Magnetic Field Finite-Element Calculations for the SNS Neutron EDM Experiment

The nEDM experiment is a new search for the electric dipole moment (EDM) of the neutron with a sensitivity of 10$^{-28}$ \textit{e-cm} at the recently constructed Spallation Neutron Source (SNS). The measurement requires a static magnetic field surrounding two target cells that contain superfluid $^{4}$He, polarized neutrons and polarized $^{3}$He atoms. The latter are used as a co-magnetometer and ultracold neutron spin precession frequency analyzer. The applied static magnetic field, $B_{0}$, is chosen to be about 10 mG resulting in a precession of the magnetic moments for both neutrons and $^{3}$He nuclei of $\sim $30 Hz. To maintain the polarization of the neutrons and $^{3}$He atoms, the magnetic field should be very uniform with gradients of the order of 0.1 $\mu$G/cm~averaged over each cell volume. A separate requirement on the volume-averaged magnetic field gradient $<$dB$_{x}$/dx$>$ in the direction of $B_{0}$ of less than 0.01 $\mu$G/cm is necessary to minimize false EDM signals. In addition, to reduce the influence of ambient external fields an overall magnetic shielding factor of $\sim $10$^{5}$ is required. We present finite-element calculation results for the complete nEDM static magnetic field configuration including magnetic field gradients and $^{3}$He relaxation rates.