Multiperiodic states and bifurcations in bunch lengthening by a localized impedance in electron storage ring

The equilibrium particle distribution of a bunch in an electron storage ring is investigated using a localized constant wake function. It is shown that, under some conditions, stable multiperiodic states can exist simultaneously. When moving around the parameter space, the system can show bifurcation phenomena which is not always reversible. We study this behavior using the Gaussian approximation and compare the results with multiparticle tracking. The results show qualitative agreement