  We report on our analysis of the 1 Ms Chandra observation of the supernova
remnant Cas A in order to localize, characterize and quantify its non-thermal
X-ray emission. More specifically, we investigated whether the X-ray
synchrotron emission from the inside of the remnant is from the outward shock,
but projected toward the inner ring, or from the inner shell. We tackle this
problem by employing a Lucy-Richardson deconvolution technique and measuring
spectral indices in the 4.2-6 keV band.
  We show that most of the continuum emission is coming from an inner ring that
coincides with the location of the reverse shock. This inner ring includes
filaments, whose X-ray emission has been found to be dominated by X-ray
synchrotron emission. The X-ray emission from these filaments, both at the
forward shock and from the inner ring, have relatively hard spectra with
spectral index > -3.1. The regions emitting hard X-ray continuum contribute
about 54% of the total X-ray emission in the 4.2-6 keV. This is lower than
suggested by extrapolating the hard X-ray spectrum as measured by BeppoSAX-PDS
and INTEGRAL. This can be reconciled by assuming a gradual steepening of the
spectrum toward higher energies. We argue that the X-ray synchrotron emission
is mainly coming from the Western part of the reverse shock. The reverse shock
in the West is almost at rest in our observation frame, corresponding to a
relatively high reverse shock velocity of ~6000 km/s in the frame of the freely
expanding ejecta.
