Depolarisation d'un faisceau de protons polarises dans un synchrotron

Froissart, M.; Stora, R.

doi:10.1016/0029-554x(60)90033-1

Cited by 205 publications

(128 citation statements)

References 3 publications

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“…The method of solution depends on the form of the function ν 0 (θ) [1,16,17,21]. If the closed-orbit spin tune changes like ν 0 = κ + αθ, the equation of spin motion can be solved in terms of confluent hypergeometric functions.…”

Section: The Froissart-stora Formulamentioning

confidence: 99%

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 Formulamentioning

confidence: 99%

Strength of higher-order spin-orbit resonances

Hoffstaetter

Vogt²

2004

Phys. Rev. E

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“…Close to a resonance, the stable spin direction is perturbed away from the vertical direction by the resonance driving fields. When a polarized beam is accelerated through an isolated resonance, the final polarization can be calculated analytically [6] and is given by P f /P i = 2e − π| | 2 2α − 1, (1.6)…”

Section: Spin Dynamics and Siberian Snakesmentioning

confidence: 99%

Configuration Manual Polarized Proton Collider at RHIC

I.¹,

Allgower²,

Bai³

et al. 2006

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“…Spink can be used to check the strength of resonances calculated by Depol using the Froissart-Stora formula [5]. Conditions are that the resonances being studied are reasonably separated (say, ten times their width) and are not too strong.…”

Section: D Froissart-storamentioning

confidence: 99%

Numerical Spin Tracking in a Synchrotron Computer Code SPINK - Examples (RHIC)

Luccio¹

1995

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Depolarisation d'un faisceau de protons polarises dans un synchrotron

Cited by 205 publications

References 3 publications

Strength of higher-order spin-orbit resonances

Strength of higher-order spin-orbit resonances

Configuration Manual Polarized Proton Collider at RHIC

Numerical Spin Tracking in a Synchrotron Computer Code SPINK - Examples (RHIC)

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