Modern synchrotron light sources are sometimes characterized with high-brightness synchrotron radiation from insertion gadgets. Inevitably, insertion units introduce nonlinear distortion to the beam motion. Symplectic tracking is essential to check the impression, particularly for the low- and medium-vitality storage rings. This paper uses a Robinson wiggler for example to illustrate an universally relevant analytical representation of the magnetic subject and to summarizes four completely different symplectic monitoring strategies. With the intention of excessive-brightness synchrotron radiation, the storage rings of fashionable synchrotron mild sources largely adopt sturdy-focusing lattices, iTagPro locator which end in giant destructive pure chromaticities and need strong sextupoles to right the chromaticity to suppress the head-tail instability. Therefore nonlinear distortion is introduced to beam motion by sturdy sextupole fields. Furthermore, insertion units, fringe fields and imperfections of magnets are further sources of nonlinearity. The nonlinear distortion from the magnets determines lengthy-term beam stability and has sturdy impression on operational performance.

The evaluation of long-term beam dynamics within the storage ring is established by symplectic particle tracking. Typically, symplectic monitoring can be divided into two steps. First, an accurate analytical expression of magnetic subject is required. Second, the symplectic integration to resolve the Hamiltonian equations of the particle’s movement inside the magnetic field is conducted stepwise aspect by aspect for multiple turns. Unlike the Runge-Kutta integration which is usually not sympletic and may introduce synthetic damping and iTagPro locator antidamping effect, sympletic integration leads to the canonical transformation of phase area vector and iTagPro geofencing 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, by which the magnetic area is assumed to be fixed within the efficient boundary of the magnet and zero exterior. On this model, ItagPro solely the longitudinal component of the vector potential is required to describe the system.

It consists of a sequence of 12 mixed-perform magnets, proven in Fig. 1, with the intention to lengthen the bunch by transferring the longitudinal damping to transverse plane. As proven in Fig. 2, the magnetic field in the RW is three-dimensional (3D), horizontally asymmetric and far more difficult than the impulse boundary mannequin, thus the splitting methods for dipoles and multipoles aren't relevant any extra. On this paper, the precept of the RW and the necessity of symplectic tracking is briefly introduced in part II. Then in section III the basic concepts for iTagPro locator symplectic integration are revisited. In part IV an analytical illustration is proposed to explain the 3D area within the RW precisely. On this foundation, three sympletic integration strategies are introduced to unravel the Hamiltonian equations of movement for electrons in part V. In part VI, a monomial map method independent of analytic expression of the magnetic area is launched to appreciate quicker monitoring.

The strategies 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). The MLS is operated in decay mode. 6 hours at a hundred and fifty mA and therefor requires 2-three injections per day. Each injection interrupts the user operation for approximately 30 minutes and iTagPro locator affects the users’ experiments for one more almost 1 hour because of thermal load adjustments on the components of optical beamlines after the injection. 12 hours at 150 mA due to the increased bunch quantity. 0.355 m for one interval) insertion gadget to the stored beam within the low-vitality storage ring is of concern and should be verified with symplectic tracking. The issue studied on this paper is the motion of a particle transferring via a static magnetic subject with a straight reference trajectory.