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The coupled-bunch instability for arbitrary multibunch configurations is investigated in its generality. The theoretical framework adopted is based on the general eigenvalue analysis based on the known formulas of the complex frequency shifts for the uniform multibunch configuration case. Closed formulas are derived for special cases. For the configuration consisting of a uniform filling pattern with a gap of missing bunches, the theoretical results are found to be in good agreement with measurements of the transverse coupled-bunch instability driven by the resistive wall impedance performed at the NSLS-II storage ring.

Impedance modeling for accelerator applications has improved over the years, largely as a result of advances in simulation capabilities. While this modeling has been successful in reproducing certain measurements, it is still a significant challenge to predict collective effects in real machines. In this paper, we review our approach to impedance modeling and the subsequent simulations of collective effects. We discuss the choice of the electrodynamics codes and the required computer power resources, modeling of the geometric, and resistive wall impedances, their comparison with analytical approaches, and their application for simulating of the collective effects with tracking and beam-induced heating.

The resonant interaction of a bunched particle beam with short-range wakefields is the cause of head-tail instability, which is a major limitation for single-bunch beam intensity in circular accelerators. There are several processes that suppress this type of instability, such as fast chromatic damping and Landau damping due to machine nonlinearity. Beam-based feedback systems (transverse dampers) provide active suppression of the beam oscillations. The combined effect of the transverse dampers and chromaticity is discussed in this article. A brief overview of theoretical and experimental studies of the head-tail instability and its mitigation is presented. Results of experimental studies of the transverse mode coupling carried out at National Synchrotron Light Source-II are compared with the theoretical model.

NSLS-II is now one of the brightest synchrotron light sources worldwide, in user operations since 2014. Currently, 20 light-generating insertion devices (IDs) are installed: 3 damping wigglers and 17 undulators of various types. These devices introduce significant distortions into the magnet lattice of the storage ring. For each ID, the distortions have been locally corrected using quadrupole magnets located nearby the ID. The insertion devices have also a significant impact on the electron beam emittance. Precise measurements of the emittance were carried out at the Coherent Hard X-ray beamline for three different lattices: without IDs, with 3 pairs of damping wigglers only, and with all IDs. A minimum horizontal emittance of 0.76 nm was achieved. The radiation energy loss and relative energy spread were also measured using a streak-camera. The measured data show good agreement with analytical formulas and numerical simulations.

An analytical expression of the low-frequency quadrupole impedance for undulators and wigglers is derived and benchmarked against beam-based impedance measurements done at the 3 GeV NSLS-II storage ring. The adopted theoretical model, valid for an arbitrary number of electromagnetic layers with parallel geometry, allows to calculate the quadrupole impedance for arbitrary values of the magnetic permeability ${\ensuremath{\mu}}_{r}$. In the comparison of the analytical results with the measurements for variable magnet gaps, two limit cases of the permeability have been studied: the case of perfect magnets (${\ensuremath{\mu}}_{r}\ensuremath{\rightarrow}\ensuremath{\infty}$), and the case in which the magnets are fully saturated (${\ensuremath{\mu}}_{r}=1$).