  The Telescope Array (TA) of central Utah was designed to detect
ultra-high-energy cosmic rays (UHECRs) and is the largest of its kind in the
Northern hemisphere. Its capabilities, however, are not limited to
extra-terrestrial sources. Scintillation detectors (SDs) in the array are
designed to measure energy deposit from charged cosmic ray secondaries, but
have recently caught bursts of electromagnetic radiation that do not match the
typical signature of cosmic ray air showers. After investigation, the bursts
were tied to individual lightning strikes. In an effort to better understand
the phenomenon, Langmuir Laboratory for Atmospheric Research at New Mexico Tech
provided specialized lightning detectors across the array, eventually
confirming the events as downward terrestrial gamma-ray flashes (TGFs) produced
in the first few microseconds of lightning flashes. After 20 identified TGFs
and 2 publications, the lightning instrumentation at Telescope Array was
upgraded in the summer of 2018 with the addition of a broadband interferometer
(INTF) for high-resolution lightning mapping. This unique variety of lightning
detectors has become one of the leading studies of downward TGFs. This
dissertation is focused on the application of this method and resultson four
events from late 2018. The individual TGFs lasted <10 us and likely consisted
of >10^12 gamma-rays, with evidence of some energies >2.6 MeV. I determined TGF
source times, plan locations, and altitudes with average uncertainties of 0.6
us, 140 m, and 25 m, respectively. This high resolution showed that TGFs in all
four of these events occured during strong initial breakdown pulses and was
driven by streamer-based fast negative breakdown in the first couple
milliseconds of negative intracloud and cloud-to-ground lightning flashes.
