Multi-bunch Longitudinal Instability due to the Electron Cloud

The mechanism of longitudinal interaction of high-energy positrons of a bunch train and secondary emitted particles of electron cloud is analyzed. We consider the case when electron cloud in solenoidal magnetic field is built mainly due to multipacting process. Positron bunches have to use some amount of their kinetic energy to give electron cloud some temperature. The field, which is responsible for the energy transformation, is longitudinal electric field. The amplitude of electric field depends on the density of electron cloud and varies with bunch spacing that leads to a resonant multi-bunch instability. Also longitudinal field acts as an oscillating force on the cloud electrons and gives, at the same time, an additional energy variation inside the positron bunches. The head of the positron bunch is accelerated and the tail is decelerated. This action of the longitudinal field is similar to the action of RF fields in a cavity. As a result the positron bunches will have different length and synchrotron frequency throughout the train.