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The design of a high-power low-velocity-spread space-charge-limited cusp gun is presented. The Lagrangian formulation is used to analyze the velocity spread and beam ripple (orbit center spread). It shows that the two electron orbit off-center mechanisms, the radial velocity and the nonideal cusp magnetic field, can be adjusted to cancel each other. The characteristics of the cusp gun including the cusp magnet are calculated by cosimulation employing the Maxwell2D, Matlab, Egun, and CST-PS codes. The cusp gun is designed to generate a beam of 8 A at 70 kV with a pitch factor from 1.0 to 1.8 and an axial velocity spread from 3% to 7%. The development of this cusp gun is in progress at the University of Califonia, Davis, for use in the development of harmonic gyrotrons, peniotrons, and gyro-traveling-wave tubes.