Analyse de la stabilite de faisceau dans un accelerateur lineaire avec passages multiples en prenant en compte les effets de toutes les cavites
The interaction of a beam with the deflecting modes of the cavities can make it unstable when the energy transferred to the mode is greater than the power lost in the walls. In a single cavity, the mechanism of the regenerative beam breakup has been clearly described. In the case of multiple passes the instability appears at a level of current in general much lower and is indeed the most severe limitation. The current threshold was evaluated earlier either in the impulse approximation or considering only one cavity where the mode is supposed to be excited ignoring the other cavities. The purpose of this paper is to take into account the effects of all the cavities whose deflecting mode frequencies coincide or overlap. The analysis is based upon the theory of the stability of the feedback systems and a simulation code in the time domain confirms the results. The only restrictive assumptions are the following: the displacement of the beam is supposed not to vary inside a cavity and the structure of bunched beams is neglected. A similar feedback analysis involving discrete-time systems which takes into account the bunched structure of the beam showed that the values of the BBU currents are exactly the same if the frequency of the deflecting mode does not coincide with the harmonics of the repetition frequency of the bunches .