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This paper describes the detailed design of an eight-beam electron gun for use in S-band multiple-beam amplifiers operating in the fundamental mode. The gun operating voltage is 45 kV with a total beam current of 32 A, evenly divided among the beamlets. Each individual beam has a perveance of 0.42 mpervs making a total beam perveance of 3.35 mpervs. The optimized electron gun is singly convergent using a four-fold symmetry with the four inner and four outer emitters interlaced 90° apart. The emitter current density has been kept below 10 A/cm2 (space-charge limited). The cathode is magnetically shielded and the longitudinal magnetic field in the interaction region is in the range of 1.1-1.8 kG. The design of the magnetic focusing system minimizes beam corkscrewing as well as electron interception on the tunnel walls. Beam optics simulations of the gun indicate excellent beam transport characteristics with a final beam-to-tunnel radial fill factor of less than 0.45. The primary computational tools used in the design process were the three-dimensional gun code MICHELLE, and the magnetostatics code MAXWELL-3D.