Sensitivity requirements for accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior boundary-value measurements

We study the sensitivity requirements for determining the vector components of the magnetic field in the interior regions of electric dipole moment experiments via exterior boundary-value measurements. The basic concept for our method is as follows. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar potential will satisfy a Laplace equation. Therefore, if either the vector field components or the normal derivative of the scalar potential can be measured on the surface of this boundary, thus defining a Dirichlet or Neumann boundary-value problem, respectively, the interior vector field components or the scalar potential (and, thus, the field components via the gradient of the potential) can be uniquely determined via solution of the Laplace equation. We discuss the applicability of this technique to the determination of the interior magnetic field components during the operating phase of neutron electric dipole moment experiments when it is not, in general, feasible to perform direct in situ measurements of the interior field components. We then study the specifications that a vector field probe must satisfy in order to determine the interior vector field components to a certain precision.