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The advection of thermonuclear ashes by magnetized domains emerging from nearthe H-shell was suggested to explain AGB star abundances. Here we verify thisidea quantitatively through exact MHD models. Starting with a simple 2Dgeometry and in an inertia frame, we study plasma equilibria avoiding thecomplications of numerical simulations. We show that, below the convectiveenvelope of an AGB star, variable magnetic fields induce a natural expansion,permitted by the almost ideal MHD conditions, in which the radial velocitygrows as the second power of the radius. We then study the convective envelope,where the complexity of macro-turbulence allows only for a schematic analyticaltreatment. Here the radial velocity depends on the square root of the radius.We then verify the robustness of our results with 3D calculations for thevelocity, showing that, for both the studied regions, the solution previouslyfound can be seen as a planar section of a more complex behavior, in whichanyway the average radial velocity retains the same dependency on radius foundin 2D. As a final check, we compare our results to approximate descriptions ofbuoyant magnetic structures. For realistic boundary conditions the envelopecrossing times are sufficient to disperse in the huge convective zone anymaterial transported, suggesting magnetic advection as a promising mechanismfor deep mixing. The mixing velocities are smaller than for convection, butlarger than for diffusion and adequate to extra-mixing in red giants.

MHD and deep mixing in evolved stars. 1. 2D and 3D analytical models for the AGB