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We have developed a quadratic nonlinear theory of a plasma-beam superheterodyne free electron laser of dopplertron type with the non-axial injection of an electron beam with respect to the guiding magnetic field. It is found out that the studied device can work in four different modes of operation. We determine the modes that have maximum gain coefficients of electromagnetic signals. It is shown that for all the operating modes the amplification factor of an electromagnetic signal is enhanced when the electron beam injection angle is increased.

Nonlinear Theory of Plasma-Beam Superheterodyne Free Electron Laser of Dopplertron Type with Non-Axial Injection of Electron Beam