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The first superconducting magnets to be installed in the union ionization cooling experiment (MICE) will be the tracker solenoids. The tracker solenoid module is a five coil superconducting solenoid with a 400 mm diameter warm bore that is used to provide a 4 T magnetic field for the experiment tracker module. Three of the coils are used to produce a uniform field (up to 4 T with better than 1 percent uniformity) in a region that is 300 mm in diameter and 1000 mm long. The other two coils are used to match the muon beam into the MICE cooling channel. Two 2.94-meter long superconducting tracker solenoid modules have been ordered for MICE. The tracker solenoid will be cooled using two-coolers that produce 1.5 W each at 4.2 K. The magnet system is described. The decisions that drive the magnet design will be discussed in this report.