  %Context: {Previous studies have indicated that the 372.4 GHz ground
transition of ortho-H$_2$D$^+$ might be a powerful probe of Proto-Planetary
Disks. The line could be especially suited for study of the disk mid-plane,
where the bulk of the mass resides and where planet formation takes place.}
%Aims: {Provide detailed theoretical predictions for the line intensity,
profile and maps expected for representative disk models.} %Methods: {We
determine the physical and chemical structure of the disks from the model
developed by Ceccarelli & Dominik (2005). The line emission is computed with
the new radiative transfer method developed recently by Elitzur & Asensio Ramos
(2006).} %Results: {We present intensity maps convolved with the expected ALMA
resolution, which delineate the origin of the H$_2$D$^+$ 372.4 GHz line. In the
disk inner regions, the line probes the conditions in the mid-plane out to
radial distances of a few tens of AU, where Solar-like planetary systems might
form. In the disk outermost regions, the line originates from slightly above
the mid-plane. When the disk is spatially resolved, the variation of line
profile across the image provides important information about the velocity
field. Spectral profiles of the entire disk flux show a double peak shape at
most inclination angles.} %Conclusions: {Our study confirms that the 372.4 GHz
H$_2$D$^+$ line provides powerful diagnostics of the mid-plane of
Proto-Planetary Disks. Current submillimeter telescopes are capable of
observing this line, though with some difficulties. The future ALMA
interferometer will have the sensitivity to observe and even spatially resolve
the H$_2$D$^+$ line emission.}
