The fine structure of the longitudinal machine impedance observed with single bunches

Abstract

Using a beam spectrum measurement the detailed structure of the CERN SPS longitudinal machine impedance has been observed over a wide frequency range. Single high intensity proton bunches were injected into the machine with RF off. The spectrum of the unstable bunch modes, produced by the different resonant impedances in the ring, was measured during slow debunching. The maximum mode amplitude as a function of frequency was recorded for many injected bunches. The central frequency of each bunch mode is close to the resonant frequency of the impedance and the width depends upon the bunch length. Using sufficiently long bunches allowed the machine impedance to be seen in detail in the frequency range 100MHz to 4GHz. The low frequency of this range is defined by the initial stable bunch spectrum, and the high frequency by the vacuum chamber cut-off frequency. The dominant peaks in the spectrum have been identified with different impedance sources in the machine -some previously unknown.

Nominal longitudinal parameters for the LHC beam in the CERN SPS

“…The single bunch reference measurements in 2001 have demonstrated significantly improved stability [2]. The change of quadrupole synchrotron frequency shift with intensity by a factor 2.5 agrees well with that expected from the reduction in the low frequency inductive impedance estimated from the impedance budget (from 12.4 Ohm to 5.6 Ohm).…”