  Rather weak fossil magnetic fields in the radiative core can produce the
solar tachocline if the field is poloidal and almost horizontal in the
tachocline region, i.e. if the field is confined within the core. This
particular field geometry is shown to result from a shallow (<~1Mm) penetration
of the meridional flow existing in the convection zone into the radiative core.
I.e., two conditions are crucial for a magnetic tachocline theory: (i) the
presence of meridional flow of a few meters per second at the base of the
convection zone, and (ii) a magnetic diffusivity inside the tachocline smaller
than 10^8 cm^2s^-1. Numerical solutions for both confined poloidal fields and
the resulting tachocline structures are presented. We find that the tachocline
thickness runs as <I>B</I>_p^-1/2 with the poloidal field amplitude falling
below 5% of the solar radius for <I>B</I>^p > 5 mG. The resulting toroidal
field amplitude inside the tachocline of about 100 G does not depend on the
<I>B</I>^p. The hydromagnetic stability of the tachocline is only briefly
discussed. For the hydrodynamic stability of latitudinal differential rotation
we found that the critical 29% of the 2D theory of Watson (1981) are reduced to
only 21% in 3D for marginal modes of about 6 Mm radial scale.
