Simple model for multibunch transverse coherent instabilities in a beam containing a gap

We use the model with exponentially decaying wakes to study transverse multibunch instabilities in a beam where a uniformly filled train of bunches is followed by the gap which is empty of bunches. Stability of both betatron and synchrobetatron modes is inspected. Contrary to cases of uniformly filled beams, the amplitudes of multibunch eigenmodes in such a beam grow towards the end of the train. This amplification of oscillation amplitudes along the beam can limit the beam performance in high-current operation of accelerators.