Study Of Nonlinear Dynamics Scaling Of Storage Rings With Superperiods

Increasing the brightness of synchrotron radiation at Hefei Light Source (HLS), a second-generation storage ring based synchrotron radiation light source in National Synchrotron Radiation Laboratory (NSRL), University of Science and Technology of China (USTC), is a very important accelerator physics and engineering task in NSRL. In this dissertation, several medium-emittance (with a horizontal natural emittance ex from 40 to 80 nmrad) and low-emittance (ex < 40 nmrad) lattices for the HLS storage ring are presented. First, two lattices, "w31" and "w32", based on the existing HLS storage ring hardware with a horizontal emittance approximately 60 nm-rad, nearly half that of the currently operating lattice, General Purpose Light Source (GPLS) lattice, are discussed. For these two medium-emittance lattices, a series of single particle dynamics studies have been carried out, including injection simulations, dynamic aperture computations, and closed orbit distortion (COD) calculations, etc. These studies show that it is possible to realize these two lattices on the HLS storage ring without physically changing or replacing any hardware. A 35 nm-rad emittance lattice with a non-zero eta-function in long straight sections, "w32u", is also developed to allow a smooth transition from w32 lattice. Using w32 lattice as the injection and energy ramping lattice, and transitioning w32 lattice to w32u lattice at the user operation energy 800 MeV, we can achieve the high-brightness operation of the HLS at 800 MeV while avoiding problems caused by the low electron beam energy at injection (200 MeV). To explore the brightness potential of the HLS, we also discuss the lowest emittance lattices that the HLS storage ring can achieve when hardware constraints are relaxed. W21 lattice, a 16.7 nm-rad lattice with eight double-bend achromat (DBA) superperiods, has been developed and studied. This lattice can be installed on the existing HLS storage ring foundation, but it will need a complete set of new storage ring hardware, including magnets, vacuum chambers, and diagnostic equipments, etc.Many modern light source storage rings use a magnetic structure consisting of a number of repetitive lattice cells, the superperiods. The study of one superperiod, the smallest unit of a periodic magnetic lattice, can reveal the dynamical proprieties of the storage ring with more clarity and with a much reduced computational effort. It is known that there exists a scaling law between the transverse dynamic aperture and the strength of magnetic multipoles such as quadrupole, sextupole, oc-tupole, etc. By using particle tracking and frequency analysis, beam dynamics of a typical triple-bend achromat (TBA) lattice, the ALS lattice, have been studied. The transverse dynamic aperture scaling with the strengths of sextupoles, octupoles, and decapoless is confirmed numerically to yield additional insight. Using the ALS superperiod to construct a series of ALS-like lattices with different numbers of superperiods, we have found a scaling relation between the dynamic aperture and the number of superperiods. This lattice scaling relation allows us to compare dynamics performance of different lattices for second- and third-generation light source storage rings.In the design of a light source storage ring lattice, inserting 2nir (n=integer) phase advances sections to a lattice while keeping linear function in the original lattice can be used to extend the lattice for more and/or longer insertion devices. Using the ALS lattice as an example, impacts on nonlinear beam dynamics brought about by additional 2nir phase advance sections are studied. Results show that these 2ri7r sections change the nonlinear characteristics in a certain predictable manner. A reduction of the transverse dynamic aperture is found as the result of the need of using stronger sextupoles to compensate for the additional chromatic effect induced by these 2mr sections. The reduction of transverse dynamic aperture with the number of 2mr sections inserted can be predicted if the horizontal and vertical chromaticities increase follow a certain relation.