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

Two-stage acceleration of interstellar ions due to the interaction of high-energy lepton plasma flow