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The possible nonlinear mechanisms for harmonic generation in bismuth have been investigated by solving the Boltzmann transfer equation for free carriers. Space diffusion of carriers has been shown to be as important as the interaction of magnetic field of the wave with current density. The results are compared with the experimental results of Bate and Wisseman for damped Alfvén wave second‐harmonic generation. Except for the behavior of harmonic power with static magnetic field, a good agreement is found.