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The global-scale interior magnetic field needed to account for the Sun'sobserved differential rotation can be effective only if confined below theconvection zone in all latitudes, including the polar caps. Axisymmetricnonlinear MHD solutions are obtained showing that such confinement can bebrought about by a very weak downwelling flow U~10^{-5}cm/s over each pole.Such downwelling is consistent with the helioseismic evidence. All threecomponents of the magnetic field decay exponentially with altitude across athin "magnetic confinement layer" located at the bottom of the tachocline. Withrealistic parameter values, the thickness of the confinement layer ~10^{-3} ofthe Sun's radius. Alongside baroclinic effects and stable thermalstratification, the solutions take into account the stable compositionalstratification of the helium settling layer, if present as in today's Sun, andthe small diffusivity of helium through hydrogen, chi. The small value of chirelative to magnetic diffusivity produces a double boundary-layer structure inwhich a "helium sublayer" of smaller vertical scale is sandwiched between thetop of the helium settling layer and the rest of the confinement layer.Solutions are obtained using both semi-analytical and purely numerical,finite-difference techniques. The confinement-layer flows are magnetostrophicto excellent approximation. More precisely, the principal force balances arebetween Lorentz, Coriolis, pressure-gradient and buoyancy forces, with relativeaccelerations and viscous forces negligible. This is despite the kinematicviscosity being somewhat greater than chi. We discuss how the confinementlayers at each pole might fit into a global dynamical picture of the solartachocline. That picture, in turn, suggests a new insight into the early Sunand into the longstanding enigma of solar lithium depletion.

Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow