We present new evidence that the bright non-thermal X-ray emission features in the interior of the Cassiopeia A supernova remnant ( SNR ) are caused by inward moving shocks based on Chandra and NuSTAR observations . Several bright inward-moving filaments were identified using monitoring data taken by Chandra in 2000–2014 . These inward-moving shock locations are nearly coincident with hard X-ray ( 15–40 keV ) hot spots seen by NuSTAR . From proper motion measurements , the transverse velocities were estimated to be in the range \sim 2,100–3,800 km s ^ { -1 } for a distance of 3.4 kpc . The shock velocities in the frame of the expanding ejecta reach values of \sim 5,100–8,700 km s ^ { -1 } , slightly higher than the typical speed of the forward shock . Additionally , we find flux variations ( both increasing and decreasing ) on timescales of a few years in some of the inward-moving shock filaments . The rapid variability timescales are consistent with an amplified magnetic field of B \sim 0.5–1 mG . The high speed and low photon cut-off energy of the inward-moving shocks are shown to imply a particle diffusion coefficient that departs from the Bohm regime ( k _ { 0 } = D _ { 0 } / D _ { 0 ,Bohm } \sim 3–8 ) for the few simple physical configurations we consider in this study . The maximum electron energy at these shocks is estimated to be \sim 8–11 TeV , smaller than the values of \sim 15–34 TeV inferred for the forward shock . Cassiopeia A is dynamically too young for its reverse shock to appear to be moving inward in the observer frame . We propose instead that the inward-moving shocks are a consequence of the forward shock encountering a density jump of \gtrsim 5–8 in the surrounding material .