Stochastic Electron Acceleration in Shell-Type Supernova Remnants II
  We discuss the generic characteristics of stochastic particle acceleration by a fully developed turbulence spectrum and show that resonant interactions of particles with high speed waves dominate the acceleration process. To produce the relativistic electrons inferred from the broadband spectrum of a few well-observed shell-type supernova remnants in the leptonic scenario for the TeV emission, fast mode waves must be excited effectively in the downstream and dominate the turbulence in the subsonic phase. Strong collisionless non-relativistic astrophysical shocks are studied with the assumption of a constant Aflven speed. The energy density of non-thermal electrons is found to be comparable to that of the magnetic field. With reasonable parameters, the model explains observations of shell-type supernova remnants. More detailed studies are warranted to better understand the nature of supernova shocks. 
Siming Liu, Zhong-Hui Fan, Christopher L. Fryer