  Abbreviated Abstract: A kinetic model of particle acceleration in supernova
remnants (SNRs) is extended to study the cosmic ray (CR) and associated high
energy gamma-ray production during SN shock propagation through the
inhomogeneous circumstellar medium of a progenitor star that emits a strong
wind. The wind forms a low-density bubble surrounded by a swept-up shell of
interstellar matter. Gamma rays are produced as a result of decay of pions
which in turn are the result of collisions of CRs with nuclei of the thermal
plasma. The time evolution of the SNRs is followed numerically, taking into
account the nonlinear backreaction of the accelerated CRs. Examples typical for
SN type Ib and SN type II explosions are considered. Apart from the
confirmation of the known fact that acceleration is extremely rapid and that
the upper momentum cutoff is reached almost immediately after the explosion due
to the high wind magnetic field, it is also shown that the CRs are accelerated
with high efficiency. The CR energy spectrum, ultimately produced in the SNRs,
has a power law form with index = 2.0 to 2.1 in a wide energy range up to a
maximum energy which is about 10^14 eV if the CR diffusion coefficient is as
small as the Bohm limiting value. However, the expected pi^0-decay gamma-ray
flux is considerably lower than in the case of a uniform interstellar medium; a
relatively high gamma-ray luminosity in the TeV band, detectable at distances
of several kpc, is only expected in the case of a relatively dense ISM with a
number density above 10/cc.
