2026/03/25 by Anonymous, Joseph P. Devlin, Georg H. Hoffstaetter +1
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #physics.acc-ph
paper · pdf · doi:10.1103/sxkc-zrh5
openalex publication_date 2026/06/10 · openalex created_date 2026/06/11 · openalex updated_date 2026/07/30
Spin-polarized beams are important for some nuclear and high-energy physics experiments, such as those planned for the future Electron-Ion Collider. 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 (ADST) is constant. However, the slope of the ADST 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. 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.