  High-intensity neutrino beam facilities may produce a beam of light dark
matter when protons strike the target. Searches for such a dark matter beam
using its scattering in a nearby detector must overcome the large neutrino
background. We characterize the spatial and energy distributions of the dark
matter and neutrino beams, focusing on their differences to enhance the
sensitivity to dark matter. We find that a dark matter beam produced by a $Z'$
boson in the GeV mass range is both broader and more energetic than the
neutrino beam. The reach for dark matter is maximized for a detector sensitive
to hard neutral-current scatterings, placed at a sizable angle off the neutrino
beam axis. In the case of the Long-Baseline Neutrino Facility (LBNF), a
detector placed at roughly 6 degrees off axis and at a distance of about 200 m
from the target would be sensitive to $Z'$ couplings as low as 0.05. This
search can proceed symbiotically with neutrino measurements. We also show that
the MiniBooNE and MicroBooNE detectors, which are on Fermilab's Booster
beamline, happen to be at an optimal angle from the NuMI beam and could perform
searches with existing data. This illustrates potential synergies between LBNF
and the short-baseline neutrino program if the detectors are positioned
appropriately.
