Novel emergent phenomena are expected to occur under conditions exceeding the QED critical electric field, where the vacuum becomes unstable to electron-positron pair production. The required intensity to reach this regime, $sim10^{29},mathrm{Wcm^{-2}}$, cannot be achieved even with the most intense lasers now being planned/constructed without a sizeable Lorentz boost provided by interactions with ultrarelativistic particles. Seeded laser-laser collisions may access this strong-field QED regime at laser intensities as low as $sim10^{24},mathrm{Wcm^{-2}}$. Counterpropagating e-beam--laser interactions exceed the QED critical field at still lower intensities ($sim10^{20},mathrm{Wcm^{-2}}$ at $sim10,mathrm{GeV}$). Novel emergent phenomena are predicted to occur in the QED plasma regime, where strong-field quantum and collective plasma effects play off one another. Here the electron beam density becomes a decisive factor. Thus, the challenge is not just to exceed the QED critical field, but to do so with high quality, approaching solid-density electron beams. Even though laser wakefield accelerators (LWFA) represent a very promising research field, conventional accelerators still provide orders of magnitude higher charge densities at energies $gtrsim10,mathrm{GeV}$. Co-location of extremely dense and highly energetic electron beams with a multi-petawatt laser system would therefore enable seminal research opportunities in high-field physics and laboratory astrophysics. This white paper elucidates the potential scientific impact of multi-beam capabilities that combine a multi-PW optical laser, high-energy/density electron beam, and high-intensity x rays and outlines how to achieve such capabilities by co-locating a 3-10 PW laser with a state-of-the-art linear accelerator.
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