Synchrotron Frequency Shift as a Probe of the CERN SPS Reactive Impedance

Longitudinal instability in the CERN SPS is a serious limitation for the future increase of bunch intensity required by HiLumi LHC project. The impedance driving this instability is not known precisely and a lot of effort goes into creating an accurate impedance model. The reactive impedance of the machine can be probed by measuring the bunch length oscillations of a mismatched bunch at injection. The frequency of these oscillations as a function of intensity has a slope that depends on the reactive impedance and the emittance. Measurements were done for three values of longitudinal emittances and then compared with particle simulations based on the impedance model using particle distribution close to the measured one. Comparison of measured and calculated frequency shifts gives an estimation of the missing impedance in the model. In addition, scanning of initial emittance for diverse particle distributions in simulations shows that the frequency shift greatly depends on emittance and initial distribution. Small variations of these parameters can lead to very different results and explain partially the discrepancy between measured and calculated values of frequency shifts.