Abstract
Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.
Highlights
The origin of nucleon spin remains an enduring puzzle in nuclear physics [1], and elucidating this puzzle is the principal focus of polarized beam experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory [2,3,4]
The invariant spin field (ISF) places an important upper bound on the maximum attainable polarization of a stored beam [6,7], and a knowledge of the ISF and how it varies with the machine optics is essential to optimizing the beam polarization
Because we have found that the accuracy of the orbital data has a significant impact on the accuracy of the spin tracking, our code relies on first performing very accurate symplectic integration for the orbital motion
Summary
The origin of nucleon spin remains an enduring puzzle in nuclear physics [1], and elucidating this puzzle is the principal focus of polarized beam experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory [2,3,4]. The invariant spin field (ISF) places an important upper bound on the maximum attainable polarization of a stored beam [6,7], and a knowledge of the ISF and how it varies with the machine optics is essential to optimizing the beam polarization Another motivation for spin-orbit tracking simulations— especially of high accuracy—derives from proposals to use storage rings in searches for a permanent electric dipole moment (EDM) in protons and deuterons [8]. In the course of that work, it was discovered that even when using TEAPOT’s orbital integrators, the code had difficulties with spin convergence [30,31], especially in the neighborhood of a strong spin resonance Addressing this issue meant slowing down what were already numerically demanding spin tracking simulations.
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