Study of the Effect of Detuning Impedance on Beam Stability

The impact of the detuning impedance on the stability of a particle beam is a relatively less studied phenomenon compared to the usual case of considering only the driving impedance. This report tries to explore the area of the detuning impedance with a specific focus on the SPS. Different studies were carried to examine the effect and some key findings were made. The analytical model for two macroparticles (developed for the case of zero chromaticity) was confirmed with simulations. The dependence of the stabilising or destabilising effect of detuning on the second harmonic voltage was observed implying that the effect depends on the actual particle distribution. A Vlasov solver was used to verify the results of particle tracking simulations. The effect of non-linearities and higher order chromaticities was also studied. It was found that these effects have a significant impact on the TMCI threshold along with the detuning impedance. Finally, an analytical model was developed for observing the bunch by bunch tunes with multiple rigid bunches in presence of wakes and the results were compared with similar simulations.