Sensitivity of fields generated within magnetically shielded volumes to changes in magnetic permeability

Abstract

Future experiments seeking to measure the neutron electric dipole moment (nEDM) require stable and homogeneous magnetic fields. Normally these experiments use a coil internal to a passively magnetically shielded volume to generate the magnetic field. The stability of the magnetic field generated by the coil within the magnetically shielded volume may be influenced by a number of factors. The factor studied here is the dependence of the internally generated field on the magnetic permeability µ of the shield material. We provide measurements of the temperature-dependence of the permeability of the material used in a set of prototype magnetic shields, using experimental parameters nearer to those of nEDM experiments than previously reported in the literature. Our measurements imply a range of 1 µ dµ dT from 0-2.7%/K. Assuming typical nEDM experiment coil and shield parameters gives µ B0 dB0 dµ = 0.01, resulting in a temperature dependence of the magnetic field in a typical nEDM experiment of dB0 dT = 0 − 270 pT/K for B 0 = 1 µT. The results are useful for estimating the necessary level of temperature control in nEDM experiments.

Electric dipole moments of atoms, molecules, nuclei, and particles

“…While these expressions are illustrative, in general, effective design of shields is aided by simulations of Maxwell's equations using finite-element approaches. Additional considerations for passive shields include penetrations (holes), the temperature dependence of the magnetic properties of the shielding material, and the applied internal field, which couples to the shield and may cause a temperature dependence of fields and gradients for the experiment (Andalib et al, 2017). Holes up to 130 mm do not notably change the damping factor.…”

Analytical model for calculation of the magnetic field of triaxial uniform coils in magnetically shielded cylinder

“…When the coil is placed inside the hollow cylinder with high permeability material, the coil then turns the innermost magnetic shielding material into a return yoke; i.e. the magnetic field lines that emanate from the coil are returned through the shield, thus increasing the coil's magnetic field [29]. The influence of the hollow cylinder with linear and uniform magnetic permeability on the internal coil can be calculated based on the equivalent current bound to the material surface.…”

“…For the Lee-Whiting coil, κ tends toward a stable value of 1.13; for the saddle coil, κ tends toward a stable value of 1.69. When the relative magnetic permeability is less than 10 000, then the permeability of the innermost magnetic shield that is affected by the temperature fluctuations will result in internal magnetic field instability for the MSC, thus causing measurement errors and sensor drift [29]. Therefore, it is recommended that a material with a relative magnetic permeability of more than 10 000 is used when designing the MSCs to ensure the internal magnetic field's stability.…”

A Three-step Model for Optimizing Coil Spacings Inside Cuboid-shaped Magnetic Shields

“…The results calculated with the three-step model and with the FEM are in acceptable agreement with the measured values. The slight difference may result from the uncertainty of the position of the SQUID chip, and the fact that µ r is not a constant 40 as was assumed both for FEM calculations and for the three-step model. Nevertheless, both models successfully predict the maximum of the field at y = 6 cm caused by the coupling to the shielding material.…”