Abstract
It has been predicted and found experimentally that the polarization direction of particles on the closed orbit of a circular accelerator can be manipulated, without a noticeable reduction of polarization, by means of a slow variation of magnetic fields. This feature has been used to avoid imperfection resonances where the spin precession frequency is close to a multiple of the circulation frequency. As a first step we show that this property is related to an adiabatic invariant of spin motion. The proof is relatively simple since it involves only two frequencies, the spin-rotation frequency and the particle's rotation frequency on the closed orbit. The invariant spin field (ISF) describes a periodic polarization state of a beam's phase-space distribution. This ISF leads to a very useful parametrization of coupled spin and orbit dynamics. We prove that this ISF gives rise to an adiabatic invariant of spin-orbit motion. This proof is much more complicated since the orbital frequencies are involved. Because of this adiabatic invariance, a beam's spin field follows slow changes of the accelerator's ISF that can occur during a slow acceleration cycle. This feature is essential when high-order spin-orbit resonances are crossed, since it allows polarization that has been reduced at the resonance condition to be recovered, to a large degree, after the resonances have been crossed.
Highlights
In order to maximize the number of collisions of particles inside experimental detectors of a storage ring system, one tries to maximize the total number of particles in the ‘‘bunches’’ and minimize the emittances, so that the particle distribution across phase space is narrow and the phasespace density is high
If the beam is spin polarized, high polarization is needed and it should be relatively stable over time
To obtain high polarization levels at useful energies, particles must first be accelerated from low energy while retaining most of their initial polarization
Summary
It has been predicted and found experimentally that the polarization direction of particles on the closed orbit of a circular accelerator can be manipulated, without a noticeable reduction of polarization, by means of a slow variation of magnetic fields. The invariant spin field (ISF) describes a periodic polarization state of a beam’s phasespace distribution This ISF leads to a very useful parametrization of coupled spin and orbit dynamics. This proof is much more complicated since the orbital frequencies are involved Because of this adiabatic invariance, a beam’s spin field follows slow changes of the accelerator’s ISF that can occur during a slow acceleration cycle.
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