title: Study and Optimisation of the nonlinear 6D dynamics of an electron beam in an ultra-low emittance storage ring
Creators: name: Hoummi, Lina
Publisher: name: University of Liverpool Repository
Year: 2021

description: Since the discovery of synchrotron radiation in 1947 and the first dedicated facilities, storage-ring-based light sources led to numerous discoveries and participated in the further advancement of sciences. To match the needs of researchers, they evolved drastically, increasing both their energies and their brilliance. The first chapter introduces synchrotron radiation and the main characteristics of synchrotrons. Today, the new challenge is the extremely brilliant sources, which aims at increasing the photon brilliance by at least a factor 100; various challenges arise in different disciplines, such as magnet designs and vacuum. To achieve such a high brilliance, fourth-generation storage-ring based light sources are designed to approach the diffraction limit of the photon source, by reducing their transverse emittances. As part of a global transition from third- to fourth- generation storage-ring-based light sources, the present thesis introduces, compares and analyses the effect of ultra-low emittance on the transverse and longitudinal dynamics of ultra-low emittance lattices, applied to the SOLEIL upgrade. Such a reduction of the natural horizontal emittance is achieved with the use of Multi-Bend Achromats (MBA) and strong focusing. Both are introduced in the second chapter, along with basic notions of accelerator physics. As strong focusing increases the natural chromaticities, ultra-low emittance lattices require strong sextupoles to correct them. Yet, they affect the stability and beam lifetime. The presence of strong sextupoles was integrated in the linear design, to minimise their effect on the lattice performances. Two specific MBA lattices are studied and compared in the present thesis. The first lattice is the ESRF-EBS-type MBA lattice, introducing a minus identity transformation to compensate the nonlinear impact of sextupoles thanks to the lattice symmetry and to a tight control of the betatron phase advance between sextupoles. The presence of two dispersion bumps maximises the efficiency of the sextupoles, further reducing their required strengths. The second scheme is the so-called High-Order Achromat (HOA) lattice. Ultra-low emittance lattices are being studied for the future upgrade of the SOLEIL 2.75 GeV storage ring. The targeted horizontal emittance of the new lattice is below 100 pm.rad, corresponding to a reduction of a factor 40 compared to the current lattice. Two 7BA lattices were designed, using either the hybrid or the HOA scheme, and a natural horizontal emittance of about 75 pm.rad was achieved with the inclusion of reverse bending magnets. Both schemes are compared in terms of magnets, strengths and number, and their bare transverse dynamics before any nonlinear optimisation. The effect of ultra-low emittance on the Touschek lifetime and Intra-Beam Scattering is finally studied on the hybrid lattice. Nonlinear optimisation of both schemes is achieved using the code MOGA-Bmad, which optimises the transverse dynamic apertures at three set energy deviations while maintaining constant chromaticities. Results are discussed in the fourth chapter, which also follows the evolution of lattice studies for the SOLEIL upgrade project: the lattices under study evolved from a 24- and 20-fold symmetry towards the maintenance of the beamlines' positions, which dropped the symmetry down to 4. The use of the HOA lattice proved more efficient and flexible to answer to the new implementation constraints. In terms of injection, since the strong focusing and the low β-functions cause the transverse dynamic apertures to be merely a few millimetres wide instead of 10-30 mm in the case of the current SOLEIL lattice, the current transverse off-axis injection scheme requires the inclusion of a high-β section in the ultra-low emittance lattices under study to locally increase the transverse acceptance. Another scheme injects the beam directly on-axis, but onto an off-momentum closed orbit thanks to a Multipole-Injector Kicker (MIK). To distinguish the closed orbits at the MIK, this scheme requires the insertion of a dispersion bump. In ultra-low emittance lattices, the increased number of dipoles and the use of reverse bending magnets ensure a low dispersion along the ring, which yields to a low zeroth-order momentum compaction factor. Some ultra-low emittance lattices, such as a 5BA lattice of 80 pm.rad natural horizontal emittance, have their first-order momentum compaction factor overtake the zeroth, which results in a perturbed longitudinal stability and an atrophied RF bucket. This yields to a reduced beam stability and lifetime. Analytical calculations of the three lowest orders in momentum compaction factor are conducted to describe the requirements of a minimisation of the first-order. Three methods developed to minimise this effect and restore the RF bucket are discussed in the fifth chapter. Among them, extension of MOGA-Bmad includes the minimisation of the first-order momentum compaction factor, while optimising the transverse on- and off-momentum dynamics. Although the hybrid scheme provides a large on-momentum transverse dynamic aperture in 4D thanks to the application of the non-interleaved principle on its sextupoles, its off-momentum performance is limited. Further studies in 6D reveal intrinsic off-momentum transverse oscillations, which are considered to result from of a nonlinear increase of the path length. The effect of the inhomogeneous sextupole distribution in the hybrid scheme is presented and compared with the HOA lattice under study, in the last chapter. The path length is described in terms of higher-order elements depending on the nonlinear magnets, using the first-order canonical perturbation theory.