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Recent observations of the remnant of SN 1006 AD by the ASCA satellite (Koyama et al.~1994) have revealed featureless power-law spectra from parts of the remnant, resolving the controversy about the presence or absence of emission lines from this young remnant. Evidently X-rays from the interior and the fainter limbs are thermal while those from the brightest limbs in X-rays (and radio) are nonthermal. Synchrotron X-rays at 10 keV imply electrons with energies of order 100 TeV. Such electrons can be produced by the shock acceleration mechanism under proper conditions. The maximum energy to which electrons can be accelerated depends on the shock velocity, the magnetic-field strength, and the nature of diffusive scattering, possibly including geometrical effects associated with the obliquity angle between the shock normal and the upstream magnetic field (Jokipii 1987). I describe calculations of X-ray synchrotron emission from adiabatic-phase SNRs expanding into a uniformly magnetized medium. The calculations include self-consistent determination of the maximum electron energy as a function of shock obliquity, evolution of the shock strength, and radiative and adiabatic losses on electrons. I present both integrated spectra from radio to X-rays, and model images at different X-ray energies. At very high energies, higher electron energies may be reached around the ``equator'' of the remnant where the obliquity angle is nearly $90^\circ$, resulting in a bipolar or ``barrel-shaped'' morphology. Although the electron energy spectrum immediately behind the shock drops exponentially above the local maximum energy, the remnant's inhomogeneity in time and space results in a much more gradual steepening of the integrated synchrotron photon spectrum, so that the spectrum may be well-fit by a power law in an X-ray bandpass.
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\noindent Jokipii, J.R. 1987, ApJ, 313, 842
\noindent Koyama, K., et al. 1994, preprint
