  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.
