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The interaction of the fast cyclotron wave of a linear electron beam guided by a magnetic field with a counter- propagating electromagnetic wave leads to the appearance of a stop-band over a wide range of the magnetic field near its resonance. Suppression of generation in backward wave oscillators and the resonant-cyclotron method of mode selection are based on this effect, termed "cyclotron absorption." In this paper, we analyze the possibility of controlling regenerative amplification in such oscillators as a traveling wave tube (TWT) by suppressing parasitic feedback using the guide magnetic field in the region of cyclotron absorption (RCA). Approaching the magnetic field to values that border this region, which contain thresholds of self-excitation, leads to a decrease in suppression of the reflected wave that is responsible for the positive feedback; in other words, this leads to an increase in gain. We illustrate amplification in the RCA using two approaches: the theory of stationary operation of a TWT accounting for the cyclotron resonance of electrons with a reflected wave, and particle-in-cell computer simulations.