  We discuss the acceleration and escape of secondary particles, especially
positrons produced by hadronic interactions in a supernova remnant (SNR) shock.
During the shock acceleration, protons would interact with ambient gas and
produce charged secondary particles, which would also be accelerated in a SNR
and injected into the interstellar medium as cosmic-rays (CRs). Some previous
studies showed that the resulting positron spectrum at the SNR shock is harder
than the primary proton spectrum, and proposed that the positron excess
observed by PAMELA can be explained with this process. We calculate the energy
spectra of CR protons and secondary CR positrons running away from the SNR into
the interstellar medium according to the phenomenological model of
energy-dependent CR escape. We show that, on the contrary to the results
presented previously, the observed spectra of secondary CR particles generated
in SNRs would be softer than those of primary CR particles, which means that
the rise in the positron fraction cannot be reproduced by this model.
