Early phase of shock formation in pair plasma colliding with electron-proton plasma

We investigate the collisionless interaction between an electron-positron pair plasma and a magnetized electron-proton plasma using a three-dimensional particle-in-cell simulation. Our aim is to resolve the early stage of the formation of a discontinuity separating the inner cocoon formed by shocked pair plasma from the outer cocoon in relativistic jets and pair-plasma winds. An initially unmagnetized pair plasma impacts a background plasma permeated by a magnetic field perpendicular to the collision direction. The relative speed is 60% of the speed of light. The drift of electrons and positrons along the sharp, initially planar magnetic boundary destabilizes the boundary, fragmenting it into an ensemble of magnetic flux tubes. The magnetically reflected pair plasma then drives a strong, mildly relativistic shock mediated by the filamentation instability in front of the boundary. The heated and compressed pair plasma pushes the flux tubes deeper into the electron-proton plasma. The electric fields induced by the moving flux tubes and by the unequal densities of electrons and positrons behind the boundary accelerate ambient protons. The simulation resolves the intrinsic spatial and temporal scales governing flux-tube formation and pair shock evolution, providing quantitative guidance for laboratory laser-plasma experiments while directly informing models of astrophysical shocks.