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This paper presents the design of a high repetition rate electron gun to be employed in future high-power broadband multiple-beam amplifiers operating in S-band. Special emphasis is placed on the geometric layout of the gun to ensure high repetition rate operation at moderate beam switching voltages, good beam optics, and optimal beam packing for long life, efficient beam-wave interaction and broad bandwidth. The resulting gun design employs an eighteen-beam magnetically shielded cathode topology capable of generating a total current of 41.6 A (evenly divided among eighteen beams) at a voltage of 42 kV. In the beam tunnels, each beamlet has a radial fill factor of 48%. The nominal beam modulation voltage is 5.2 kV. With an estimated gun capacitance of 150 pF, a repetition rate in excess of 10 kHz is feasible with the current state-of-the-art in modulator technology.