The available information on isotopic abundances in the atmospheres of low-mass Red Giant Branch ( RGB ) and Asymptotic Giant Branch ( AGB ) stars requires that episodes of extensive mixing occur below the convective envelope , reaching down to layers close to the hydrogen burning shell ( Cool Bottom Processing ) .
Recently ( 5 ) suggested that dynamo-produced buoyant magnetic flux tubes could provide the necessary physical mechanisms and also supply sufficient transport rates .
Here , we present an \alpha - \Omega dynamo in the envelope of an RGB/AGB star in which shear and rotation drain via turbulent dissipation and Poynting flux .
In this context , if the dynamo is to sustain throughout either phase , convection must resupply shear .
Under this condition , volume-averaged , peak toroidal field strengths of \left < B _ { \phi } \right > \simeq 3 \times 10 ^ { 3 } G ( RGB ) and \left < B _ { \phi } \right > \simeq 5 \times 10 ^ { 3 } G ( AGB ) are possible at the base of the convection zone .
If the magnetic fields are concentrated in flux tubes , the corresponding field strengths are comparable to those required by Cool Bottom Processing .