  High intensity laser facilities are expanding their scope from laser and
particle-acceleration test beds to user facilities and nuclear physics
experiments. A basic goal is to confirm long-standing predictions of
strong-field quantum electrodynamics, but with the advent of high-repetition
rate laser experiments producing GeV-scale electrons and photons, novel
searches for new high-energy particle physics also become possible. The common
figure of merit for these facilities is the invariant $\chi\simeq
2\gamma_e|\vec E_{\rm laser}|/E_c$ describing the electric field strength in
the electron rest frame relative to the ``critical'' field strength of quantum
electrodynamics where the vacuum decays into electron-positron pairs. However,
simply achieving large $\chi$ is insufficient; discovery or validation requires
statistics to distinguish physics from fluctuations. The number of events
delivered by the facility is therefore equally important. In high-energy
physics, luminosity quantifies the rate at which colliders provide events and
data. We adapt the definition of luminosity to high-intensity laser-electron
collisions to quantify and thus optimize the rate at which laser facilities can
deliver strong-field QED and potentially new physics events. Modeling the
pulsed laser field and electron bunch, we find that luminosity is maximized for
laser focal spot size equal or slightly larger than the diameter of the dense
core of the electron bunch. Several examples show that luminosity can be
maximized for parameters different from those maximizing the peak value of
$\chi$ in the collision. The definition of luminosity for electron-laser
collisions is straightforwardly extended to photon-laser collisions and lepton
beam-beam collisions.
