Abstract
Small perturbative fields in a synchrotron influence both the spin and orbital motion of a stored beam. Their effect on the beam polarization consists of two contributions, a direct kick and an effect of the ring lattice due to orbit perturbation. Spin response function is an analytic technique to account for both contributions. We develop such a technique for the spin-transparent synchrotrons where the design spin motion is degenerate. Several perspective applications are illustrated or discussed. In particular, we consider the questions of the influence of lattice imperfections on the spin dynamics and spin manipulation during an experiment. The presented results are of a direct relevance to NICA (JINR), RHIC (BNL), EIC (BNL) and other existing and future colliders when they arranged with polarization control in the spin-transparent mode.
Highlights
The Spin-Transparent (ST) technique has been proposed as an efficient, high flexibility method to control the beam polarization, from acceleration to long term maintenance and spin manipulation in real time of an experimental run of a collider [1,2,3,4,5]
In addition to the “accelerator reference frame” connected to the design orbit and allowing one to describe small orbital deviations from it, we introduce a “spin reference frame” connected to the spin dynamics when the particles travel on the design orbit
The ST resonance strength ω is determined by the magnitude of the ST resonance spin field ω, which consists of two parts: a coherent part arising due to additional transverse and longitudinal fields on the closed orbit deviating from the design orbit and an incoherent part associated with the particles’ betatron and synchrotron oscillations [2,24]
Summary
The Spin-Transparent (ST) technique has been proposed as an efficient, high flexibility method to control the beam polarization, from acceleration to long term maintenance and spin manipulation in real time of an experimental run of a collider [1,2,3,4,5]. At a first glance, such a situation is not constructive since particles are in the ν = 0 resonance In this case spin dynamics is highly sensitive to any small perturbative fields associated with lattice errors, focusing fields and other. The response function was used in the above studies to analyze rings where the design lattice defines a unique (distinct) stable spin direction (n-axis) [11]. We call such a mode of spin motion a “Distinct Spin” (DS) mode. Extension of the response function formalism to the ST case is the subject of this paper
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