Modern synchrotron gentle sources are sometimes characterized with excessive-brightness synchrotron radiation from insertion gadgets. Inevitably, insertion units introduce nonlinear distortion to the beam movement. Symplectic monitoring is crucial to review the impression, iTag Pro especially for the low- and medium-power storage rings. This paper uses a Robinson wiggler as an example as an example an universally applicable analytical representation of the magnetic area and to summarizes 4 completely different symplectic tracking strategies. With the purpose of excessive-brightness synchrotron radiation, the storage rings of fashionable synchrotron gentle sources largely adopt strong-focusing lattices, which lead to giant detrimental natural chromaticities and need robust sextupoles to appropriate the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam motion by robust sextupole fields. Furthermore, iTagPro Tracker insertion gadgets, fringe fields and iTag Pro imperfections of magnets are further sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-term beam stability and has sturdy affect on operational performance.
The evaluation of long-time period beam dynamics within the storage ring is established by symplectic particle tracking. Typically, symplectic tracking can be divided into two steps. First, an accurate analytical expression of magnetic field is required. Second, the symplectic integration to solve the Hamiltonian equations of the particle’s movement inside the magnetic field is performed stepwise component by element for a number of turns. Unlike the Runge-Kutta integration which is usually not sympletic and will introduce artificial damping and antidamping impact, iTag Pro sympletic integration results in the canonical transformation of section area vector iTag Pro and satisfies Liouville’s theorem. In monitoring codes the impact of dipoles and multipoles are usually modeled with an impulse boundary approximation, also called laborious-edge mannequin, by which the magnetic field is assumed to be fixed inside the efficient boundary of the magnet and zero outdoors. On this mannequin, iTagPro Item Finder only the longitudinal element of the vector potential is required to describe the system.
It consists of a series of 12 combined-operate magnets, shown in Fig. 1, with the purpose to lengthen the bunch by transferring the longitudinal damping to transverse plane. As shown in Fig. 2, the magnetic subject within the RW is three-dimensional (3D), horizontally asymmetric and way more difficult than the impulse boundary mannequin, thus the splitting strategies for dipoles and multipoles aren't applicable any more. In this paper, the principle of the RW and the necessity of symplectic monitoring is briefly launched in part II. Then in section III the essential ideas for symplectic integration are revisited. In section IV an analytical representation is proposed to explain the 3D area within the RW precisely. On this foundation, three sympletic integration methods are introduced to solve the Hamiltonian equations of movement for electrons in section V. In part VI, a monomial map approach independent of analytic expression of the magnetic discipline is introduced to appreciate sooner monitoring.
The strategies on this paper are universally relevant to all wigglers and undulators with a straight reference trajectory. The Metrology Light Source (MLS) is an electron storage ring owned by the Physikalisch-Technische Bundesanstalt (PTB) and operated and designed by the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB). The MLS is operated in decay mode. 6 hours at 150 mA and therefor requires 2-3 injections per day. Each injection interrupts the user operation for roughly 30 minutes and affects the users’ experiments for another nearly 1 hour resulting from thermal load changes on the components of optical beamlines after the injection.