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According to the traditional knowledge, it is believed that the nonlinearity in the arc would not reduce the beam-beam performance, since the beam-beam force is dominated in the beam core region while the lattice nonlinearity is dominated in the beam halo region. However in the recent few e+e− storage ring colliders, it has been shown that the lattice nonlinearity may be important to the luminosity performance. In this paper, we'll try to review the related story in DAΦNE, and its upgrade with crab waist scheme, KEKB, BEPCII, and Super-KEKB.
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