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Landau damping of the vertical coherent motions due to lattice nonlinearities in storage rings

The systematic measurements of the vertical coherent motion were made with various chromaticities, octupole magnetic currents, beam currents and betatron tunes to study its damping mechanism at the Photon Factory storage ring (PF-ring). The polarity of the octupole magnetic currents corresponding to the sign of the amplitude dependent tune shift played an important roll in the damping of the vertical coherent motions. This is the same as the horizontal coherent motions.