Abstract The spin-orbital dynamics at the COSY accelerator has been investigated. It has been shown in the numerical experiment that spin-decoherence of the beam is determined by the nonlinear part of the solution of the equation of synchronous acceleration principle. It has been shown that the effects of spin-decoherence are defined by the three parameters of the lattice: horizontal and vertical chromaticity, as well as the nonlinear momentum compaction factor.
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