  The past few years have seen a renewed interest in the search for light
particle dark matter. ABRACADABRA is a new experimental program to search for
axion dark matter over a broad range of masses, $10^{-12}\lesssim
m_a\lesssim10^{-6}$ eV. ABRACADABRA-10 cm is a small-scale prototype for a
future detector that could be sensitive to QCD axion couplings. In this paper,
we present the details of the design, construction, and data analysis for the
first axion dark matter search with the ABRACADABRA-10 cm detector. We include
a detailed discussion of the statistical techniques used to extract the limit
from the first result with an emphasis on creating a robust statistical footing
for interpreting those limits.
