New era of synchrotron radiation: fourth-generation storage ring

There had been remarkable progress in developing third-generation electron storage rings as the main sources of very bright photon beams. Fourth-generation storage rings based on the multi-bend achromat lattice concept may be able to surpass the brightness and coherence that are attained using present third-generation storage rings. In this paper, we survey ongoing work around the world to develop concepts and designs for fourth-generation electron storage rings.

Alpha-buckets in High Energy Electron Storage Rings (Review of Existing Experiments and Feasibility Studies for Future Developments)

Electron storage rings operating at high energies have proven to be invaluable source of synchrotron radiation. Two and even three simultaneous beams of particles have been observed at different light source facilities worldwide. So called alpha-buckets were studied at Metrological Light Source (MLS) in Berlin (Germany), SOLEIL facility in France, DIAMOND light source in UK, NSLS ring in Brookhaven (USA). It is widely recognized that alpha buckets are general phenomena which is not restricted to a certain storage ring. However, earlier measurements showed essential limitations on parameters of alpha-buckets, strong dependence on high order (sextupole and octupoles) magnetic field imperfections and associated fast decay of electron current as well as reduced life time. Also a rising relevance of high order non-linear longitudinal beam dynamics is associated with new generation of diffraction limited light sources (DLSR) approaches, which all suffer nonlinear momentum compaction factor. A large variety of future generation electron synchrotrons require a comprehensive investigation of the physical processes involved into the operation of such rings. In this paper, we present review of high order non-linear longitudinal beam dynamics based on the longitudinal equations of motion and Hamiltonian expanded to a high order of the momentum compaction factor. Roots of the third order equation with a free term are derived in a form suitable for analytical estimations. The momentum independent term of orbit lengthening due to particle transverse excursions is estimated and taken into account. The results from simulations were benchmarked against existing experiments at the Karlsruhe Research Accelerator (KARA), SOLEIL and MLS rings. Parameters of three simultaneous beams and alpha buckets at MLS and SOLEIL have been reproduced with high accuracy. General conditions for stable operation of alpha buckets are presented. Based on analytical formulas and computer simulations, studies of longitudinal motion at KARA have been performed with an objective to estimate feasibility of filling and storing of beam in α-buckets. A Computer model was used to describe the behavior and dynamics of simultaneous beams in the KARA storage ring.

Reevaluation of spin-orbit dynamics of polarized e+e− beams in high energy circular accelerators and storage rings: An approach based on a Bloch equation

We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev–Kondratenko formulas.

The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.