Non relativistic Broad Band wake fields and potential-well distortion

The study of the interaction between a particle beam and wake fields is usually based on the assumption of ultra relativistic beams. This is not the case, for example, for the Proton Synchrotron Booster(PSB), in which protons cover the energy range. There are some examples in literature which derive nonultra relativistic formulae for the resistive wall impedance. In this paper we have extended the Broad-Band resonator model, allowing the impedance to have poles even in the upper half complex plane, in order to obtain a wake function different from zero for. The Haissinski equation has been numerically solved showing longitudinal bunch shape changes with. In addition some longitudinal bunch profile measurements, taken for two different bunch intensities at the PSB, are shown