  This paper studies the response of a thin accretion disk to an external
radial magnetic field. Our focus is on protoplanetary disks (PPDs), which are
exposed during their later evolution to an intense, magnetized wind from the
central star. A radial magnetic field is mixed into a thin surface layer, is
wound up by the disk shear, and is pushed downward by a combination of
turbulent mixing and ambipolar and Ohmic drift. The toroidal field reaches much
greater strengths than the seed vertical field that is usually invoked in PPD
models, even becoming superthermal. Linear stability analysis indicates that
the disk experiences the magnetorotational instability (MRI) at a higher
magnetization than a vertically magnetized disk when both the effects of
ambipolar and Hall drift are taken into account. Steady vertical profiles of
density and magnetic field are obtained at several radii between 0.06 and 1 AU
in response to a wind magnetic field $B_r \sim (10^{-4}$-$10^{-2})(r/{\rm
AU})^{-2}$ G. Careful attention is given to the radial and vertical ionization
structure resulting from irradiation by stellar X-rays. The disk is more
strongly magnetized closer to the star, where it can support a higher rate of
mass transfer. As a result, the inner $\sim 1$ AU of a PPD is found to evolve
toward lower surface density. Mass transfer rates around $10^{-8}\,M_\odot$
yr$^{-1}$ are obtained under conservative assumptions about the MRI-generated
stress. The evolution of the disk, and the implications for planet migration,
are investigated in the accompanying paper.
