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