One possible method of measuring the electric dipole moment of an elementary particle consists in measuring the average spin precession frequency of a polarized beam. The problem of maximizing the spin coherence time of a bunched beam is reduced to the minimization of the particles' orbit length dispersion. This is achieved by introducing sextupoles with fields minimizing the chromaticity of the spin frequency. We have found experimentally that minimizing the chromaticity of betatron motion leads to the minimization of the chromaticity of the spin frequency. In this paper we explore this relationship.
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