Feedback system analysis for beam breakup in a multipass multisection electron linac

A recirculating electron accelerator based upon superconducting cavities technology is envisaged in different laboratories to produce a high duty cycle beam with energy in the GeV region. Beam break up is a severe limitation in this kind of accelerator due to the positive feedback of the returning beams. We present here an analysis based upon feedback system theory which takes into account the different cavities of the linac, the optics of the linac and of the recirculating path. An example is given for the Saclay proposal of a 2 GeV accelerator consisting of 4 passes in a 500 MeV, 100 m-long superconducting linac