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The KEKB accelerator has achieved the highest luminosity of 1.39E1034cm-2s-1 at June-03-2004. For getting the higher luminosity over 1E1035cm-2s-1, the KEKB accelerator group continues to study the upgraded machine of the KEKB, that is the Super-KEKB. The designed machine parameters for this Super-KEKB are the vertical beta of 3 mm at the interaction point (IP), the LER and HER currents of 9.4 A and 4.1 A, and the half crossing angle of 15 mrad for the target luminosity of 1-5E1035cm-2s-1. For achieving these beam parameters, the superconducting magnets (final focus quadrupoles and compensation solenoids) are newly required to design. The magnet-cryostats have very tight spatial constraints against the Belle particle detector and the beam pipe so that the beam and the synchrotron light do not have any interference with the beam pipe. In this design, the final focus quadrupoles generate the field gradient of 42.3 T/m and their effective magnetic lengths are 0.30m and 0.36m in each side with respect to the IP, respectively. The compensation solenoids are overlaid with the quadrupoles. We will report the design of these magnets in detail and show the difficulties for the Super-KEKB-IR.
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