  We present an interpretation of the time variability of the $X$-ray flux
recently reported from a multi-epoch campaign of $15$ years observations of the
supernova remnant Cassiopeia A by {\it Chandra}. We show for the first time
quantitatively that the $[4.2-6]$ keV non-thermal flux increase up to $50\%$
traces the growth of the magnetic field due to vortical amplification mechanism
at a reflection inward shock colliding with inner overdensities. The fast
synchrotron cooling as compared with shock-acceleration time scale
qualitatively supports the flux decrease.
