Effective impedance for the threshold of loss of Landau damping

Loss of Landau damping (LLD) in the longitudinal plane is an important intensity limitation in existing and future hadron accelerators. One of the outcomes of the recent study [I. Karpov, T. Argyropoulos, and E. Shaposhnikova. Phys. Rev. Accel. Beams, 24, 011002, 2021] is an expression to estimate an effective impedance for the evaluation of the LLD threshold. In this project, the applicability of the formula was investigated for an impedance model given by a sum of broadband and narrowband resonators. Agreement at below 70% error was achieved by using a new method for choosing the truncation point in the sum over harmonics. Applying the new method to the SPS impedance, the LLD threshold was predicted with a maximum error of 40% in a wide range of bunch lengths.