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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.

From the beginning of the NSLS-II project, the vacuum chamber of the NSLS-II storage ring has been optimized to reduce its impedance. The optimization, performed in close collaboration with the Diagnostic, Vacuum, RF, and Mechanical Engineering groups, has been achieved via calculating the impedance of the vacuum chamber components with the use of both analytical and numerical tools, with the numerical computations carried out with the GdfidL code. For reliable NSLS-II operation with the total beam current of 500 mA, each component of the vacuum chamber has been individually optimized to minimize the beam-induced heating and to prevent single-bunch and coupled-bunch instabilities. In this article, the impedance calculation and optimization know-how are summarized for all the chamber components, and the total longitudinal impedance budget is analyzed. As a result of this extensive research and engineering effort, the design beam current of 500 mA has been recently accumulated in NSLS-II without any major problem caused by the collective effects.

A fast and precise technique of local impedance measurement has been developed and tested at NSLS-II. This technique is based on in-phase sine-wave (AC) excitation of four fast correctors adjacent to the vacuum chamber section, impedance of which is measured. The beam position is measured using synchronous detection. Use of the narrow-band sine-wave signal allows us to improve significantly the accuracy of the orbit bump method. Beam excitation by fast correctors results in elimination of the systematic error caused by hysteresis effect. The systematic error caused by orbit drift is also eliminated because the measured signal is not affected by the orbit motion outside the excitation frequency range. In this article, the measurement technique is described and the result of proof-of-principle experiment carried out at NSLS-II is presented.

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.

The NSLS-II storage ring is designed to operate with superconducting RF-cavities with the aim to store an average current of 500 mA distributed in 1080 bunches, with a gap in the uniform filling for ion clearing. At the early stage of the commissioning (phase 1), characterized by a bare lattice without damping wigglers and without Landau cavities, a normal conducting 7-cell PETRA-III RF-cavity structure has been installed with the goal to store an average current of 25 mA. In this paper we discuss our analysis of coupled-bunch instabilities driven by the Higher Order Modes (HOMs) of the 7-cell PETRA-III RF-cavity. As a cure of the instabilities, we apply a well-known scheme based on a proper detuning of the HOMs frequencies based upon cavity temperature change, and the use of the beneficial effect of the slow head–tail damping at positive chromaticity to increase the transverse coupled-bunch instability thresholds. In addition, we discuss measurements of coupled-bunch instabilities observed during the phase 1 commissioning of the NSLS-II storage ring. In our analysis we rely, in the longitudinal case, on the theory of coupled-bunch instability for uniform fillings, while in the transverse case we complement our studies with numerical simulations with OASIS , a novel parallel particle tracking code for self-consistent simulations of collective effects driven by short and long-range wakefields.

The heat transfer analysis has been performed for the stripline kicker, design of which is used at many accelerator facilities as a part of the transverse bunch-by-bunch feed-back system, including NSLS-II. The experimental data of the electrode temperature have been collected from a special diagnostic stripline designed with six infrared view ports. The temperature analysis is based on the power loss calculations and the loss factor computed by the 3-D electromagnetic simulation code GdfidL. To estimate the power loss, we analyze the real part of the longitudinal impedance and the loss factor for two different regimes. We use the ANSYS finite element code to correlate the temperature with the power loss. Lambertson and Shafer formalisms of the longitudinal and transverse beam impedances are discussed for the simplified stripline geometries. The required characteristic impedances and the geometric factors are determined analytically for the simplified geometries and compared with the results for the designed stripline geometry using the 2-D POISSON code by solving the Laplace’s equation in two dimensions. Lambertson’s equations are compared with numerical results. We introduce the frequency range, within which we can apply the analytical approach.

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 (${\ensuremath{\mu}}_{r}=1$).

One of the important issues of the in-vacuum undulator design is the coupling impedance of the vacuum chamber, which includes tapered transitions with variable gap size. To get complete and reliable information on the impedance, analytical estimate, numerical simulations and beam-based measurements have been performed at Diamond Light Source, a forthcoming upgrade of which includes introducing additional insertion device (ID) straights. The impedance of an already existing ID vessel geometrically similar to the new one has been measured using the orbit bump method. The measurement results in comparison with analytical estimations and numerical simulations are discussed in this paper. © 2014 Published by the American Physical Society.

Consideration of transverse wakefields and impedances due to the tapered vacuum chambers for superconducting mini-gap undulators revealed the existence of trapped modes. To investigate this phenomenon, a series of analytical and numerical calculations were performed for both elliptical and rectangular chambers. A rectangular prototype was built and measured and the experimental results were found to be in very good agreement with theory. Knowledge about the impedance of tapered vacuum chambers is important for the evaluation of transverse instabilities in high-energy accelerators.

We consider the longitudinal point-charge wakefield, w(s), for an axisymmetric collimator having inner radius b, outer radius d, inner length g, and taper length L. The taper angle {alpha} is defined by tan {alpha} = (d-b)/L. Using the electromagnetic simulation code ECHO, we explore the dependence of the wakefield on a collimator's geometric parameters over a wide range of profiles: from small-angle tapers to step-function transitions. The point-charge wakefield is determined using an approximation introduced by Podobedov and Stupakov. We have found it useful to exhibit the wakefield as a function of the scaled variable s/d{alpha}. For small taper angles, our results illustrate the satisfaction of the longitudinal scaling found by Stupakov, Bane, and Zagorodnov; and for larger taper angles, the breaking of this longitudinal scaling is clearly depicted. The use of the scaled variable s/d{alpha} turns out to be especially well suited to describing the wakefield for a collimator with step-function profile ({alpha} = {pi}/2).

We use the program ECHO to study numerically the loss factor of axisymmetric cavities and collimators with and without tapering. We consider a Gaussian driving bunch of length $\ensuremath{\sigma}$, and structures with inner radius $b$, outer radius $d$, cavity gap (or collimator inner length) $g$, and taper length $L$. In all cases we consider a short bunch with $\ensuremath{\sigma}\ensuremath{\ll}b$. For the untapered structures ($L=0$), in certain regimes, we describe our numerical results using the known expressions for a step transition and for the diffraction model. In addition, we identify new regimes where $gl\ensuremath{\sigma}$ and/or $d\ensuremath{-}bl\ensuremath{\sigma}$, for which the data must be described by new phenomenological expressions. For a tapered collimator with $d\ensuremath{-}bgb$, we present a phenomenological formula which accurately describes the dependence of the loss factor on the parameters $\ensuremath{\sigma}$, $b$, $d$, and $L$. This formula also holds for a tapered cavity with $gg{d}^{2}/\ensuremath{\sigma}$ and $d\ensuremath{-}bgb$.