Spin decoherence in electron storage rings

Barber, D. P.; Bogé, M.; Heinemann, K.; Mais, H.; Ripken, G.

doi:10.1063/1.48866

Cited by 11 publications

(26 citation statements)

References 7 publications

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“…in (6.21) are very small owing to the smoothness of the fields. See [24], p. 66, for a hint of how the Fourier coefficients come in here. We hope in the future to be able to present a rigorous treatment of this approximation.…”

Section: Discussionmentioning

confidence: 99%

“…We now construct, by the method pointed out in Remark 1 of Sec. II, a standard form for the principal solution matrix in order to compute Floquet parameters used in, or implied by, other treatments of spin motion on the closed orbit [15,24,39]. We first show that the matrix (2.6) exists and can be chosen to be 2-periodic in .…”

Section: Remarksmentioning

confidence: 99%

“…Note that if an ISF S exists, then an IFF V is easily constructed in analogy with the construction of V in Sec. III if there is a 2-periodic smooth unit vector which is nowhere parallel to S (see also [24]). However, if there is no such unit vector then it can happen that an IFF V with the third column S does not exist.…”

Section: The Invariant Spin Field and The Quasiperiodicity Of Thementioning

confidence: 99%

“…They are used in the program SPRINT for the numerical calculation of the spin tune [6,8,9,12,13,23,25]. If the IFF is uniform, then v 1 ; v 2 are called u 1 ; u 2 -axes (see also [22,24]). An example of a numerical calculation of u 1 ; u 2 -axes can be found in [13]; see also Sec.…”

Section: The Invariant Spin Field and The Quasiperiodicity Of Thementioning

confidence: 99%

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Quasiperiodic spin-orbit motion and spin tunes in storage rings

Barber

Ellison

Heinemann

2004

Phys. Rev. ST Accel. Beams

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We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters, and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchrobetatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case, too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchrobetatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g., where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ''measure'' spin tune during computer simulations of spin motion on synchrobetatron orbits.

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Section: Discussionmentioning

confidence: 99%

Section: Remarksmentioning

confidence: 99%

Section: The Invariant Spin Field and The Quasiperiodicity Of Thementioning

confidence: 99%

Section: The Invariant Spin Field and The Quasiperiodicity Of Thementioning

confidence: 99%

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Quasiperiodic spin-orbit motion and spin tunes in storage rings

Barber

Ellison

Heinemann

2004

Phys. Rev. ST Accel. Beams

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“…This invariant spin field vector is again determined by the adiabatic motion of the initially parallel spin vector. Spin vectors that are non-parallel to n( z, θ) precess uniformly around n( z, θ) [4,9,10]. The spin tune ν sp is the number of spin precessions per revolution of particles in the ring around n in this orthonormal coordinate system.…”

Section: Spin Tune Calculationmentioning

confidence: 99%

Spin resonance crossing in the Relativistic Heavy Ion Collider (RHIC)

Lehrach

Luccio²,

MacKay³

et al.

PACS2001. Proceedings of the 2001 Particle Accelerator Conference (Cat. No.01CH37268)

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In a high energy accelerator the polarization distribution of the beam can vary substantially across the beam. This decreases the amount of beam polarization provided to experiments. A method has been developed to calculate the beam polarization distribution based on adiabatic particle and spin excitation by inducing coherent betatron oscillations using an ac dipole. In earlier studies we calculated the beam polarization distribution in Brookhaven's Relativistic Heavy Ion Collider (RHIC) at fixed energy to compare spin motion on and away from strong spin resonances [1]. In this paper we present calculations of the beam polarization distribution during spin resonances crossing in RHIC. Furthermore beam polarization losses during spin resonance crossing for different vertical beam emittances have been studied.

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