F. Meot

The ray-tracing code Zgoubi

Abstract The ray-tracing code Zgoubi computes particle trajectories in arbitrary magnetic and/or electric field maps or analytical models. The code is a genuine compendium of numerical recipes for simulation of most types of optical elements encountered in beam optics. It contains a built-in fit procedure, synchrotron radiation calculation, spin tracking, many Monte Carlo processes, etc. The high accuracy of the integration method allows efficient multiturn tracking in periodic machines.

Principles of the non-linear tuning of beam expanders

Abstract It is now common to consider employing non-linear multipole lenses to achieve transverse uniformization of particle beams used for the irradiation of extended targets in high intensity linac installations. In a previous report [F. Meot and T. Aniel, On beam uniformization by non-linear optics, Internal report CEA/DSM/GECA/GT/95-05, CEA Saclay, July 1995] we gave an analytical treatment of the uniformization of transverse beam densities by an octupole lens, in terms of the transport of random variables and their probability density functions, in the frame of a very basic optical scheme built up to two straight sections on both sides of the non-linear lens, following a pioneering work [P.F. Meads, A nonlinear lens system to smooth the intensity distribution of a Gaussian beam, IEEE Trans. Nucl. Sci. NS- 30 (1983)]. In the present paper, we extend the method to the more realistic configuration where the non-linear lens is preceded and followed by regular first order imaging optics, which leads to analytical expressions that provide the tuning of the non-linear lens w.r.t. the dimensions and nominal uniformization of the extended beam footprint at the target. This formalism is finally applied to the computation of the particle populations in the transverse tail distributions.

Optics design and performance of LESB3, a two-stage separated 800-MeV/c kaon beamline

Abstract The optics design and the measured performance are described for LESB3, the 800-MeV/ c kaon beamline at the Brookhaven AGS used by E787 to search for rare K + decays. The beamline provides a flux of ∼5×10 5 K + /10 12 protons on target, with a K/π ratio of >3.

A numerical method for combined spin tracking and ray tracing of charged particles

A numerical method for the resolution of the differential equation S′ = S × ω that governs the spin motion of a particle in a magnetic field is presented. This method has been straightforwardly implemented in the ray-tracing program Zgoubi which solves in a similar way the equation of motion of the particle, u′ = u × b. This is illustrated by several examples: a comparison with analytical calculations in a long quadrupole; the calculation of spin transfer matrices of some classical optical elements; the depolarization in the QDD spectrometer SPES 2 of Saclay, and finally a study of the depolarization near the resonance γG = νz in the synchrotron Saturne 2. Provided with this new feature, Zgoubi proves to be well adapted to the study of such devices as siberian snakes and long beam lines, as well as for multiturn tracking of spin in the depolarizing processes of periodic machines.

Zgoubi users guide

Notice: This technical note has been authored by employees of Brookhaven Science Associates, LLC under Contract No. with the U.S. Department of Energy. The publisher by accepting the technical note for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this technical note, or allow others to do so, for United States Government purposes. USDOE Office of Science (SC) Collider Accelerator Department October 2012 F. Meot Zgoubi users guide BNL-98726-2012-TECH

On the effects of detector solenoids on n → 0 in RHIC and eRHIC

Two effects, in RHIC, from STAR solenoid and from a model of sPHENIX detector solenoid, are reviewed based on tracking simulations: a change in the stable spin precession direction ~n0 around the ring, and coupling. The method can be applied, mutatis mutandis, to eSTAR, sPHENIX and BeAST detector solenoids in Aand e-eRHIC. eRHIC Note 60 BNL C-AD

Design of a modified Halbach magnet for the CBETA Project

A modified Halbach magnet has been designed to be installed in the splitter/merger section of the CBETA project which is under construction at Cornell University. The splitter/merger of the CBETA consists of 4 beam lines and is shown in Fig. 1. Two of the functions of the splitter/merger lines are; first to match the beam parameters at the exit of the Energy Recovery Linac (ERL) to those at the entrance of the Fixed Field Alternating Gradient (FFAG) arc, and second to place the trajectories of the reference particles of the beam bunches at the entrance of the FFAG arc on specified trajectories as they determined by the beam optics of the FFAG arc. In this technical note we present results from the 2D and 3D electromagnetic analysis of the S4.BEN01 magnet which is one of the dipole magnets of the 150 MeV line of the splitter/merger. The present design of the S4.BEN01 magnet, is based on a modified Halbach-type permanent magnet. To justify our suggestion of using a Halbach type of magnet instead of an electromagnet for the S4.BEN01 magnet we devote an APPENDIX A in which we provide details on the design of an electromagnet for the S4.BEN01 magnet and in the section under conclusion will list the pros and cons of the two designs.

Re-visiting RHIC snakes: OPERA fields, n 0 dance

Tech. Note C-A/AP/590 BNL C-AD

Intrinsic resonances and AC-dipole simulations of 3He in the AGS Booster

Polarized He collisions are part of future RHIC physics programs and of the eRHIC project. The anomalous magnetic moment of He (G=-4.184) is roughly three times greater than that of protons (G=1.793), a polarized species that is already used at the Collider-Accelerator complex at BNL. Because of the higher anomolous magnetic moment and possibly injecting into the AGS at rigidities beyond 7 T · m, He may have to cross depolarizing intrinsic resonances while accelerating in the Booster. To overcome these strong intrinsic resonances we look to an AC-dipole, which will need to be installed in the Booster. An AC-dipole is a magnet that induces large betatron oscillations which forces the entire bunch to experience a stronger resonance and induce a spin flip of all particles. An artificial intrinsic resonance is created, with close proximity to the original intrinsic resonance, which requires simulations to gauge what magnet strength is required. Simulations have been performed using zgoubi regarding the resonances 0 + νy, 12− νy, and 6 + νy and show that the AC-dipole is effective at overcoming these resonances. Benefits of avoiding the 0 + νy and crossing the 12− νy and 6 + νy in the Booster presents the advantage of allowing injection above the 0 + νy in the AGS and minimizes the orbit distortions from the snakes.

RHIC Spin flipper, fast-sweep efficiency simulations

Polarization flip simulations have been performed during Ru n 17 in parallel to resuming spin flipper experiments in RHIC. They are reported here, including some guidance they brought. -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1