  We use the Chandra X-ray Observatory to study the region in the Tycho
supernova remnant between the blast wave and the shocked ejecta interface or
contact discontinuity. This zone contains all the history of the shock-heated
gas and cosmic-ray acceleration in the remnant. We present for the first time
evidence for significant spatial variations of the X-ray synchrotron emission
in the form of spectral steepening from a photon index of 2.6 right at the
blast wave to a value of 3.0 several arcseconds behind. We interpret this
result along with the profiles of radio and X-ray intensity using a
self-similar hydrodynamical model including cosmic ray backreaction that
accounts for the observed ratio of radii between the blast wave and contact
discontinuity. Two different assumptions were made about the post-shock
magnetic field evolution: one where the magnetic field (amplified at the shock)
is simply carried by the plasma flow and remains relatively high in the
post-shock region [synchrotron losses limited rim case], and another where the
amplified magnetic field is rapidly damped behind the blast wave [magnetic
damping case]. Both cases fairly well describe the X-ray data, however both
fail to explain the observed radio profile. The projected synchrotron emission
leaves little room for the presence of thermal emission from the shocked
ambient medium. This can only be explained if the pre-shock ambient medium
density in the vicinity of the Tycho supernova remnant is below 0.6 cm-3.
