Stochastic Electron Acceleration in Shell-Type Supernova Remnants
  We study the stochastic electron acceleration by fast mode waves in the turbulent downstream of weakly magnetized collisionless astrophysical shocks. The acceleration is most efficient in a dissipative layer, and the model characteristics are determined by the shock speed, density, magnetic field, and turbulence decay length. The model explains observations of shell-type supernova remnants RX J1713.7-3946 and J0852.0-4622 and can be tested by observations in hard X-rays with the HXMT and NuSTAR or gamma-rays with the GLAST. 
Siming Liu, Zhong-Hui Fan, Christopher L. Fryer, Jian-Min Wang, and   Hui Li