  We present the particle-in-cell (PIC) simulation results of the interaction
of a high-energy lepton plasma flow with background electron-proton plasma and
focus on the acceleration processes of the protons. It is found that the
acceleration follows a two-stage processes. In the first stage, protons are
accelerated transversely (perpendicular to the lepton flow) by the turbulent
magnetic field "islands" generated via the strong Weibel-type instabilities.
The accelerated protons shows a perfect inverse-power energy spectrum. As the
interaction continues, a shockwave structure forms and the protons in front of
the shockwave are reflected at twice of the shock speed, resulting in a
quasi-monoenergetic peak located near 200MeV under the simulation parameters.
