A generalization of the Froissart-Stora formula to piecewise-linear spin-orbit resonance crossings
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915891108642816 |
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| author | Devlin, Joseph P. Hoffstaetter, Georg H. Barber, Desmond P. |
| author_facet | Devlin, Joseph P. Hoffstaetter, Georg H. Barber, Desmond P. |
| contents | Spin-polarized beams are important for some nuclear and high-energy physics experiments, such as those planned for the future Electron-Ion Collider (EIC). However, maintaining polarization during the acceleration of a charged-particle beam is difficult because the periodic nature of circular accelerators leads to spin-orbit resonances where the spin-precession frequency is a sum of integer multiples of the orbital frequencies. Usually, the dominant depolarization mechanisms are first-order spin-orbit resonances and the depolarization associated with crossing such a resonance can be computed using the Froissart-Stora formula. However, accelerating polarized hadron beams to high energy requires special magnet structures called Siberian snakes. When these are implemented to maintain a spin-precession frequency of one-half the revolution frequency, there will be no first-order spin-orbit resonance crossings. The dominant depolarization mechanisms are then higher-order spin-orbit resonances. The Froissart-Stora formula can be applied to higher-order resonances when the slope of the amplitude-dependent spin tune is constant. However, the slope of the amplitude-dependent spin tune often changes at the moment of resonance crossing. This work introduces a generalization of the Froissart-Stora formula which is applicable when the slope changes in this manner. The applicability of this formula is demonstrated through tracking simulations of a higher-order resonance crossing in both a toy model and the Relativistic Heavy Ion Collider (RHIC). It is additionally shown that the Froissart-Stora formula is mathematically equivalent to the Landau-Zener formula for the diabatic transition probability in two-level systems with a linearly increasing energy gap and constant coupling. This work therefore also extends the Landau-Zener formula to the case of changing slope. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24510 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A generalization of the Froissart-Stora formula to piecewise-linear spin-orbit resonance crossings Devlin, Joseph P. Hoffstaetter, Georg H. Barber, Desmond P. Accelerator Physics Spin-polarized beams are important for some nuclear and high-energy physics experiments, such as those planned for the future Electron-Ion Collider (EIC). However, maintaining polarization during the acceleration of a charged-particle beam is difficult because the periodic nature of circular accelerators leads to spin-orbit resonances where the spin-precession frequency is a sum of integer multiples of the orbital frequencies. Usually, the dominant depolarization mechanisms are first-order spin-orbit resonances and the depolarization associated with crossing such a resonance can be computed using the Froissart-Stora formula. However, accelerating polarized hadron beams to high energy requires special magnet structures called Siberian snakes. When these are implemented to maintain a spin-precession frequency of one-half the revolution frequency, there will be no first-order spin-orbit resonance crossings. The dominant depolarization mechanisms are then higher-order spin-orbit resonances. The Froissart-Stora formula can be applied to higher-order resonances when the slope of the amplitude-dependent spin tune is constant. However, the slope of the amplitude-dependent spin tune often changes at the moment of resonance crossing. This work introduces a generalization of the Froissart-Stora formula which is applicable when the slope changes in this manner. The applicability of this formula is demonstrated through tracking simulations of a higher-order resonance crossing in both a toy model and the Relativistic Heavy Ion Collider (RHIC). It is additionally shown that the Froissart-Stora formula is mathematically equivalent to the Landau-Zener formula for the diabatic transition probability in two-level systems with a linearly increasing energy gap and constant coupling. This work therefore also extends the Landau-Zener formula to the case of changing slope. |
| title | A generalization of the Froissart-Stora formula to piecewise-linear spin-orbit resonance crossings |
| topic | Accelerator Physics |
| url | https://arxiv.org/abs/2603.24510 |