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We present a mathematical nonlinear model of the parasitic backward-wave oscillation in the generic helix TWT under permanent periodic magnetic (PPM) focusing. The model accounts for the interaction of the electromagnetic wave existing on the helix slow-wave circuit and the electron beam alternating rotation in the PPM focusing field. We obtain an equation system, which permits us to find the start-oscillation length of the parasitic backward-wave oscillation and real starting Pierce's relative velocity parameter as functions of the PPM focusing field period and amplitude, and the electrical parameters of the TWT in the large-signal regime. We show that the electron beam alternating rotation in the PPM focusing field has a significant effect on the TWT stability with respect to the parasitic backward-wave oscillation in the nonlinear regime, as it has in the linear one.