  (shortened) We calculate the vertical structure of a local patch of an
accretion disk in which heating by dissipation of MRI-driven MHD turbulence is
balanced by radiative cooling. Heating, radiative transport, and cooling are
computed self-consistently with the structure by solving the equations of
radiation MHD in the shearing-box approximation. Using a fully 3-d and
energy-conserving code, we compute the structure of this disk segment over a
span of more than five cooling times. After a brief relaxation period, a
statistically steady-state develops. Measuring height above the midplane in
units of the scale-height H predicted by a Shakura-Sunyaev model, we find that
the disk atmosphere stretches upward, with the photosphere rising to about 7H,
in contrast to the approximately 3H predicted by conventional analytic models.
This more extended structure, as well as fluctuations in the height of the
photosphere, may lead to departures from Planckian form in the emergent
spectra. Dissipation is distributed across the region within roughly 3H of the
midplane, but is very weak at greater altitudes. Because fluctuations in the
dissipation are particularly strong away from the midplane, the emergent
radiation flux can track dissipation fluctuations with a lag that is only
0.1--0.2 times the mean cooling time of the disk. Long timescale asymmetries in
the dissipation distribution can also cause significant asymmetry in the flux
emerging from the top and bottom surfaces of the disk. Radiative diffusion
dominates Poynting flux in the vertical energy flow throughout the disk.
