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A magnetic cusp gun (MCG) is developed to generate axis-encircling electron beam, or called large orbit beam (LOB). A higher harmonic gyrotron employing a LOB is advantageous in the beam-wave coupling between the sth cyclotron harmonic and TEmn modes, where m=s. This reduces the requirement of the magnetic field strength to as low as about 1/s of the fundamental gyrotron. The major challenges in MCG development are simultaneously minimizing electron beam guiding center radius and velocity spread. A novel high power cusp gun configuration, which employs an inner and an outer focusing electrodes, is proposed with detailed theoretical analysis and intensive optimization. The key parameters, such as transverse velocity spread and the ratio of the guiding-center radius to Larmor radius, exhibit excellent stability, over wide tuning range of beam current and magnetic field. These merits enable the 4th harmonic 394 GHz gyrotron or even the frequency tunable terahertz gyrotrons.