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In low-mass Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars, anomalous mixing must transport material near the hydrogen-burning shell to the convective envelope. Recently, it was suggested that buoyant magnetic flux tubes could supply the necessary transport rate [l]. The fields are assumed to originate from a dynamo operating in the stellar interior. Here, we show what is required of an α-Ω dynamo in the envelope of an AGB star to maintain these fields. Differential rotation and rotation drain via turbulent dissipation and Poynting flux, so if shear can be resupplied by convection, then large-scale toroidal field strengths of ≃3×104 G can be sustained at the base of the convection zone. [ABSTRACT FROM AUTHOR]