Calculation of the bunch lengthening threshold [particle accelerator]

A new analysis of the bunch lengthening instability, based on a single synchrotron mode in a distorted potential well, is presented. The nonlinearity of the wakefield plays a critical role. It distorts the equilibrium density from its Gaussian shape, which results in asymmetric corrections to the Sacherer equation. This modified equation will have unstable eigenmodes when the beam current reaches a threshold value. The calculated threshold agrees very well with our multiparticle simulation for SPEAR parameters.<>