Explicitly time-dependent , nonlinear kinetic theory of cosmic ray ( CR ) acceleration in supernova remnants ( SNRs ) has been employed to investigate the properties of SNR RX J1713.7-3946 . Observations of the nonthermal radio and X-ray emission spectra as well as earlier H.E.S.S . measurements of the very high energy \gamma -ray emission were used to constrain the astronomical and the particle acceleration parameters of the system . The model assumes that the object was a core collapse supernova ( SN ) with a massive progenitor , has an age of \approx 1600 yr and is at a distance of \approx 1 kpc . It is shown that an efficient production of nuclear CRs , leading to strong shock modification and a large downstream magnetic field strength B _ { \mathrm { d } } \sim 100 \mu G , can reproduce the observed synchrotron emission from radio to X-ray frequencies together with the \gamma -ray spectral characteristics as observed by the H.E.S.S . telescopes . Small-scale filamentary structures observed in nonthermal X-rays provide empirical confirmation for this field amplification scenario which leads to a strong depression of the inverse Compton and Bremsstrahlung fluxes . The results are compared with the latest H.E.S.S . observations .