  Energetic positrons have been observed in the interstellar medium, and
high-energy positrons with relativistic energies up to approximately 1 TeV have
been detected in Galactic cosmic rays. We conducted a study on the acceleration
of particles, specifically positrons, in a nonrelativistic quasiparallel
collisionless shock induced by a plasma consisting of protons, electrons, and
positrons. The positron-to-proton number density ratio in the plasma is 0.1. We
focused on a representative shock with a sonic Mach number of 17.1 and an
Alfv\'{e}nic Mach number of 16.8 in the rest frame of the shock. To investigate
the acceleration mechanisms of particles including positrons in the shock, we
utilized one-dimensional particle-in-cell (PIC) simulations. It was found that
all three species of particles in the shock can be accelerated and exhibit
power law spectra. At the shock front, a significant portion of incoming
upstream particles are reflected and undergo significant energy increase, and
these reflected particles can be efficiently injected into the process of
diffusive shock acceleration (DSA). Moveover, the reflected positrons can be
further accelerated by an electric field parallel to the magnetic field when
they move along the magnetic field upstream of the shock. As a result,
positrons can be preferentially accelerated to be injected in the DSA process
compared to electrons.
