A magnet system for providing a localized, substantially homogeneous magnetic field for use in nuclear magnetic resonance imaging. The magnet system includes a vacuum vessel defining a bore for receiving the subject of the imaging. It further includes a cryogenic containment vessel supported within the vacuum vessel. A single coil or "simple" solenoid is positioned within the containment vessel for providing the magnetic field. This coil includes a winding made up of thousands of turns of small superconductive wire, with the winding having a modular geometry including a plurality of axially spaced wire modules. The coil further includes an insulative substance, having a greater coefficient of thermal contraction than that of the wire, distributed in the winding. As the temperature of the coil is reduced from room temperature to its cryogenic operating temperature, the development of localized stress concentrations of sufficient magnitude to rupture the wire, are avoided. A method of winding the coil is also disclosed.