New aspects of longitudinal instabilities in electron storage rings

www.nature.com/scientificreports OPEN Received: 23 February 2018 Accepted: 26 July 2018 Published: xx xx xxxx New aspects of longitudinal instabilities in electron storage rings A. Blednykh1, B. Bacha1, G. Bassi1, W. Cheng1, O. Chubar1, A. Derbenev1, R. Lindberg2, M. Rakitin1, V. Smaluk1, M. Zhernenkov 1, Yu-chen Karen Chen-Wiegart3,1 & L. Wiegart1 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. Successful construction, commissioning and operation of several ultra-low emittance storage rings have had a decisive impact on the development direction of future synchrotron light source facilities. For example, PETRA-III, NSLS-II, and, recently, MAX-IV, have all demonstrated reliable operation with a horizontal electron beam emittance equal to or smaller than 1 nm-rad1–3. While these and the new generation of storage ring light sources such as the ESRF-EBS4, APS-U5, ALS-U6 and Sirius7 significantly reduce the horizontal emittance, they do not offer any improvement of another important part of the full 6-dimensional electron beam emittance, namely, the energy spread. The electron beam energy spread can limit the peak harmonic flux from undulators, particularly at the high harmonics that are extensively used in medium-energy storage rings. In addition, the energy spread affects the angular divergence of the emitted radiation, and may ultimately limit the x-ray brightness in future ultra-low-emittance storage ring based light sources. Therefore, it is important to have a detailed understanding of what determines the electron beam energy spread in storage ring facilities under a variety of operating conditions. The energy spread of a low-current electron beam in a storage ring is determined by the equilibrium between radiation damping and quantum fluctuations8. As the beam current increases, the intra-bunch particle interaction via short-range wakefields induced by the beam in a vacuum chamber modifies the longitudinal particle distribution as a function of the beam intensity (see, e.g.9,10). The energy spread is not changed by the collective effects if the beam intensity is low enough, but the longitudinal microwave instability occurs above a certain threshold current and results in the energy spread growth and in the beam brightness degradation. This instability typically manifests itself as a high-frequency perturbation of the beam that increases both the energy spread and bunch length until a new quasi-equilibrium state is established. One of the goals of a storage ring design is to keep the instability threshold above the operating current. In this paper, we study the onset of the microwave instability and its behavior well above the threshold current using precise measurements at the NSLS-II storage ring11. Our measurements show that the energy spread growth is not monotonic with the beam current, but rather is characterized by a number of local minima and maxima. In addition, spectral analysis of the beam motion show that as the energy spread goes through a local minimum, the oscillation frequency of the perturbation changes almost discontinuously by a value comparable to the 1 Brookhaven National Laboratory, Upton, NY, 11973, USA. 2Advanced Photon Source, Argonne National Laboratory, Argonne, IL, 60439, USA. 3Department of Materials Science and Chemical Engineering, Stony Brook University, Stony Brook, NY, 11794, USA. Correspondence and requests for materials should be addressed to A.B. (email: ) Scientific REPOrTS | (2018) 8:11918 | DOI:10.1038/s41598-018-30306-y 1 www.nature.com/scientificreports/ Figure 1. Horizontal beam size measured by the SLM and the measured FWHM of the SMI IVU spectrum at the 7th harmonic. These measurements have been done with VRF = 2.6 MV for the bare lattice. synchrotron frequency. Thus, we find evidence for the higher-order instability thresholds, and observe this general phenomenology over a wide range of accelerating radio frequency (RF) voltages and electron bunch lengths. We then reproduce the energy spread growth and spectral features with the simulation code SPACE12, and finally compare the measurements and simulations to a recently developed theory extending Sacherer’s13,14 insights to interpret these microwave instability thresholds in terms of a succession of classical mode coupling. We find that the predictions based on the mode coupling theory are quite successful and appear to provide a useful way for better understanding of the microwave instability over a wide range of beam parameters. The main results of this paper hinge upon experimental data for the energy spread σδ as a function of single-bunch current I0 in the NSLS-II storage ring, where δ = (E − E0)/E0 is the relative energy deviation with respect to the reference energy E0, and I0 = Q/T0, where Q is the bunch charge and T0 is the revolution period. Two independent diagnostic methods have been applied to measure the current-dependent energy spread σδ(I0)15,16. The first method is based on measurements of horizontal beam profile using a synchrotron light monitor (SLM) installed in a low-dispersion area17, where the energy spread σδ is related to the horizontal beam size σx as18: σδ(I0) = σx2(I0) − βxεx /ηx , (1) where εx is the horizontal emittance; βx and ηx are, respectively, the horizontal beta function and dispersion in the bending magnet, in which the beam generates light detected by the SLM. In our case, βx = 2.77 m and ηx = 0.13 m. The second method is based on the measurement of photon energy spectrum from the in-vacuum undulator (IVU) of the Soft Matter Interfaces (SMI) X-ray beamline19. In addition to the energy spread measurements, spectra of the beam motion were also measured using a stripline, which is a part of NSLS-II bunch-by-bunch transverse feedback system20,21. This study of longitudinal beam dynamics in the spectral domain allows us to characterize the current-dependent behavior of the synchrotron frequency and its harmonics above the first threshold of microwave instability. N (...truncated)