Amplification of magnetic field downstream of inward shocks in supernova remnant Cassiopeia A

X-Ray observations of the supernova remnant Cassiopeia A have shown a rapid and strong variation (up to 50%) in the non-thermal flux over 15 years of multi-epoch observations that alone cannot be explained by shock compression of the magnetic field. Combined Chandra and NuSTAR observations investigated six distinct inwards shocks in the central/west regions of Cas A that were possibly created when the forward shock collided with a molecular cloud in the interstellar medium. We use an analytic model based on MHD jump conditions at rippled shocks and synchrotron theory to give the first quantitative explanation for the X-ray variability at two of such shocks, W2-W4. The predicted flux is based on the assumption that the speed of the inward shocks was constant across all times and only the downstream magnetic amplification governs the flux increase. We found a scale of the clumps that cause the amplification to be 10^18 cm, consistent with the shock W3, previously determined with the same method. We have found that the amplification is relatively modest across W2-W4, consistent with low Mach number.