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Summary form only given, as follows. The article is devoted to the investigation of the nonlinear interaction between extraordinary polarized electromagnetic eigenmodes of a cylindrical metal waveguide, which is partially filled by a cold magnetoactive plasma, and an electron beam, which is rotated around the plasma column. The ASW propagates with azimuthal wavenumber across the external steady axial magnetic field. The problem is solved using the method of macro particles. The set of differential equation is calculated numerically. Dependences of the ASW's amplitude and phase on time are obtained. The distribution of the beam particles in the waveguide and phase space is examined. The regime of nonlinear saturation of the beam-plasma instability is accompanied by formation of electron bunches in a shape of "electron needles in a magnetrons". The investigation fulfilled can be applied in the branch of plasma electronics.