Observation of a Second-Order Spin-Depolarizing Resonance

Ohmori, C.; Sato, Hikaru; Alexeeva, L. V.; Anferov, V. A.; Caussyn, D.D.; Chu, C. M.; Crandell, D. A.; Gladycheva, S. E.; Hu, S.-Q.; Krisch, A. D.; Phelps, R. A.; Varzar, S. M.; Wong, V. K.; Lee, S. Y.; Rinckel, T.; Schwandt, P.; Sperisen, F.; Stephenson, E. J.; Przewoski, B. von; Baiod, R.; Russell, A. D.

doi:10.1103/physrevlett.75.1931

Cited by 20 publications

(7 citation statements)

References 13 publications

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“…In fact, the resonances with j y = 2 are among the most destructive spin-orbit resonances in HERA-p after Siberian Snakes are included. For the IUCF cooler ring with a partial snake running, second-order resonances have been observed experimentally [33]. When a parameter τ is being varied, the spin motion is described in the coordinate system [ u 1 , u 2 , n] by Eq.…”

Section: The Froissart-stora Formula For Higher-order Resonancesmentioning

confidence: 99%

“…If (31) can be approximated well by a SRM, there is however a different and much less cumbersome method for determining the relevant resonance strength and the resonant frequency. Observation of the amplitudedependent spin tune ν( J ) allows the determination of all parameters which are required to evaluate the FroissartStora formula for higher-order resonances: The spin tune jumps by 2ǫ κ , the center of the jump is located at the frequency κ itself, and the rate of change of ν with changing energy is used to determine the parameter α for (33). In the SRM this parameter is ν0−κ θ where ν 0 is the frequency of spin rotations when the resonance strength vanishes.…”

Section: The Froissart-stora Formula For Higher-order Resonancesmentioning

confidence: 99%

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Strength of higher-order spin-orbit resonances

Hoffstaetter

Vogt²

2004

Phys. Rev. E

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When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel. This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies. When such resonance conditions are crossed, partial depolarization or spin flip can occur. The amount of polarization that survives after resonance crossing is a function of the resonance strength and the crossing speed. This function is commonly called the Froissart-Stora formula. It is very useful for predicting the amount of polarization after an acceleration cycle of a synchrotron or for computing the required speed of the acceleration cycle to maintain a required amount of polarization. However, the resonance strength could in general only be computed for first-order resonances and for synchrotron sidebands. When Siberian Snakes adjust the spin tune to be 1 2 , as is required for high energy accelerators, first-order resonances do not appear and higherorder resonances become dominant. Here we will introduce the strength of a higher-order spin-orbit resonance, and also present an efficient method of computing it. Several tracking examples will show that the so computed resonance strength can indeed be used in the Froissart-Stora formula. HERA-p is used for these examples which demonstrate that our results are very relevant for existing accelerators.

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Section: The Froissart-stora Formula For Higher-order Resonancesmentioning

confidence: 99%

Section: The Froissart-stora Formula For Higher-order Resonancesmentioning

confidence: 99%

Strength of higher-order spin-orbit resonances

Hoffstaetter

Vogt²

2004

Phys. Rev. E

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“…[42] However, because of their small spin resonance strength, depolarizing resonances due to sextupoles are not important as long as the betatron tunes are chosen to avoid the resonance condition, which for a spin tune of 1/2 is…”

Section: Sextupole Depolarizing Resonancesmentioning

confidence: 99%