Sympletic Tracking Methods For Insertion Devices: A Robinson Wiggler Example

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Modern synchrotron mild sources are sometimes characterized with excessive-brightness synchrotron radiation from insertion units. Inevitably, ItagPro insertion units introduce nonlinear distortion to the beam movement. Symplectic tracking is essential to check the influence, particularly for the low- and iTagPro key finder medium-energy storage rings. This paper uses a Robinson wiggler for iTagPro key finder instance for example an universally relevant analytical illustration of the magnetic subject and to summarizes four completely different symplectic tracking strategies. With the goal of excessive-brightness synchrotron radiation, the storage rings of trendy synchrotron mild sources largely undertake strong-focusing lattices, which result in giant detrimental natural chromaticities and want robust sextupoles to correct the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam movement by sturdy sextupole fields. Furthermore, insertion units, fringe fields and imperfections of magnets are extra sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-term beam stability and has sturdy influence on operational efficiency.



The analysis of lengthy-time period beam dynamics in the storage ring is established by symplectic particle monitoring. Usually, symplectic tracking might be divided into two steps. First, an accurate analytical expression of magnetic field is needed. Second, the symplectic integration to unravel the Hamiltonian equations of the particle’s motion contained in the magnetic area is carried out stepwise factor by ingredient for multiple turns. Unlike the Runge-Kutta integration which is normally not sympletic and may introduce synthetic damping and antidamping effect, iTagPro key finder sympletic integration results in the canonical transformation of part area vector and satisfies Liouville’s theorem. In tracking codes the effect of dipoles and multipoles are normally modeled with an impulse boundary approximation, also known as laborious-edge model, through which the magnetic field is assumed to be constant inside the effective boundary of the magnet and iTagPro key finder zero outside. On this mannequin, iTagPro smart tracker solely the longitudinal component of the vector potential is required to explain the system.



It consists of a series of 12 mixed-perform magnets, proven in Fig. 1, with the purpose to lengthen the bunch by transferring the longitudinal damping to transverse airplane. As proven in Fig. 2, the magnetic discipline within the RW is three-dimensional (3D), horizontally asymmetric and iTagPro online way more complicated than the impulse boundary mannequin, thus the splitting methods for dipoles and multipoles will not be relevant any more. In this paper, the principle of the RW and the necessity of symplectic tracking is briefly launched in section II. Then in section III the essential concepts for symplectic integration are revisited. In section IV an analytical illustration is proposed to explain the 3D field in the RW precisely. On this foundation, three sympletic integration strategies are introduced to solve the Hamiltonian equations of movement for electrons in section V. In section VI, a monomial map approach impartial of analytic expression of the magnetic discipline is launched to realize sooner 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 iTagPro support operated and iTagPro device designed by the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB). The MLS is operated in decay mode. 6 hours at a hundred and fifty mA and therefor requires 2-3 injections per day. Each injection interrupts the consumer operation for iTagPro key finder roughly half-hour and affects the users’ experiments for one more nearly 1 hour attributable to thermal load changes on the components of optical beamlines after the injection. 12 hours at 150 mA due to 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 iTagPro key finder needs to be verified with symplectic monitoring. The problem studied on this paper is the movement of a particle moving by way of a static magnetic area with a straight reference trajectory.