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The collision of ultrashort high-density $e^-$ or $e^-$ and $e^+$ beams at10s of GeV, to be available at the FACET II and in laser wakefield acceleratorexperiments, can produce highly collimated $\gamma$ rays (few GeVs) with peakbrilliance of $10^{27}~\mathrm{ph/s~mm^2 mrad^2 0.1\% BW}$ and up to $10^5$nonlinear Breit-Wheeler pairs. We provide analytical estimates of the photonsource properties and of the yield of secondary pairs, finding excellentagreement with full-scale 3D self-consistent particle-in-cell simulations thatinclude quantum electrodynamics effects. Our results show that beam-beamcollisions can be exploited as secondary sources of $\gamma$ rays and providean alternative to beam-laser setups to probe quantum electrodynamics effects atthe Schwinger limit.

Bright $\gamma$ rays source and copious nonlinear Breit-Wheeler pairs in the collision of high density particle beams