As part of the collaboration program between CERN and KEK for the LHC, we h
ave been developing a high field gradient superconducting insertion quadrup
ole magnet with a field gradient of 240 T/m in an aperture of 70 mm. To dat
e two model magnets have been built and their quench characteristics and fi
eld qualities have been studied. Based on these results, we have performed
the final adjustment of the magnet design. In this paper we present the sum
mary of the design which will include short sample limits and field quality
analysis for both the straight section and the end regions.