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Sympletic Tracking Methods for Insertion Devices: A Robinson Wiggler Example
(image: https://canary.contestimg.wish.com/api/webimage/5fb37d952902320b24792b9c-large.jpg)Modern synchrotron mild sources are sometimes characterized with high-brightness synchrotron radiation from insertion units. Inevitably, insertion devices introduce nonlinear distortion to the beam movement. Symplectic monitoring is essential to review the affect, particularly for the low- and medium-energy storage rings. This paper uses a Robinson wiggler as an example as an instance an universally relevant analytical representation of the magnetic subject and to summarizes 4 totally different symplectic tracking methods. With the intention of excessive-brightness synchrotron radiation, the storage rings of modern synchrotron mild sources mostly adopt sturdy-focusing lattices, which lead to massive unfavorable natural chromaticities and want sturdy sextupoles to correct the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam motion by robust sextupole fields. Furthermore, iTagPro insertion units, fringe fields and imperfections of magnets are additional sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-time period beam stability and has robust impact on operational performance.
(image: https://s3.thehackerblog.com/findthatmeme/b1bc9930-76e7-4cee-b2f9-5029b57a2d0c.jpeg)The analysis of long-term beam dynamics in the storage ring is established by symplectic particle monitoring. Usually, symplectic monitoring may be divided into two steps. First, an accurate analytical expression of magnetic subject is required. Second, iTagPro Smart Tracker the symplectic integration to unravel the Hamiltonian equations of the particle’s motion contained in the magnetic subject is carried out stepwise factor by component for multiple turns. Unlike the Runge-Kutta integration which is normally not sympletic and should introduce synthetic damping and antidamping impact, sympletic integration leads to the canonical transformation of phase area vector and satisfies Liouville’s theorem. In tracking codes the impact of dipoles and multipoles are normally modeled with an impulse boundary approximation, also known as exhausting-edge model, wherein the magnetic subject is assumed to be fixed throughout the efficient boundary of the magnet and zero outdoors. On this model, solely the longitudinal element of the vector potential is required to describe the system.
(image: https://wiki.nptracker.co.za/images/d/dc/NPS-CLOUD_Dashboard.png)
It consists of a chain of 12 mixed-perform magnets, shown in Fig. 1, iTagPro Smart Tracker with the intention to lengthen the bunch by transferring the longitudinal damping to transverse plane. As shown in Fig. 2, the magnetic area within the RW is three-dimensional (3D), horizontally asymmetric and far more complicated than the impulse boundary model, thus the splitting methods for dipoles and multipoles usually are not relevant any more. On this paper, the principle of the RW and the necessity of symplectic tracking is briefly launched in part II. Then in part III the essential ideas for symplectic integration are revisited. In section IV an analytical representation is proposed to describe the 3D discipline within the RW accurately. On this foundation, three sympletic integration strategies are introduced to resolve the Hamiltonian equations of motion for electrons in part V. In section VI, a monomial map approach unbiased of analytic expression of the magnetic field is introduced to realize faster monitoring.
The methods in 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).
Website: https://ctpedia.org/index.php/ITag_Pro_-_A_Comprehensive_Overview
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