Sympletic Tracking Methods For Insertion Devices: A Robinson Wiggler Example

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Modern synchrotron light sources are sometimes characterized with high-brightness synchrotron radiation from insertion gadgets. Inevitably, insertion devices introduce nonlinear distortion to the beam movement. Symplectic tracking is essential to review the influence, particularly for the low- and medium-energy storage rings. This paper uses a Robinson wiggler as an example to illustrate an universally relevant analytical illustration of the magnetic field and to summarizes 4 completely different symplectic monitoring strategies. With the intention of high-brightness synchrotron radiation, the storage rings of fashionable synchrotron gentle sources principally undertake robust-focusing lattices, which lead to giant detrimental pure chromaticities and need robust sextupoles to correct the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam motion by strong sextupole fields. Furthermore, insertion gadgets, fringe fields and imperfections of magnets are further sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-time period beam stability and has sturdy influence on operational performance.



The analysis of lengthy-term beam dynamics in the storage ring is established by symplectic particle monitoring. Typically, symplectic tracking will be divided into two steps. First, an accurate analytical expression of magnetic discipline is needed. Second, the symplectic integration to resolve the Hamiltonian equations of the particle’s motion contained in the magnetic discipline is carried out stepwise component by ingredient for a number of turns. Unlike the Runge-Kutta integration which is usually not sympletic and will introduce synthetic damping and antidamping impact, sympletic integration results in the canonical transformation of phase area vector and iTagPro device satisfies Liouville’s theorem. In tracking codes the effect of dipoles and multipoles are usually modeled with an impulse boundary approximation, additionally known as exhausting-edge model, in which the magnetic area is assumed to be fixed throughout the efficient boundary of the magnet and zero exterior. In this mannequin, only the longitudinal part of the vector potential is needed to explain the system.



It consists of a series of 12 combined-perform magnets, proven in Fig. 1, with the aim to lengthen the bunch by transferring the longitudinal damping to transverse plane. As shown in Fig. 2, iTagPro online the magnetic area within the RW is three-dimensional (3D), horizontally asymmetric and way more difficult than the impulse boundary model, thus the splitting strategies for dipoles and multipoles are usually not applicable any more. On this paper, the precept of the RW and the necessity of symplectic tracking is briefly introduced in section II. Then in part III the fundamental ideas for symplectic integration are revisited. In part IV an analytical illustration is proposed to explain the 3D field in the RW accurately. On this basis, iTagPro portable three sympletic integration methods are introduced to unravel the Hamiltonian equations of motion for iTagPro tracker electrons in section V. In section VI, itagpro tracker a monomial map approach impartial of analytic expression of the magnetic subject is launched to understand quicker monitoring.



The strategies on this paper are universally applicable 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 one hundred fifty mA and therefor requires 2-3 injections per day. Each injection interrupts the user operation for ItagPro approximately 30 minutes and affects the users’ experiments for another almost 1 hour due to thermal load modifications on the elements of optical beamlines after the injection. 12 hours at a hundred and fifty mA because of the increased bunch volume. 0.355 m for one period) insertion device to the stored beam within the low-power storage ring is of concern and wireless item locator needs to be verified with symplectic monitoring. The problem studied in this paper is the movement of a particle moving by a static magnetic discipline with a straight reference trajectory.

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