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We study theoretically the influence of the spread of initial energies and velocities in the electron beam on the starting conditions and efficiency of a gyrotron. We compare various analytical and numerical models and the results of experimental studies of gyrotrons in which the interaction takes place at the first and second harmonics of the cyclotron frequency. The aftercavity interaction of the electron beam with the high-frequency field in the output waveguide transition is taken into account. The influence of the energy spread on the recuperation efficiency is estimated. Permissible spreads of the initial energies and electron velocities are determined.

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The review summarizes recent experimental results in the field of THz gyrotrons developed for various applications. A CW gyrotron with the operation frequency of 0.26 THz has been successfully used for DNP spectroscopy A pulsed high-harmonic Large Orbit Gyrotron (LOG) with the frequency of 0.55 THz and kW level of output power has been used for THz breakdown and obtaining dense plasma in gases. A powerful pulsed 0.67 THz/200 kW gyrotron is under development for remote detection of ionization sources.