The nonlinear kinetic model of cosmic ray ( CR ) acceleration in supernova remnants ( SNRs ) is used to describe the relevant properties of Cassiopeia A ( Cas A ) .
In order to reproduce the SNR ’ s observed size , expansion rate and thermal X-ray emission we employ a piecewise homogeneous model for the progenitor ’ s circumstellar medium developed by .
It consists of a tenuous inner wind bubble , a dense shell of swept-up red supergiant wind material , and a subsequent red supergiant wind region .
A quite large SNR interior magnetic field B _ { \mathrm { d } } \approx 1 \mathrm { mG } is required to give a good fit for the radio and X-ray synchrotron emission .
The steep radio spectrum is consistent with efficient proton acceleration which produces a significant shock modification and leads to a steep electron spectrum at energies \epsilon _ { \mathrm { e } } < 1 \mathrm { GeV } .
The calculated integral \gamma -ray flux from Cas A , F _ { \gamma } \propto \epsilon _ { \gamma } ^ { -1 } , is dominated by \pi ^ { 0 } -decay \gamma -rays due to relativistic protons .
It extends up to roughly 30 \mathrm { TeV } if CR diffusion is as strong as the Bohm limit .
At TeV energies it satisfactorily agrees with the value 5.8 \times 10 ^ { -13 } \mathrm { cm } ^ { -2 } \mathrm { s } ^ { -1 } detected by the HEGRA collaboration .