Beam response measurements at SPEAR

Two types of beam response measurements were carried out in SPEAR with the aim of gaining understanding of high intensity phenomena. In the first case, the beam was kicked horizontally with the injection kicker magnet and the amplitude of the resulting betatron oscillation was observed as a function of time. This experiment was carried out for different beam intensities. At large currents, the decay of the oscillation is dominated by the head-tail damping due to the transverse impedance. It shows the expected dependence on the chromaticity. At small currents, the decay of the excited betatron oscillation is due mostly to Landau damping. Another series of experiments dealt with the longitudinal behavior of a single bunch. A network analyzer was used to modulate the phase or amplitude of the RF voltage and thereby excite dipole or quadrupole synchrotron oscillations. The modulating frequency was swept through the dipole or quadrupole frequency and the beam response in phase and amplitude, the longitudinal bunched-beam transfer function, was observed. The behavior of the transfer function changed significantly as the beam current was increased. In this paper, the authors outline a theoretical framework for the interpretation of these measurements