Measurement and interpretation of longitudinal instabilities in the ESR

We have investigated experimentally the longitudinal instability with coasting beams in the ESR far beyond the stability boundary. The longitudinal coupling impedance has been varied by tuning the eigenfrequency of an ESR cavity to different values. For the eigenfrequency regulation a small RF cavity gap voltage was present. The development of special software analysis routines enabled us to observe the beam dynamics up to 1000 ms with a much improved time resolution. In this paper measurements are interpreted by using the linear kinetic theory as well as the particle-in-cell (PIC) code PATRIC.