  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 (Busso et al. 2007). The fields
are assumed to originate from a dynamo operating in the stellar interior. Here,
we show what is required of an $\alpha-\Omega$ 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
$\left<B_\phi\right>\simeq3\times10^4$ G can be sustained at the base of the
convection zone.
