The Northern wraps of the Sagittarius Stream as traced by Red Clump stars: distances, intrinsic widths and stellar densities

We trace the tidal Stream of the Sagittarius dwarf spheroidal galaxy (Sgr dSph) using Red Clump stars from the catalog of the Sloan Digital Sky Survey - Data Release 6, in the range 150{\deg} < RA < 220{\deg}, corresponding to the range of orbital azimuth 220{\deg} < Lambda < 290{\deg}. Substructures along the line of sight are identified as significant peaks in the differential star count profiles (SCP) of candidate Red Clump stars. A proper modeling of the SCPs allows us to obtain: (a) <10% accurate, purely differential distances with respect to the main body of Sgr, (b) estimates of the FWHM along the line of sight, and © estimates of the local density, for each detected substructure. In the range 255{\deg} < Lambda < 290{\deg} we cleanly and continuously trace various coherent structures that can be ascribed to the Stream, in particular: the well known northern portion of the leading arm, running from d~43 kpc at Lambda ~ 290{\deg} to d ~ 30 kpc at Lambda ~ 255{\deg}, and a more nearby coherent series of detections lying at constant distance d ~ 25 kpc, that can be identified with a wrap of the trailing arm. The latter structure, predicted by several models of the disruption of Sgr dSph, was never traced before; comparison with existing models indicates that the difference in distance between these portions of the leading and trailing arms may provide a powerful tool to discriminate between theoretical models assuming different shapes of the Galactic potential. A further, more distant wrap in the same portion of the sky is detected only along a couple of lines of sight.[abridged]