Symplectic orbit and spin tracking code for all-electric storage rings

• Main Authors: Richard M. Talman, John D. Talman
• Format: Article
• Language: English
• Published: American Physical Society 2015-07-01
• Series: Physical Review Special Topics. Accelerators and Beams
• Online Access: http://doi.org/10.1103/PhysRevSTAB.18.074003

Proposed methods for measuring the electric dipole moment (EDM) of the proton use an intense, polarized proton beam stored in an all-electric storage ring “trap.” At the “magic” kinetic energy of 232.792 MeV, proton spins are “frozen,” for example always parallel to the instantaneous particle momentum. Energy deviation from the magic value causes in-plane precession of the spin relative to the momentum. Any nonzero EDM value will cause out-of-plane precession—measuring this precession is the basis for the EDM determination. A proposed implementation of this measurement shows that a proton EDM value of 10^{-29}e-cm or greater will produce a statistically significant, measurable precession after multiply repeated runs, assuming small beam depolarization during 1000 s runs, with high enough precision to test models of the early universe developed to account for the present day particle/antiparticle population imbalance. This paper describes an accelerator simulation code, eteapot, a new component of the Unified Accelerator Libraries (ual), to be used for long term tracking of particle orbits and spins in electric bend accelerators, in order to simulate EDM storage ring experiments. Though qualitatively much like magnetic rings, the nonconstant particle velocity in electric rings gives them significantly different properties, especially in weak focusing rings. Like the earlier code teapot (for magnetic ring simulation) this code performs exact tracking in an idealized (approximate) lattice rather than the more conventional approach, which is approximate tracking in a more nearly exact lattice. The Bargmann-Michel-Telegdi (BMT) equation describing the evolution of spin vectors through idealized bend elements is also solved exactly—original to this paper. Furthermore the idealization permits the code to be exactly symplectic (with no artificial “symplectification”). Any residual spurious damping or antidamping is sufficiently small to permit reliable tracking for the long times, such as the 1000 s assumed in estimating the achievable EDM precision. This paper documents in detail the theoretical formulation implemented in eteapot. An accompanying paper describes the practical application of the eteapot code in the Universal Accelerator Libraries (ual) environment to “resurrect,” or reverse engineer, the “AGS-analog” all-electric ring built at Brookhaven National Laboratory in 1954. Of the (very few) all-electric rings ever commissioned, the AGS-analog ring is the only relativistic one and is the closest to what is needed for measuring proton (or, even more so, electron) EDM’s. The companion paper also describes preliminary lattice studies for the planned proton EDM storage rings as well as testing the code for long time orbit and spin tracking.