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| URL | https://doi.org/10.18429/JACoW-NAPAC2025-TUP046 |
|---|---|
| Title | Fast spin tracking using a Magnus expansion |
| Authors |
|
| Abstract | Spin motion in particle accelerators obeys the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation. Due to the structure of the T-BMT equation, the spin-transfer quaternion of a magnet is generally a nonlinear function of the entrance coordinates even if the phase-space motion is linear. This nonlinear function can be written as a Dyson expansion, for example as employed in the program SPRINT, which normalized the first-order expansion of the spin-transfer quaternion. Alternatively, this nonlinear function can be written as a Magnus expansion. This paper points out that in cases where the phase-space coordinates change little, as is generally the case for accelerator elements, the Magnus expansion is a much more appropriate method to describe the nonlinear spin motion because this expansion terminates after the first term when the phase-space coordinates are constant. We will demonstrate, with several examples, that an approximation based on the Magnus expansion leads to very good agreement with time-consuming numerical integration, and to significantly better agreement than obtained with historical codes like SPRINT. |
| Paper | download: TUP046.pdf |
| Cite | BibTeX, LaTeX, Text/Word, RIS, EndNote |
| Conference | 6th North American Particle Accel. Conf. (NAPAC2025) |
| Series | |
| Location | Sacramento, CA, USA |
| Date | 10-15 Aug 2025 |
| Publisher | JACoW Publishing, Geneva, Switzerland |
| Editorial Board | Tor O. Raubenheimer (SLAC), Roark A. Marsh (LLNL), Eric Prebys (UC Davis), Ling Wang (MSU), Petr M. Anisimov (LANL), Kip Bishofberger (LANL), Gustavo Bruno (ANL), Zhichu Chen (SARI), Jan Chrin (PSI), Kelly Jaje (ANL), Jaeyu Lee (POSTECH), Magdalena Montes-Loera (SLAC), Mary Saethre (PHENOTYPE), Tasha Summers (SLAC), Kent Wootton (ANL) |
| Online ISBN | 978-3-95450-261-5 |
| Online ISSN | 2673-7000 |
| Received | 06 August 2025 |
| Revised | 11 August 2025 |
| Accepted | 11 August 2025 |
| Issued | 28 January 2026 |
| DOI | 10.18429/JACoW-NAPAC2025-TUP046 |
| Pages | 457-460 |
| Copyright | Published by JACoW Publishing under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s), the published article's title, publisher, and DOI. |