Non relativistic resistive wall wake fields and single bunch stability

The usual approach for the resistive pipe wall assumes the beam moves with the speed of light. For many low energy rings, such as the Proton Synchrotron Booster (PBS), possible performance limitations may arise from non relativistic resistive wall wake fields. In this regime not only the head of the bunch can interact with the tail but also the vice versa holds. In this paper we analyze numerical results showing the resistive wake field calculated from non relativistic impedance models. In addition we analyze the well known two particles model assuming that even the trailing particle can affect the leading one. We observe significant changes in the stability domain.