We propose an unconventional structure of an electron gun to produce an annular beam for the frequency-tunable gyrotrons. The proposed gun takes advantage of the nonadiabatic electron motion during the acceleration of electrons by placing an emitter on the concave region of the cathode with a relatively weak electric field. The commonly employed adiabatic theory fails to predict the simulated transverse velocity spread, which suggests that the nonadiabatic effect plays an important role during the acceleration of electrons. Simulations are carried out by the EGUN code and verified with the commercial Computer Simulation Technology (CST) Particle Studio. From the change in the kinetic energy and the magnetic moment, we can define a section of the nonadiabatic electron motion. The rapid change in the beam-quality parameters within the nonadiabatic section is associated with the significant change in the electric field near the cathode. By considering the nonadiabatic electron motion, simulations predict appropriate parameters, namely, a pitch factor of 1.5 and a transverse velocity spread of 2.8%, over a wide range of the magnetic field (7.4–8.0 T) and the beam voltage (12–22 kV) with a high structural tolerance on the cathode geometry. The promising results enable the development of frequency-tunable gyrotrons. [ABSTRACT FROM AUTHOR]