We propose an unconventional electron gun structure in which the emitter is located on a concave cathode surface with a non-uniform electric field. Such a design violates the intuition that an emitter should place close to a uniform electric field to reduce the velocity spread. The commonly employed design guide based on the adiabatic condition predicts a huge velocity spread of 24%, but the simulation using EGUN code and verified with CST particle studio shows a very low spread of 2.8%. Examining the magnetic moment and the kinetic energy of the beam reveals that the electrons experience a relatively long acceleration process due to the much weak electric field. That's why the non-adiabatic effect matters. In addition to the cyclotron compression and the E × B drift, the "resonant" polarization drift plays a crucial role in reducing the overall velocity spread. Simulations show a decent beam quality with the pitch factor of 1.5 and the 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. The promising results with the wide working range enable the development of continuous frequency-tunable gyrotrons.Gyrotrons based on the mechanism of the electron cyclotron maser (ECM) 1-3 is capable of producing high-power, coherent, terahertz (THz) waves as compared with the classical vacuum electronic tubes. Through decades of development, frequency-tunable gyrotrons receive more and more attentions 4-6 because of the frequency-sensitive applications, such as the enhancement of nuclear magnetic resonance by dynamic nuclear polarization (DNP-NMR) and the measurement of the hyperfine splitting of positronium (Ps-HFS). The beam-wave synchronism for gyrotrons is described as:where ω is the angular frequency, k z is the wavenumber, and s is the cyclotron harmonic number. Ω c is the relativistic electron cyclotron frequency which is related to the magnetic field (B 0 ) and the relativistic gamma factor (γ 0 ), i.e., Ω c = eB 0 /m 0 γ 0 . e and m 0 are the charge and the rest mass of an electron. v z is the electron axial velocity which is associated with the beam voltage (V b ). Equation (1) predicts that the frequency tunability of gyrotrons 7,8 is attainable by adjusting either B 0 or V b . Since the output power of gyrotrons is strongly related to the quality of the electron beam, high-performance electron guns deserve in-depth studies for frequency-tunable gyrotrons. Many types of electron guns have been proposed 9-11 to generate a high-quality beam with a high pitch factor (α) and a low velocity spread (∆v/v). Magnetron injection gun (MIG) 12-14 consisting of a conical-shaped cathode is one of the commonly used electron sources for gyrotrons. Electrons emitted from a convex surface with a maximal electric field are quickly accelerated to a constant value of energy, i.e., p 2 ⊥ + p 2 z = (1 + α 2 )p 2 z = const.. Then, electrons undergo a magnetic compression according to the adiabatic a) Electronic mail: thschang@phys.nthu....