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The design of a new pulsed magnet system for the generation of intense electron beams is presented. Determined by the required magnetic field profile along the axis, the magnet system consists of two coils (Coil 1 and 2) separated by a 32-mm axial gap. Each coil is energized independently. Both coils are internally reinforced with HM Zylon fiber/epoxy composite. Coil 1 made with Al-15 Glidcop wire has a bore of 110-mm diameter and is 200-mm long; it is energized by a 1.3-MJ, 13-kV capacitor bank. The magnetic field at the center of this coil is 30 T. Coil 2 made with CuNb wire has a bore diameter of 45 mm, generates 60 T with a pulse duration of 60 ms, and is powered by a 4.0-MJ, 17.7-kV capacitor bank. We present design criteria, coupling of the magnets, and normal and fault conditions during operation.