Electron Cloud Effects in the Circulant Matrix Model

The existing models for the electron cloud driven instabilities either reduce the complexity of the cloud dynamics to the one of an impedance, in order to use well established analytical beam stability models or rely on large computational power for full description of this dynamics by macro-particles. This paper proposes a novel approach based on the derivation of the electron cloud and beam motion in a self-consistent manner within the circulant matrix model, using linearised integrated forces between the charged particles. It is shown that such a model can efficiently describe the instability properties over a large range of parameters, nevertheless the accuracy of the predictions for realistic machine configurations are currently limited since the treatment does not take into account external magnetic fields.