Diffusive Shock Acceleration of Electrons and Radio Emission from Large   Diameter Shell-Type Supernova Remnants
  In present study I examine the capability of diffusive shock acceleration mechanism to explain existing data on radio emission from evolved large diameter shell-type adiabatic supernova remnants (SNRs). Time-dependent ''onion-shell'' model for the radio emission of SNRs is developed, which is based on the assumptions: a) acceleration takes place from thermal energies and test-particle approximation is valid; b) the problem of injection is avoided by introducing, like Bell (1978), two injection parameters; c) to take into consideration very late stages of SNR evolution the analytic approximation of Cox and Andersen (1982) for the shell structure is used; c)no radiative cooling. Constructed Surface Brightness - Diameter $(\Sigma -D)$ tracks are compared with the empirical $\Sigma -D$ diagram. The main conclusion of the study is that the DSA mechanism is capable of explaining all the statistics of radio SNRs including very large diameter remnants and giant galactic loops. 
A.I.Asvarov