[en] The Fermilab Collider Detector Facility (CDF) is a large detector system designed to study anti pp collisions at very high center of mass energies. The central detector for the CDF shown employs a large axial magnetic field volume instrumented with a central tracking chamber composed of multiple layers of cylindrical drift chambers and a pair of intermediate tracking chambers. The purpose of this system is to determine the trajectories, sign of electric charge, and momenta of charged particles produced with polar angles between 10 and 170 degrees. The magnetic field volume required for tracking is approximately 3.5 m long an 3 m in diameter. To provide the desired δp_Tp_T less than or equal to 1.5% at 50 GeV/c using drift chambers with approx. 200μ resolution the field inside this volume should be 1.5 T. The field should be as uniform as is practical to simplify both track finding and the reconstruction of particle trajectories with the drift chambers. Such a field can be produced by a cylindrical current sheet solenoid with a uniform current density of 1.2 x 10₆ A/m (1200 A/mm) surrounded by an iron return yoke. For practical coils and return yokes, both central electromagnetic and central hadronic calorimetry must be located outside the coil of the magnet. This geometry requires that the coil and the cryostat be thin both in physical thickness and in radiation and absorption lengths. This dual requirement of high linear current density and minimal coil thickness can only be satisfied using superconducting technology. In this report we describe the design for an indirectly cooled superconducting solenoid to meet the requirements of the Fermilab CDF. The components of the magnet system are discussed in the following chapters, with a summary of parameters listed in Appendix A