Accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior measurements, I. Boundary-value techniques

摘要

We propose a new concept for determining the interior magnetic field vectorcomponents in neutron electric dipole moment experiments. If a closedthree-dimensional boundary surface surrounding the fiducial volume of anexperiment can be defined such that its interior encloses no currents orsources of magnetization, each of the interior vector field components and themagnetic scalar potential will satisfy a Laplace equation. Therefore, if eitherthe vector field components or the normal derivative of the scalar potentialcan be measured on the surface of this boundary, thus defining a Dirichlet orNeumann boundary-value problem, respectively, the interior vector fieldcomponents or the scalar potential (and, thus, the field components via thegradient of the potential) can be uniquely determined via solution of theLaplace equation. We discuss the applicability of this technique to thedetermination of the interior magnetic field components during the operatingphase of neutron electric dipole moment experiments when it is not, in general,feasible to perform direct in situ measurements of the interior fieldcomponents. We also study the specifications that a vector field probe mustsatisfy in order to determine the interior vector field components to a certainprecision. The technique we propose here may also be applicable to experimentsrequiring monitoring of the vector magnetic field components within some closedboundary surface, such as searches for neutron-antineutron oscillations along aflight path or measurements in storage rings of the muon anomalous magneticmoment $g-2$ and the proton electric dipole moment.