Longitudinal Single Bunch Instability Caused by Wake Field of Electron Cloud

The electron cloud accumulated in the vicinity of positron beam generates longitudinal electric field during the passage of bunch. The longitudinal interaction between bunch and electron cloud can lead to the distortion of the bunch shape. We use a simple analytic formula to calculate the longitudinal electric field due to electron cloud. Based on the longitudinal wake field, the macro-particle tracking method is used to simulate the variation of bunch longitudinal profile in different electron cloud densities and the simulation also shows that the synchrotron oscillation tune is slightly shifted by the wake field. By comparing the simulation results and the analytical estimation from potential distortion theory, the longitudinal wake field from electron cloud can be seen as a potential well effect.