A major goal of the Tokamak Fusion Core Experiment (TFCX) study was to minimize the size of the device and achieve lowest cost. Two key factors influencing the size of the device employing superconducting magnets are toroidal field (TF) winding current density and its nuclear heat load withstand capability. Lower winding current density requires larger radial build of the winding pack. Likewise, lower allowable nuclear heating in the winding requires larger shield thickness between the plasma and coil. To achieve a low-cost device, it is essential to maximize the winding's current density and nuclear heating withstand capability. To meet this objective, the TFCX design specification adopted as goals a nominal winding current density of 3500 A/cm2 with 10-T peak field at the winding, peak nuclear heat load limits of 1 mW/cm3 for the nominal design and 50 mW/cm3 for an advanced design. This study developed justification for these current density and nuclear heat load limits.