  The scientific community is currently witnessing an expensive and worldwide
race to achieve the highest possible light intensity. Within the next decade
this effort is expected to reach nearly $10^{24}\,\mathrm{W}/\mathrm{cm^2}$ in
the lab frame by focusing of 100 PW, near-infrared lasers. A major driving
force behind this effort is the possibility to study strong-field vacuum
breakdown and an accompanying electron-positron pair plasma via a quantum
electrodynamic (QED) cascade [Edwin Cartlidge, "The light fantastic", Science
359, 382 (2018)]. Whereas Europe is focusing on all-optical 10 PW-class laser
facilities (e.g., Apollon and ELI), China is already planning on co-locating a
100 PW laser system with a 25 keV superconducting XFEL and thus implicitly also
a high-quality electron beam [Station of Extreme Light (SEL) at the Shanghai
Superintense-Ultrafast Lasers Facility (SULF)]. This white paper elucidates the
seminal scientific opportunities facilitated by colliding dense, multi-GeV
electron beams with multi-PW optical laser pulses. Such a multi-beam facility
would enable the experimental exploration of extreme HEDP environments by
generating electron-positron pair plasmas with unprecedented densities and
temperatures, where the interplay between strong-field quantum and collective
plasma effects becomes decisive.
