  Recent observations of non-thermal X-rays from supernova remnants have been
attributed to synchrotron radiation from the loss-steepened tail of a
non-thermal distribution of electrons accelerated at the remnant blast wave. In
diffusive shock acceleration, the maximum particle energy depends on the
energy-dependence of the diffusion coefficient kappa. Most work on shock
acceleration has made the plausible assumption that kappa is proportional to
the particle gyroradius, implying a wavelength-independent spectrum of MHD
turbulence, where Kolmogorov or Kraichnan spectra might be more physically
plausible. I derive the wave-spectrum-dependence of the maximum electron energy
resulting from limitations due to radiative (synchrotron and inverse-Compton)
losses and to finite remnant age (or size). I then exhibit calculations of
synchrotron X-ray spectra, and model images, for supernova remnants as a
function of spectrum, and compare to earlier results. Spectra can be
considerably altered, and images are dramatically different, for Kolmogorov or
Kraichnan spectra of turbulence. The predicted images are quite unlike observed
remnants, suggesting that the turbulence near SNRs is generated by the
high-energy particles themselves.
