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The design of a 50 kAmpere conductor for use in a 20 MJ Induction Heating Coil is described. The conductor is a wide flat cable of 36 subcables, each of which contains six Nb-Ti strands around a stainless steel core strand. It is cryostable, with a pool-boiling, fully-normal equivalent heat transfer from the unoccluded strand surface of 0.26 Watts/cm2. A thin, tough polyester amide-imide insulation enhances heat transfer and prevents interstrand coupling. The tightly-twisted strands are configured using Cu-Ni elements to provide low AC losses with Nb-Ti filaments in an all-copper matrix. AC losses are expected to be approximately: (1) 0.3% of 20 MJ for a -7.5 T to 7.5 T one-second 1/2-cosinusoidal bipolar operation in a 20 MJ coil, and (2) for additional reference, 0.1% of 100 MJ for a 1.8 second -8 T to +8 T ramped operation in a 100 MJ coil with a heat transfer of 0.36 Watts/ cm2. The design is based on the manufacture and testing of prototype strands and subcables.