  The extensive observations of the supernova SN 1993J at radio wavelengths
make this object a unique target for the study of particle acceleration in a
supernova shock. To describe the radio synchrotron emission we use a model that
couples a semianalytic description of nonlinear diffusive shock acceleration
with self-similar solutions for the hydrodynamics of the supernova expansion.
The synchrotron emission, which is assumed to be produced by relativistic
electrons propagating in the postshock plasma, is worked out from radiative
transfer calculations that include the process of synchrotron self-absorption.
The model is applied to explain the morphology of the radio emission deduced
from high-resolution VLBI imaging observations and the measured time evolution
of the total flux density at six frequencies. Both the light curves and the
morphology of the radio emission indicate that the magnetic field was strongly
amplified in the blast wave region shortly after the explosion, possibly via
the nonresonant regime of the cosmic-ray streaming instability operating in the
shock precursor. The turbulent magnetic field was not damped behind the shock
but carried along by the plasma flow in the downstream region. Cosmic-ray
protons were efficiently produced by diffusive shock acceleration at the blast
wave. We find that during the first ~8.5 years after the explosion, about 19%
of the total energy processed by the forward shock was converted to cosmic-ray
energy. However, the shock remained weakly modified by the cosmic-ray pressure.
The high magnetic field amplification implies that protons were rapidly
accelerated to energies well above 1 PeV. The results obtained for this
supernova support the scenario that massive stars exploding into their former
stellar wind are a major source of high-energy Galactic cosmic rays.
