  The spectrum of cosmic ray protons and electrons released by supernova
remnants throughout their evolution is poorly known, because of the difficulty
in accounting for particle escape and confinement in the downstream of a shock
front, where both adiabatic and radiative losses are present. Here we calculate
the spectrum of cosmic ray protons released during the evolution of supernovae
of different types, accounting for the escape from upstream and for adiabatic
losses of particles advected downstream of the shock and liberated at later
times. The same calculation is carried out for electrons. The magnetic field in
the post-shock region is calculated by using an analytic treatment of the
magnetic field amplification due to non--resonant and resonant streaming
instability and their saturation. We find that when the field is the result of
the growth of the cosmic-ray--driven non--resonant instability alone, the
spectrum of electrons and protons released by a supernova remnant are indeed
different, but such a difference becomes appreciable only at energies $\gtrsim
100-1000$ GeV, while observations of the electron spectrum require such a
difference to be present at energies as low as $\sim 10$ GeV. An effect at such
low energies requires substantial magnetic field amplification in the late
stages of the supernova remnant evolution (shock velocity $\ll 1000$ km/s),
perhaps not due to streaming instability but hydrodynamical processes. We
comment on the feasibility of such conditions and speculate on the possibility
that the difference in spectral shape between electrons and protons may reflect
either some unknown acceleration effect, or additional energy losses in cocoons
around the sources.
