  Recent studies of narrow, X-ray synchrotron radiating filaments surrounding
young supernova remnants indicate that magnetic fields strengths are relatively
high, B ~ 0.1 mG, or even higher, and that diffusion is close to the Bohm
limit. I illustrate this using Cas A as an example. Also older remnants such as
RCW 86 appear to emit X-ray synchrotron radiation, but the emission is more
diffuse, and not always confined to a region close to the shock front. I argue
that for RCW 86 the magnetic field is likely to be low (B ~ 17 microGauss), and
at the location where the shell emits X-ray synchrotron radiation the shock
velocity is much higher than the average shock velocity of ~600 km/s.
