The U.S. Dept. of Energy's goal for multifilamentary (MF) strand intended for accelerator applications includes current densities, Jc, of up to 1200 A/mm2in fields of 12-16 T. Although MgB2films possess Bc2s at 0 K as high as 50 T, and Jcs (self field) as high as 107A/cm2have been reported, it may be several years before the above goal is attained in round MF MgB2wire. But when its electrical properties become suitable MgB2's critical temperature of 39 K will be an added advantage in the accelerator magnets' high radiation environment. In the meantime, some near-term applications have been identified. Continually improving properties may enable MgB2to be used in the windings of: (i) undulator magnet upgrades and replacements, (ii) wiggler magnets, (iii) light source bending magnet replacements, or (iv) some of the lower field solenoids of a proposed muon collider. Active research-and-development programs are yielding MgB2strands with some remarkable properties: critical fields Bc2and Birrin the ranges 28-33 T and 24-29 T, respectively, and Jc(4.2 K)s in the range 1.1-5.5times105A/cm2, 5-2 T, respectively. Recent superconducting undulator (SCU) magnets are calling for Jc, BW(winding-field), B0(beam-line field) combinations such as 1.1times105A/cm2, 3.3 T, 1.0 T. These specifications, in the light of its existing performance levels, indicate MgB's potential suitability for the windings of SCU's. A model MgB2coil-set is described
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