High-latitude laminar confinement of the interior field \mathbf { B } _ { i } is shown to be possible .
Mean downwelling U as weak as 2 \times 10 ^ { -6 } cm s ^ { -1 } – gyroscopically pumped by turbulent stresses in the overlying convection zone and/or tachocline – can hold the field in advective–diffusive balance within a confinement layer of thickness scale \delta \sim 1.5 Mm \sim 0.002 { \hskip { 0.6 pt } } R _ { \odot } .
The confinement layer sits at the base of the high-latitude tachocline , near the top of the radiative envelope and just above the ‘ tachopause ’ marking the top of the helium settling layer .
A family of exact , laminar , frictionless , axisymmetric confinement-layer solutions is obtained in cylindrical polar coordinates , for uniform downwelling in the limit of strong rotation \Omega _ { i } and stratification N .
The downwelling can not penetrate the helium layer and must therefore feed into an equatorward flow immediately above the tachopause .
The retrograde Coriolis force on that flow is balanced by a prograde Lorentz force within the confinement layer .
Buoyancy forces keep the tachopause approximately horizontal .
For typical solar N values \sim 10 ^ { -3 } s ^ { -1 } this type of dynamics holds over a substantial range of colatitudes , e.g .
nearly out to colatitude 40 ^ { \circ } when U \lesssim { \hskip { 0.6 pt } } 10 ^ { -5 } cm s ^ { -1 } for modest | \mathbf { B } _ { i } | values \sim tens of gauss .

The angular-momentum budget implied by the downwelling and equatorward flow , importing low and exporting high angular momentum , dictates that the confinement layer must exert a net retrograde torque on its surroundings through laminar Maxwell stresses .
Some of that torque is exerted downward through the tachopause upon the interior , against the Ferraro constraint , and the rest is exerted across the periphery of the confinement layer at some outer colatitude \lesssim 40 ^ { \circ } .
The profiles of velocity and magnetic field within the confinement layer are fixed by two external conditions , first the partitioning of the torque between the contributions exerted on the interior and across the periphery , and second the vertical profile of Maxwell stress at the periphery .
In default of detailed models of what happens near the periphery , we provisionally suggest that a natural simplest choice of model would be one in which all the net torque is exerted on the interior .