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Several young supernova remnants (SNRs), including SN1006, emit synchrotronX-rays in narrow filaments, hereafter thin rims, along their periphery. Thewidths of these rims imply 50 to 100 $\mu$G fields in the region immediatelybehind the shock, far larger than expected for the interstellar mediumcompressed by unmodified shocks, assuming electron radiative losses limit rimwidths. However, magnetic-field damping could also produce thin rims. Here wereview the literature on rim width calculations, summarizing the case formagnetic-field amplification. We extend these calculations to include anarbitrary power-law dependence of the diffusion coefficient on energy, $D\propto E^{\mu}$. Loss-limited rim widths should shrink with increasing photonenergy, while magnetic-damping models predict widths almost independent ofphoton energy. We use these results to analyze Chandra observations of SN 1006,in particular the southwest limb. We parameterize the full widths at halfmaximum (FWHM) in terms of energy as FWHM $\propto E^{m_E}_{\gamma}$. Filamentwidths in SN1006 decrease with energy; $m_E \sim -0.3$ to $-0.8$, implyingmagnetic field amplification by factors of 10 to 50, above the factor of 4expected in strong unmodified shocks. For SN 1006, the rapid shrinkage rulesout magnetic damping models. It also favors short mean free paths (smalldiffusion coefficients) and strong dependence of $D$ on energy ($\mu \ge 1$).

Magnetic-Field Amplification in the Thin X-ray Rims of SN1006