal beam dynamics in SIR and proposes a simple analytical model explaining these results.