Context :

Aims : Nonlinear kinetic theory of cosmic ray ( CR ) acceleration in supernova remnants ( SNRs ) is used to investigate the properties of Kepler ’ s SNR and , in particular , to predict the \gamma -ray spectrum expected from this SNR .

Methods : Observations of the nonthermal radio and X-ray emission spectra as well as theoretical constraints for the total supernova ( SN ) explosion energy E _ { \mathrm { sn } } are used to constrain the astronomical and particle acceleration parameters of the system .

Results : Under the assumption that Kepler ’ s SN is a type Ia SN we determine for any given explosion energy E _ { \mathrm { sn } } and source distance d the mass density of the ambient interstellar medium ( ISM ) from a fit to the observed SNR size and expansion speed .
This makes it possible to make predictions for the expected \gamma -ray flux .
Exploring the expected distance range we find that for a typical explosion energy E _ { \mathrm { sn } } = 10 ^ { 51 } erg the expected energy flux of TeV \gamma -rays varies from 2 \times 10 ^ { -11 } to 10 ^ { -13 } erg/ ( cm ^ { 2 } s ) when the distance changes from d = 3.4 kpc to 7 kpc .
In all cases the \gamma -ray emission is dominated by \pi ^ { 0 } -decay \gamma -rays due to nuclear CRs .
Therefore Kepler ’ s SNR represents a very promising target for instruments like H.E.S.S. , CANGAROO and GLAST .
A non-detection of \gamma -rays would mean that the actual source distance is larger than 7 kpc .

Conclusions :