Stimulated regenerative BBU instability of a bunch train in a single linac section

Stimulated multi-bunch transverse instability caused by hybrid dipole mode is studied using single cavity model. An accurate solution for the transverse displacement is found for sequence of bunches at presence and in absence of the input of signal. Threshold currents are calculated for resonant and non-resonant instability build-up including interaction with backward wave and Lorentz’ force contribution into the transverse wakefield. Linear amplification gain below the threshold was analyzed analytically. Transition from the cavity model to the waveguide model and validity of single-mode approximation is considered. It is shown, that for resonantly stimulated BBU the increment can be higher and threshold current lower than that for spontaneous instability.