Design and Implementation of the ABRACADABRA-10 cm Axion Dark Matter Search

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.