Design and Experimental Field Mapping of Merritt Coil System for Polarized ³He Precision Measurements

Highly polarized ³He is widely used in precision magnetometry, neutron spin filtering, and fundamental symmetry tests, where magnetic field gradients can shorten relaxation and coherence times and introduce systematic uncertainties. We present the design, modeling, and experimental characterization of a compact four-square-coil Merritt system developed to provide a uniform holding field for precision measurements of polarized ³He. The magnetic field is calculated directly from analytical vector potentials and analyzed using a near-center expansion. By combining Maxwell's equations with the spatial symmetries of square- and circular-coil systems, we show that the dominant second-order transverse gradients within the small central cell volume are determined by the axial curvature of Bz. The relevant gradient performance can therefore be characterized using a single axial scan, without routine complete three-dimensional mapping. The calculated performance of the Merritt configuration is quantitatively compared with that of the Helmholtz, Lee-Whiting, and Garrett systems. A prototype is constructed and measured using a three-axis fluxgate magnetometer mounted on a motorized translation stage.The measured axial field agrees well with the calculated profile, and the normalized magnetic field gradient in the central 10 cm region is below 10-4 cm^-1. This region fully covers the cylindrical ³He cell, whose diameter and length are both no greater than 5 cm. The Merritt configuration therefore provides a practical compromise between gradient suppression, compactness, optical access, and mechanical simplicity for polarized noble- gas sensors and precision measurements.