The ESRF is currently setting up a beam line for very hard photons well above 250 keV. This requires the installation of a high field three polewavelength shifter. The nominal and target fields of the wiggler magnet are 4 and 5 tesla respectively while the nominal field integral over the central pole is 0.256 T-m at 4 T. The proposed magnet is a system of superconducting main and two side pole coils connected in series. An additional superconducting correction coil system enables to tune the field integral. The coils, made of high performing NbTi, are enclosed and prestressed in an aluminium coil housing. About 15% field enhancement, shielding and force balancing is achieved with two iron plates sandwiching the coil housing. The cooling concept is a cryostat with a closed helium re-condensation system. Cooling is provided by a mechanical hybrid GM and JT refrigerator with a cooling capacity of about 2.5 W at 4.4 K. The paper reports on the design concepts and optimisations and a preferred solution is presented
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