Precision Measurements of the Neutron Magnetic Form Factor to High Momentum Transfer using Durand's Method

Elastic electron-nucleon scattering provides insights into the spatial distributions of charge and current within nucleons through their electromagnetic form factors. Accurate knowledge of these form factors over a broad range of $Q^2$, the squared four-momentum transfer in the scattering process, reveals details about the nucleon's internal structure. However, high-$Q^2$ data of the nucleon electromagnetic form factor is scarce due to the challenges associated with such measurements. This thesis reports preliminary results from high-precision measurements of the neutron magnetic form factor ($G_M^n$) to unprecedented $Q^2$ using Durand's method, also known as the "ratio" method. Systematic errors are greatly reduced by extracting $G_M^n$ from the ratio of neutron-coincident ($D(e,e'n)$) to proton-coincident ($D(e,e'p)$) quasi-elastic electron scattering from deuteron. The scattered electrons were detected in the BigBite spectrometer, which features multiple Gas Electron Multiplier (GEM) layers with large active area for high-precision tracking at very high rates. Simultaneous nucleon detection was performed by the Super BigBite spectrometer, which utilizes a dipole magnet with large solid angle acceptance at forward angles and a novel hadron calorimeter with very high and comparable detection efficiencies for both protons and neutrons. This setup could handle very high luminosity, making high-$Q^2$ measurements feasible. Data were collected at five $Q^2$ points: $3,$ $4.5,$ $7.4,$ $9.9,$ and $13.6$ (GeV/c)$^2$. Preliminary results are reported for all, with the lowest two $Q^2$ points in good agreement with existing world data, while the higher points significantly extend the $Q^2$ range in which $G_M^n$ is known accurately. The precision of the highest $Q^2$ point is expected to remain unmatched for years to come.