A theory of stimulated scattering of electromagnetic waves by high-current relativistic electron beams is developed, with the transverse inhomogeneity of incident and scattered waves, and the presence of a magnetic field of 20 kG focusing the particles taken into account. The nonlinear results including the coupling coefficient versus the longitudinal magnetic field and the radius of electron beam, the excitation curves, powers and efficiency etc. are obtained on a set of input parameters of our recently establishing accelerator and FEL system with an electron energy of 600 keV and a current of 3 kA. It is shown that the electrodynamic system of backward wave oscillator (BWO) in the form of a cylindrical waveguide with a periodically corrugated wall can have a high Q-factor for oscillations at wavelengths much shorter than the corrugation period of 1.95 cm and the wavelengths of incident pump waves. The relativistic 3.2 cm backward wave oscillator provided powerful scattered radiation at 3 - 8 mm with integral power of 30 MW and efficiency up to 13%.
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