skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Proton spin tracking with symplectic integration of orbit motion

Abstract

Symplectic integration had been adopted for orbital motion tracking in code SimTrack. SimTrack has been extensively used for dynamic aperture calculation with beam-beam interaction for the Relativistic Heavy Ion Collider (RHIC). Recently proton spin tracking has been implemented on top of symplectic orbital motion in this code. In this article, we will explain the implementation of spin motion based on Thomas-BMT equation, and the benchmarking with other spin tracking codes currently used for RHIC. Examples to calculate spin closed orbit and spin tunes are presented too.

Authors:
 [1];  [1];  [1];  [1];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1188263
Report Number(s):
BNL-107422-2015-CP
R&D Project: KBCH139; 18031; KB0202011; TRN: US1500259
DOE Contract Number:
SC00112704
Resource Type:
Conference
Resource Relation:
Conference: 6th International Particle Accelerator Conference (IPAC’15), Richmond, VA (United States), 3-8 May 2015
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BEAM DYNAMICS; S CODES; PROTONS; SPIN; BROOKHAVEN RHIC; ORBITS; APERTURES; BEAM-BEAM INTERACTIONS; BENCHMARKS; TUNING

Citation Formats

Luo, Y., Dutheil, Y., Huang, H., Meot, F., and Ranjbar, V. Proton spin tracking with symplectic integration of orbit motion. United States: N. p., 2015. Web.
Luo, Y., Dutheil, Y., Huang, H., Meot, F., & Ranjbar, V. Proton spin tracking with symplectic integration of orbit motion. United States.
Luo, Y., Dutheil, Y., Huang, H., Meot, F., and Ranjbar, V. Sun . "Proton spin tracking with symplectic integration of orbit motion". United States. doi:. https://www.osti.gov/servlets/purl/1188263.
@article{osti_1188263,
title = {Proton spin tracking with symplectic integration of orbit motion},
author = {Luo, Y. and Dutheil, Y. and Huang, H. and Meot, F. and Ranjbar, V.},
abstractNote = {Symplectic integration had been adopted for orbital motion tracking in code SimTrack. SimTrack has been extensively used for dynamic aperture calculation with beam-beam interaction for the Relativistic Heavy Ion Collider (RHIC). Recently proton spin tracking has been implemented on top of symplectic orbital motion in this code. In this article, we will explain the implementation of spin motion based on Thomas-BMT equation, and the benchmarking with other spin tracking codes currently used for RHIC. Examples to calculate spin closed orbit and spin tunes are presented too.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun May 03 00:00:00 EDT 2015},
month = {Sun May 03 00:00:00 EDT 2015}
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share:
  • Symplectic tracking with point magnets is achieved using a reference orbit made up of circular arcs and straight lines. For this choice of the reference orbit, results are given for the transfer functions, transfer matrices and the transit times of the magnets.
  • We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation δ m from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to η/δ m, where η is the electric dipole moment for an initially vertically polarized beam. As a result, the method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.
  • We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation δ m from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to η/δ m, where η is the electric dipole moment for an initially vertically polarized beam. As a result, the method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.
  • The use of nonsymplectic procedures in particle tracing codes for relativistic electrons leads to errors that can be reduced only at the expense of using very small integration steps. More accurate results are obtained with symplectic transformations for position and momentum. A first-order symplectic integration procedure requires an iterative calculation of the new position coordinates using the old momenta, but the process usually converges in three or four steps. A first-order symplectic algorithm has been coded for cylindrical as well as Cartesian coordinates using the relativistic equations of motion with Hamiltonian variables. The procedure is applied to the steering ofmore » a beam of 80-keV electrons by a weak transverse magnetic field superposed on a strong magnetic field in the axial direction. The steering motion is shown to be parallel to the transverse field rather than perpendicular as would be the case without the strong axial field.« less