Modern synchrotron light sources are sometimes characterized with high-brightness synchrotron radiation from insertion units. Inevitably, insertion devices introduce nonlinear distortion to the beam movement. Symplectic tracking is essential to check the impression, especially for iTagPro technology the low- and medium-power storage rings. This paper uses a Robinson wiggler for iTagPro bluetooth tracker instance to illustrate an universally applicable analytical representation of the magnetic area and to summarizes four totally different symplectic monitoring methods. With the purpose of high-brightness synchrotron radiation, the storage rings of trendy synchrotron mild sources principally adopt sturdy-focusing lattices, which lead to giant unfavorable natural chromaticities and need sturdy sextupoles to right the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam movement by strong sextupole fields. Furthermore, insertion gadgets, iTagPro bluetooth tracker fringe fields and imperfections of magnets are extra sources of nonlinearity. The nonlinear distortion from the magnets determines long-time period beam stability and has robust impression on operational efficiency.

The analysis of long-time period beam dynamics within the storage ring is established by symplectic particle tracking. Basically, symplectic tracking could be divided into two steps. First, an accurate analytical expression of magnetic field is needed. Second, portable tracking tag the symplectic integration to unravel the Hamiltonian equations of the particle’s motion inside the magnetic field is performed stepwise component by component for multiple turns. Unlike the Runge-Kutta integration which is often not sympletic and should introduce artificial damping and antidamping effect, sympletic integration results in the canonical transformation of part 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 hard-edge model, during which the magnetic area is assumed to be constant within the efficient boundary of the magnet and zero outdoors. In this model, only the longitudinal element of the vector potential is required to explain the system.

It consists of a series of 12 combined-operate magnets, shown in Fig. 1, with the aim to lengthen the bunch by transferring the longitudinal damping to transverse aircraft. As shown in Fig. 2, the magnetic discipline in the RW is three-dimensional (3D), horizontally asymmetric and rather more complicated than the impulse boundary model, thus the splitting methods for dipoles and multipoles should not applicable any extra. On this paper, the principle of the RW and the necessity of symplectic tracking is briefly launched in section II. Then in part III the fundamental ideas for symplectic integration are revisited. In section IV an analytical illustration is proposed to explain the 3D discipline in the RW accurately. 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 method unbiased of analytic expression of the magnetic discipline is introduced to appreciate faster monitoring.

The strategies on 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 ItagPro 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 half-hour and impacts the users’ experiments for an additional practically 1 hour as a result of thermal load changes on the elements of optical beamlines after the injection. 12 hours at 150 mA due to the increased bunch volume. 0.355 m for ItagPro one interval) insertion system to the stored beam within the low-energy storage ring is of concern and should be verified with symplectic tracking. The problem studied on this paper is the motion of a particle shifting by way of a static magnetic field with a straight reference trajectory.