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S.P. Reynolds (NC State U.)
Recent observations of nonthermal X-rays from supernova remnants have been attributed to synchrotron radiation from the loss-steepened tail of a nonthermal distribution of electrons accelerated at the remnant blast wave. In the test-particle limit of diffusive shock acceleration, in which the energy in shock-accelerated particles is unimportant, the slope of a shock-accelerated power-law is independent of the diffusion coefficient \kappa, and on how \kappa depends on particle energy. However, the maximum energy to which particles can be accelerated depends on the rate of acceleration, and that does depend on the energy-dependence of the diffusion coefficient. If the time to accelerate an electron from thermal energies to energy E \gg me c2 is \tau(E), and if \kappa \propto E\beta, then \tau(E) \propto E\beta as well. Most work on shock acceleration has made the plausible assumption that \kappa \propto rg (where rg is the particle gyroradius), so that \beta = 1 at relativistic energies. However, that choice corresponds to a particular (wavelength-independent) spectrum of MHD turbulence, where Kolmogorov or Kraichnan spectra might be more physically plausible. I derive the \beta-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 \beta and compare to earlier \beta = 1 results. The dependences of spectra on shock velocity and magnetic-field strength are considerably altered for \beta \ne 1.