Microbunching instability (MBI) has been one of the most challenging issues in designs of high-brightness beam transport lines for single-pass or recirculating accelerators. Although the intrabeam scattering (IBS) has long been studied in lepton or hadron storage rings as a slow diffusion process or in high-intensity proton linear accelerators as one mechanism for the beam halo, the effects of IBS on single-pass or recirculating electron accelerators have drawn attention only in the recent two decades due to emergence of linac-based or energy-recovery-linac-based fourth-generation light sources, which require high-quality electron beams during the beam transport. In this paper we develop a theoretical formulation of microbunching instability in the presence of IBS for single-pass or recirculation accelerators. To quantify MBI with inclusion of IBS, we start from the Vlasov-Fokker-Planck (VFP) equation, combining both collective interactions and incoherent IBS effects. The linearized VFP equation and the corresponding friction and diffusion coefficients are derived. The evolutions of the resultant density and energy modulations are formulated as a set of coupled integral equations. The theoretical formulation is then applied to a recirculating beamline design. The results from the semianalytical calculation are compared and show good agreement with massive particle tracking simulations.

It has been known that a high-brightness electron beam emits broadband synchrotron radiation when traversing a curved orbit. The radiation reaction at wavelengths comparable to the bunch length or to the wavelength of a phase space modulated beam may lead to collective instabilities. In this paper, we investigate a potential single-pass instability mechanism of coherent-radiation-induced longitudinal multibunch beam breakup (BBU) instability in the presence of a closely spaced microbunch train in an undulator, particularly when the microbunch spacing is close to the resonant wavelength of the undulator. This problem is formulated based on the macroparticle model together with the slippage constraint on the beam-wave interaction. The set of coupled differential equations for individual microbunches can be solved analytically for the first few microbunches with linearization of the coherent radiation wakefield, and numerically in general nonlinear cases for unequal spacing or nonuniform filling charges. The underlying mechanisms, including the slippage effect, the potential-well effect leading to extra focusing, dependence of microbunch spacing and filling patterns, are discussed. The analysis is then applied to the recently proposed steady-state microbunching (SSMB) mechanism with two examples serving for the high average coherent radiation power sources for extreme ultraviolet (EUV) and infrared wavelength regions. For the specific scenario considered in this paper, it is found that when the microbunch spacing is close to the fundamental resonant wavelength, the coherent radiation can provide extra longitudinal focusing for the individual microbunches, leading to more stable multibunch oscillations. For the preliminary nominal SSMB designs with the average beam current of 1 A, our studies show that the single-pass longitudinal BBU instability should not be a severe issue.

Multibend magnetic bunch compressors are commonly used to produce beams with high peak current in modern accelerators that call for high-brightness beams. If not well controlled, the coherent synchrotron radiation (CSR) in the dipoles of magnetic bunch compressors can severely affect the produced beam qualities, e.g., leading to emittance dilution. In contrast to the case without bunch compression, suppression of the CSR-induced emittance growth with bunch compression can be more challenging mainly due to the difficulties of analyzing the net CSR effect that involves a varying bunch length. In this paper, with the aid of the CSR point-kick model, theoretical CSR cancelation conditions of a double-bend achromat (DBA) with bunch compression are obtained. Such conditions point to an asymmetric DBA design, having dipoles of different bending angles or different radii or both and satisfying a certain transfer matrix relation. Taking a DBA with dipoles of different bending angles as an example, it is demonstrated that the CSR-induced emittance growth can be significantly suppressed if the proposed conditions are satisfied. As a numerical demonstration of application, we implement multiple DBA cells basically satisfying the proposed conditions in a 180° arc compressor, showing promising performance in suppressing the CSR-induced emittance growth. This study suggests a new appealing way to design practical arc compressors and is promising to serve as a starting point for the design and optimization of CSR-immune arc transfer lines in energy recovery linacs and other modern recirculation accelerators.

In modern high-brightness electron accelerators, the goal of preserving the beam quality from the source has long been pursued to ensure the fulfillment of their scientific missions. However, when delivering the electron beam through a beam transfer line, which may consist of bending magnets, the performance of a high-brightness electron beam may be degraded by the coherent synchrotron radiation (CSR) and the residual longitudinal dispersion. It is of critical importance to preserve the transverse emittance and control the bunch length variation as well as maintain the longitudinal phase space distribution in such a beam transfer line. For a multipass beam transfer line, the achromatic cell designs with stable optics would bring great convenience. In this study, for the periodic stable symmetric triple-bend achromat designs with identical dipoles, it is discovered that the CSR-induced emittance growth and the longitudinal dispersion up to high orders can be minimized simultaneously when a certain transfer matrix relation is satisfied; to be specific, the matrix entries between the first two dipoles should follow $[m_{11},m_{21}({\mathrm{m}}^{-1})]\approx (-2,0)$. Numerical optimizations demonstrate that the normalized transverse emittance, the bunch length, and the longitudinal phase space distribution are well preserved. In addition, such a design strategy shows the potential merit of effectively mitigating the microbunching instability.

The study of collective beam instabilities has long been an important and active research topic in particle accelerators. The collective effects are typically divided into two categories: the short-range single-bunch instabilities and the long-range multibunch or multiturn instabilities. Robinson instability can be the mostly encountered long-range multiturn instability. We recently explored a collective multiturn instability driven by the short-range coherent undulator radiation in the laser cavity modulator of a steady-state microbunching (SSMB) storage ring. In this paper, we formulate and compare such an instability with the Robinson instability. Considering the radiation slippage effect and the finite duration, the functional form of the radiation wakes is essentially different from that of the Robinson case. We also relate a special case of the newly explored instability to the high-gain free-electron laser process and find that a similar cubic dispersion equation can be obtained. The discussions and comparisons presented in this paper may shed light on the underlying physical mechanisms of the collective beam dynamics in the laser cavity modulator of an SSMB storage ring.

The studies of incoherent single-particle and collective multi-particle effects are, in general, separated in accelerator beam dynamics in that the two dynamical phenomena involve quite different time scales. Recent experimental measurements indicate that in some parameter regime, the small-angle, multiple scattering effects within a high-brightness electron beam can have a strong influence on microbunched beam dynamics. In this paper, we apply our recently developed semi-analytical kinetic analysis to investigate the collective phase space microbunched dynamics in the presence of incoherent single-particle effects. Particular emphasis will be placed on evaluation of the intrinsic or slice energy spread. An example of two linear beam transport lines, followed by two identical, interleaving bunch compressor chicanes, is then presented. The semi-analytical calculations are consistent with particle tracking simulations. Moreover, the threshold condition is derived, indicating the relation among relevant physical quantities. At threshold, the incoherent effect can be beneficial for effective suppression of the collective microbunching instability. We expect that this work could shed light on high-brightness electron transport beamline design to improve short-wavelength free-electron laser performance.