Longitudinal Space Charge in the SPS

Longitudinal instabilities due to the SPS beam coupling impedance are a major issue for future projects and it is essential to have an accurate SPS impedance model to study them. The longitudinal space charge effect can be modelled by a pure reactive impedance and should also be included in simulations as it may have an impact at low energy. In this Note, the effect of the longitudinal space charge in the SPS is evaluated by taking into account the variation of the transverse beam size and vacuum chamber geometry along the ring. Scaling laws are used to investigate what are the most important parameters for the evaluation of the longitudinal space charge impedance.