摘要： The concept of Compton-type free-electron lasers (FELs) operating in short wavelength ranges with a high e?ciency and power level is currently underway at the IAP RAS (Nizhny Novgorod). This concept is aimed at reducing the energy of a driving relativistic electron beam and thereby increasing the e?ciency of the electron–wave interaction in FELs, as well as making the oscillator relatively compact. The basis of this concept is microwave undulators of a new type — the so-called “?ying” undulators. This paper is devoted to the results of the current studies of these undulators, their simulation, and “cold” electrodynamic tests in the Ka band. For powering microwave undulators, a spatially extended narrow-band ˇCerenkov surface-wave oscillators (SWOs) are developed in the speci?ed frequency range driven by Sinus-6, a high-current accelerator, with a particle energy of 0.5 MeV, a current of 5 kA, and a pulse duration of 25 ns. The required sub-gigawatt power level of output radiation combined with a high stability of the narrow-band oscillation regime is achieved under conditions of a strongly oversized oscillator by using two-dimensional distributed feedback provided in a 2D doubly-periodic slow-wave structure. The design parameters of a 32 GHz/0.5 GW SWO intended for powering microwave undulators are presented and the results of its simulation and reported.