Sympletic Tracking Methods for Insertion Devices: A Robinson Wiggler Example > 자유게시판

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Modern synchrotron light sources are sometimes characterized with high-brightness synchrotron radiation from insertion devices. Inevitably, insertion devices introduce nonlinear distortion to the beam movement. Symplectic monitoring is essential to check the impression, ItagPro especially for the low- and medium-vitality storage rings. This paper makes use of a Robinson wiggler as an example as an example an universally relevant analytical representation of the magnetic area and to summarizes four totally different symplectic monitoring methods. With the aim of excessive-brightness synchrotron radiation, the storage rings of modern synchrotron mild sources mostly undertake robust-focusing lattices, which lead to giant detrimental natural chromaticities and need strong sextupoles to right the chromaticity to suppress the head-tail instability. Therefore nonlinear distortion is introduced to beam motion by strong sextupole fields. Furthermore, insertion devices, 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 affect on operational performance.

The evaluation of lengthy-term beam dynamics in the storage ring is established by symplectic particle tracking. Basically, symplectic tracking may be divided into two steps. First, ItagPro an correct 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 conducted stepwise ingredient by element for ItagPro multiple turns. Unlike the Runge-Kutta integration which is usually not sympletic and will introduce synthetic damping and antidamping impact, sympletic integration leads to the canonical transformation of phase space vector and satisfies Liouville’s theorem. In tracking codes the impact of dipoles and multipoles are normally modeled with an impulse boundary approximation, additionally known as arduous-edge mannequin, during which the magnetic field is assumed to be fixed throughout the efficient boundary of the magnet and zero exterior. In this mannequin, solely the longitudinal element of the vector potential is needed to explain the system.

It consists of a series of 12 mixed-function magnets, shown in Fig. 1, with the goal to lengthen the bunch by transferring the longitudinal damping to transverse airplane. As shown in Fig. 2, the magnetic field in the RW is three-dimensional (3D), horizontally asymmetric and far more difficult than the impulse boundary model, thus the splitting strategies for ItagPro dipoles and multipoles will not be relevant any more. On this paper, the principle of the RW and the necessity of symplectic tracking is briefly introduced in section II. Then in section III the basic concepts for symplectic integration are revisited. In part IV an analytical illustration is proposed to describe the 3D field in the RW accurately. On this basis, three sympletic integration methods are launched to unravel the Hamiltonian equations of motion for electrons in part V. In part VI, a monomial map strategy independent of analytic expression of the magnetic area is introduced to appreciate quicker monitoring.

The methods 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 150 mA and therefor requires 2-three injections per day. Each injection interrupts the consumer operation for iTagPro USA approximately half-hour and affects the users’ experiments for another almost 1 hour resulting from thermal load changes on the elements of optical beamlines after the injection. 12 hours at a hundred and fifty mA due to the increased bunch quantity. 0.355 m for ItagPro one interval) insertion system to the saved beam within the low-vitality storage ring is of concern and needs to be verified with symplectic monitoring. The problem studied in this paper is the movement of a particle shifting via a static magnetic subject with a straight reference trajectory.