Magnetic Field Approximation with Radial Basis Function Interpolation for the LANL nEDM Experiment

The Los Alamos neutron EDM experiment aims to measure the neutron’s electric dipole moment with a uncertainty of 3 × 10⁻²⁷ e·m in a double ultracold neutron storage cell apparatus. To reach this target, we require magnetic effective field stability of < 150 fT over 500 s, accomplished with a combination of magnetic shielding and magnetometry. The experiment will use an array of external scalar magnetometers with optically pumped magnetometers (OPMs) as well as potential ¹⁹⁹Hg comagnetometers. Since scalar magnetometers and the neutron spins measure only the field magnitude, we can approximate the magnitude of the field averaged over the storage cells using interpolation techniques. Radial Basis Function (RBF) interpolation is well-suited for interpolation problems with sparse, irregularly spaced (meshless) measurement nodes. An RBF φ(r) must be positive definite and depends only on the radial distance from each measurement node. The interpolation algorithm optimizes over a linear combination of the RBFs from each node. In simulations of a magnetic field with 10 pT variations across the two cells, the RBF interpolation with stable magnetometers at 35 measurement nodes recovered the change of the field to ∼10 fT. Ongoing work has the goal to reach the sensitivity goal or better with a reduced number of magnetometers.