Light dark matter in the context of dark sector theories is an attractive candidate for the dark matter thought to make up the bulk of the mass of our universe. We explore here the possibility of using a low-pressure, negative-ion, time projection chamber detector to search for light dark matter behind the beam dump of an electron accelerator. The sensitivity of a 10 m long detector is several orders of magnitude better than existing limits. This sensitivity includes regions of parameter space where light dark matter is predicted to have a required relic density consistent with measured dark matter density. Backgrounds at shallow depth will need to be considered carefully. However, several signatures exist, including a powerful directional signature, which will allow a detection even in the presence of backgrounds.
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