Nonlinear Particle Acceleration at Reverse Shocks in Supernova Remnants
  Without amplification, magnetic fields in expanding ejecta of young supernova remnants (SNRs) will be orders of magnitude below those required to shock accelerate thermal electrons, or ions, to relativistic energies or to produce radio synchrotron emission at the reverse shock. The reported observations of such emission give support to the idea that diffusive shock acceleration (DSA) can amplify magnetic fields by large factors. Furthermore, the uncertain character of the amplification process leaves open the possibility that ejecta fields, while large enough to support radio emission and DSA, may be much lower than typical interstellar medium values. We show that DSA in such low reverse shock fields is extremely nonlinear and efficient in the production of cosmic-ray (CR) ions, although CRs greatly in excess of mc^2 are not produced. These nonlinear effects, which occur at the forward shock as well, are manifested most importantly in shock compression ratios much greater than four and cause the interaction region between the forward and reverse shocks to become narrower, denser, and cooler than would be the case if efficient cosmic-ray production did not occur. The changes in the SNR structure and evolution should be clearly observable, if present, and they convey important information on the nature of DSA and magnetic field amplification with broad astrophysical implications. 
Donald C. Ellison, Anne Decourchelle and Jean Ballet