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We investigated the attainable stability of the monofilar-helix traveling wave tube (TWT) with respect to the parasitic backward-wave oscillation under periodic magnetic focusing. We accounted for the effect of the electron beam rotation in the nonhomogeneous focusing magnetic field, magnetic field amplitude and periodicity, and the specific coupling of the electron beam with the synchronous harmonics of the electromagnetic wave existing on the slow-wave circuit. This specific coupling takes place in the monofilar-helix TWT only and decreases its stability with respect to the parasitic backward-wave oscillation in comparison to other types of helix TWT. For the purpose of this analysis, we developed further the linear two-dimensional (2-D) multiwave theory of the helix TWT described in our previous work . In this theory, we account for space charge fields by means of waveguide excitation model based on the direct solution of Maxwell equations. Differently from , the present version of our theory allows for accounting of the coupling of the synchronous 0th spatial harmonic (forward employed for the amplification) and -1st (parasitic backward) harmonic of the circuit wave with the electron beam in the monofilar-helix TWT. By numerical modeling, we obtained quantitative data on the starting conditions for the parasitic backward-wave oscillation in the typical monofilar-helix TWT in the intersection point of the dispersion curves of these two harmonics. The described coupling mechanism does not exist in the bifilar-helix TWT. Therefore, the TWT with the bifilar helix is more stable with respect to the parasitic backward-wave oscillation than the TWT having the monofilar helix. These theoretical results correlate with the existing experimental evidence. The results of the present study, in particular, explain why the backward-wave oscillation suppression by tailoring of the focusing magnetic field has a significant effect in the bifilar-helix TWT but does not work in the monofilar-helix TWT.