Studies of coherent transverse beam stability for the FAIR synchrotrons

Collective instabilities are a potential limiting factor for the performance of the FAIR rings at GSI Darmstadt. Here, we discuss results of numerical investigations for SIS 100 and for the SIS 18 Upgrade together with experimental investigations in the SIS 18 synchrotron. Within our experimental investigations, the first measurement of the transverse Beam Transfer Function (BTF) in SIS 18 were performed [1] on October 25, 2006. The BTF is obtained by exciting a beam with a periodic signal and measuring the resulting beam response (amplitude and phase). The BTF signal contains a wealth of important information on beam and machine properties. The beam response was measured with the Schottky probe and compared with the excitation using a network analyzer in a frequency sweep. The inversed BTF, represented in the complex plane, gives the stability diagram, which provides threshold of instabilities. Figure 1 presents raw data (black line) for the stability diagram in the impedance plane V + iU ∝ Z⊥, measured for the slow wave at the harmonic number m = 24. The experimental stability diagram is compared with three theoretical distributions. We conclude that the Gaussian distribution is the most suitable one to describe the particle momentum distribution. Using these BTF measurements, the vertical tune, the momentum spread and the chromaticity were obtained too [1].