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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.

Transverse head-tail instability is a major limitation for the single-bunch beam current in circular accelerators. Beam-based feedback is one of the potential tools to suppress this type of instability. The feedback systems (transverse dampers) provide active suppression of the beam oscillations by electromagnetic fields, the amplitude of which is calculated in real time from the measured beam position. The effciency of the transverse dampers in combination with various chromaticity settings is discussed., CERN Yellow Reports: Conference Proceedings, Vol. 9 (2020): Proceedings of the ICFA mini-Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators, Zermatt, Switzerland, 23–27 September 2019

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.

Novel features of the longitudinal instability of a single electron bunch circulating in a low-emittance electron storage ring are discussed. Measurements and numerical simulations, performed both in time and frequency domain, show a non-monotonic increase of the electron beam energy spread as a function of single bunch current, characterized by the presence of local minima and maxima, where a local minimum of the energy spread is interpreted as a higher-order microwave instability threshold. It is also shown that thresholds related to the same zero-intensity bunch length depend linearly on the accelerating radio frequency voltage. The observed intensity-dependent features of the energy spread, confirmed by measurements with two independent diagnostics methods, i.e. horizontal beam profile measurements by a synchrotron light monitor and photon energy spectrum measurements of undulator radiation, are given a theoretical interpretation by applying a novel eigenvalue analysis based on the linearized Vlasov equation.

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.

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 $d\ensuremath{-}bgb$.

The wakefield and impedance produced by the components of the NSLS-II storage ring have been computed for an electron bunch length of 3 mm rms. The results are summarized in a table giving for each component, the loss factor (kappapar ), the imaginary part of the longitudinal impedance at low frequency divided by the revolution harmonic (ImZpar/n), and the transverse kick factors (kappax,kappay).

A new high-brightness synchrotron light source (NSLS-II) is under design at BNL. The 3-GeV NSLS-II storage ring has a double-bend achromatic lattice with damping wigglers installed in zero-dispersion straights to reduce the emittance below 1 nm. In this paper, we present an overview of the impact of collective effects upon the performance of the storage ring. Subjects discussed include instability thresholds, Touschek lifetime and intra-beam scattering.

CESR-B type superconducting cavities are under consideration for acceleration of the electron beam in the 3 GeV NSLS-II storage ring. In this paper we present detailed investigation of longitudinal and transverse impedance of CESR-B cavity and transitions. Ferrite material is included in impedance analysis. Its effect on short range wakepotential has been studied using GdfidL code. The summary results of loss factors and kick factors are presented for a 3 mm rms bunch length.

In this paper we discuss computation of the coupling impedance of the vacuum chambers for the NSLS-II storage ring using the electromagnetic simulator GdfidL [1]. The impedance of the vacuum chambers depends on the geometric dimensions of the cross-section and height of the slot in the chamber wall. Of particular concern is the complex geometry of the infrared extraction chambers to be installed in special large-gap dipole magnets. In this case, wakefields are generated due to tapered transitions and large vertical-aperture ports with mirrors near the electron beam.

The vertical impedances of the preliminary designs of National Synchrotron Light Source II (NSLS-II) Mini Gap Undulators (MGU) are calculated by means of GdfidL code. The Transverse Mode Coupling Instability (TMCI) thresholds corresponding to these impedances are estimated using an analytically solvable model.

NSLS-II is a 3 GeV ultra-high brightness storage ring planned to succeed the present NSLS rings at BNL. Ultra-low emittance combined with short bunch length means that it is critical to minimize the effects of Touschek scattering and coherent instabilities. Improved lifetime and stability can be achieved by including a third-harmonic RF cavity in the baseline design. This paper describes the required harmonic RF parameters and the expected system performance.

We propose an approach to the optimization of segmented in-vacuum undulators, in which different segments along an undulator may have different gaps and periods. This enables close matching between the gaps and the vertical "envelope" of electron beam motion in a storage ring straight section (carefully satisfying the associated vertical "stay clear" constraint) and, at the same time, precise tuning of all the segments to the same fundamental photon energy. Placing together undulator segments with different periods may introduce small kicks to electron trajectories at the segment junctions, which can be easily compensated, without introducing any significant radiation phase error, by active correction magnets or by special design of terminating magnets in the segments. Thanks to this, the entire multi-segment structure can operate as one long undulator. On the other hand, since the vertical gaps in segments located close to straight section center can be smaller than at extremities, such structure can offer better magnetic performance, compared to the case of a standard undulator with constant gap (and period) over its length. We present magnetic field, radiation flux and brightness calculation results for such segmented adaptive-gap in-vacuum undulators if used in low-beta straight sections of NSLS-II, and demonstrate their gain in spectral performance, especially in hard X-ray range, over standard room-temperature and even cryo-cooled in- vacuum undulators.