Nonlinear Behavior of bunch lengthening by using a localized wake in electron storage rings

The equilibrium particle distribution of a bunch is investigated by using a localized delta' wake in an electron storage ring. A mapping method is performed to show the dynamical behavior of the particle distribution by using the Gaussian approximation. It is shown that stable multi-periodic states, a limit cycle, and chaos can exist under some conditions. When moving around the parameter space, the system can show bifurcation phenomena.X111sci