We present the results of studying theoretically and experimentally the peculiarities of mode excitation in a generator of diffraction radiation with the two-and three-cascade interaction space in one open resonator. To describe the multistage interaction mechanism, the theoretical model used considers the excitation of the TEM 0nq modes, which have n in-phase field "spots," i.e., cascades, along the direction of the electron beam motion. It is shown that even the use of the two-cascade interaction space with the TEM 01q modes allows one to reduce the starting current of the generator by 1.91 times. The results of studying experimentally the two-cascade generator in the 5 and 1.5-mm wavelength ranges are presented. The in-phase property of the electron beam with the resonance field was achieved by disrupting the periodicity of the lattice slots at the center of the interaction space. The output power of the two-stage generator of 5-mm diffraction radiation in the TEM 013 mode ranged from 3 to 5 W. We also observed a 4-5-fold increase in the starting current for the regime of surface waves.

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