Development of a Stepwise Ray-tracing Based On-line Model at Ags

A model of the Alternating Gradient Synchrotron is being developed based on stepwise ray-tracing numerical tools. It provides a realistic representation of the lattice, and accounts for the two helical partial Siberian snake insertions. The aim is to make this stepwise ray-tracing based model an aid for the understanding of the AGS, in matter of both beam dynamics and polarization transmission. INTRODUCTION A model of the Alternating Gradient Synchrotron lattice including the two siberian snakes [?] is being developed, based on the use of the stepwise ray-tracing code Zgoubi [?]. There are several reasons for opting for stepwise integration method, amongst the many possible ways of tracking in an accelerator: a lattice based on combined function dipoles featuring quadrupole and sextupole components, fringe fields possibly, presence of the snakes, with helical magnetic structures requiring dedicated modelling means, interest of the method for its inherent accuracy in the modelling of magnetic fields, including possible extensive (if not exclusive) use of measured or OPERAtype field maps in representing the main dipoles. On the other hand, the method has proven to be effective in difficult exercises, including highly non-linear ring optics [?] and spin dynamics in presence of snakes [?, ?]. The ultimate goal in modelling the AGS is to work at getting the best understanding of the machine optics, which will help maximize the preservation of the polarization during the acceleration of the polarized protons for injection into RHIC. It is believed in particular that stepwise integration methods offer best possible accuracy on computation of spin motion in magnetic field models. A first Section presents the ingredients on which modelling of AGS lattice in the ray-tracing code Zgoubi is based. A second Section shows the effectiveness of the method by illustrating it via beam and spin dynamics. Comparisons with the MAD model of AGS are performed wherever useful. MODELLING OF THE AGS Reference Line (OCO) A reference line, “OCO” (Optimum Closed Orbit), has been defined in the AGS, Fig. ?? [?]. The OCO coincides with the closed orbit in the straight sections between the Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. Figure 1: OCO line in the AGS, the reference optical axis. Table 1: Angles, Equivalent Quadrupole Shift and Typical Strengths (Values at Injection, Here) Entering in the Definition of an “OCO Line” in Zgoubi. θ/2 ∆x K1 K2 arc length (mrad) (cm) (10m) (10m) (m) BF 11.751 23.17 5.0828 5.0563 2.006646 CD 13.982 -24.07 -5.0760 4.3783 2.387677 AF “ 23.00 5.0689 4.3617 2.387678 BD 11.751 -23.93 -5.0793 5.0017 2.006595 CF 13.982 23.00 5.0757 4.4226 2.387678 AD “ -24.07 -5.0702 4.3048 2.387677 240 main dipoles. In the dipoles themselves, the OCO coincides with the chord of the arc of trajectory, it is localized by its distance to the socket line (the survey line). OCO coincides with the optical axis of all elements placed in the drifts, as tuning quads, sextupoles, control instrumentation, etc. The model of AGS dipoles and lattice in Zgoubi sticks to these principles, as shown in the next Section: the closed orbit in Zgoubi coincides with the OCO line, all lenses introduced further in the lattice are by default (i.e., in the absence of explicit request for a different alignment) centered on that line.