Signatures for strong-field QED in the quantum limit of beamstrahlung

Signatures of strong-field quantum electrodynamics are determined for collisions between round ultrarelativistic leptonic beams in the quantum limit of beamstrahlung. In the low disruption regime, we derive the integrated beamstrahlung photon spectrum that features a characteristic peak close to the beam energy. The conditions to precisely observe this peak experimentally are given regarding the beam parameters. Moreover, the effects of electron-positron pair creation and beam disruption on the photon spectrum are discussed and explored with 3-dimensional particle-in-cell QED simulations. The photon spectrum is associated with the emission of ultrashort and highly collimated gamma-ray beams with a peak spectral brightness exceeding $10^{30}\ \mathrm{photons}/(\mathrm{s}\ \mathrm{mm}^2\ \mathrm{mrad}^2\ 0.1\% \mathrm{BW})$ at $100\ \mathrm{GeV}$-level photon energies (close to the beam energy).