Sympletic Tracking Methods For Insertion Devices: A Robinson Wiggler Example
Modern synchrotron light sources are sometimes characterized with excessive-brightness synchrotron radiation from insertion units. Inevitably, insertion units introduce nonlinear distortion to the beam motion. Symplectic tracking is essential to study the affect, particularly for the low- and medium-power storage rings. This paper makes use of a Robinson wiggler for example for instance an universally relevant analytical representation of the magnetic field and to summarizes 4 completely different symplectic tracking strategies. With the intention of high-brightness synchrotron radiation, pet gps alternative the storage rings of modern synchrotron mild sources mostly adopt sturdy-focusing lattices, which result in giant unfavourable pure chromaticities and need strong sextupoles to correct the chromaticity to suppress the top-tail instability. Therefore nonlinear distortion is introduced to beam motion by strong sextupole fields. Furthermore, insertion gadgets, 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 affect on operational performance.
The evaluation of lengthy-time period beam dynamics within the storage ring is established by symplectic particle monitoring. On the whole, symplectic tracking will be divided into two steps. First, an correct analytical expression of magnetic subject is needed. Second, the symplectic integration to unravel the Hamiltonian equations of the particle’s movement contained in the magnetic discipline is conducted stepwise component by element for multiple turns. Unlike the Runge-Kutta integration which is often not sympletic and ItagPro will introduce artificial damping and antidamping impact, sympletic integration leads to the canonical transformation of phase area vector and satisfies Liouville’s theorem. In tracking codes the effect of dipoles and pet gps alternative multipoles are often modeled with an impulse boundary approximation, additionally known as arduous-edge model, during which the magnetic field is assumed to be fixed throughout the effective boundary of the magnet and zero outside. On this model, only the longitudinal element of the vector ItagPro potential is required to explain the system.
It consists of a chain of 12 mixed-function magnets, shown in Fig. 1, with the purpose 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 much more sophisticated than the impulse boundary mannequin, thus the splitting methods for dipoles and multipoles should not applicable any more. In this paper, the principle of the RW and the necessity of symplectic tracking is briefly introduced in section II. Then in part III the basic ideas for symplectic integration are revisited. In section IV an analytical representation is proposed to explain the 3D discipline in the RW accurately. On this basis, three sympletic integration methods are introduced to unravel the Hamiltonian equations of motion for electrons in section V. In part VI, iTagPro smart tracker a monomial map strategy unbiased of analytic expression of the magnetic subject is launched to appreciate sooner monitoring.
The strategies in this paper are universally relevant to all wigglers and ItagPro 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 one hundred fifty mA and therefor requires 2-3 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 consequence of thermal load adjustments on the components of optical beamlines after the injection. 12 hours at 150 mA because of the elevated bunch quantity. 0.355 m for one period) insertion system to the saved beam in the low-power storage ring is of concern and ought to be verified with symplectic monitoring. The problem studied on this paper is the movement of a particle moving via a static magnetic discipline with a straight reference trajectory.