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PETRA III is a low-emittance storage ring dedicated to synchrotron radiation. For efficient injection in the top-up mode, the dynamic aperture has to be larger than 30 mm-mrad in the horizontal plane. This paper presents the choice of tunes and the optimization of the sextupole configuration. Tracking simulations have been performed, including the non-linear effects of 20 four-meters-long damping wigglers and a representative set of undulators. Misalignment and multipole errors are considered as well, leading to specifications for the magnet design and alignment procedure.
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