Generating ultradense pair beams using 400 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>GeV</mml:mi><mml:mo>/</mml:mo><mml:mi>c</mml:mi></mml:math> protons

A previously unexplored experimental scheme is presented for generating low-divergence, ultra-dense, relativistic, electron-positron beams using 400 GeV/c protons available at facilities such as HiRadMat and AWAKE CERN. Preliminary Monte-Carlo Particle-in-cell simulations demonstrate the possibility of containing $10^{13}-10^{14}$ pairs sufficiently high densities to drive collisionless beam-plasma instabilities, which are expected play an important role in magnetic field generation related radiation signatures relativistic astrophysical phenomena. The pair quasi-neutral, with size exceeding several skin-depths all dimensions, allowing first time examination effect competition between transverse longitudinal instability modes on growth fields. Furthermore, allows controlling relative density hadrons beam, making it possible explore parameter spaces different environments.