Superconducting pancake coil FEM analysis for very low frequency levitated gravity accelerometers

Abstract

State-of-the-art detectors are necessary to measure very tiny variations of gravity produced by spiraling neutron stars, merging black holes and moving tectonic plates. We are developing a superconducting gravity gradiometer and aim to achieve 0.1 mE Hz−1/2 (1 E ≡ 10–9 s–2) in the frequency band of 0.1 mHz to 0.1 Hz. The superconducting test masses are levitated by a superconducting current-carrying monolayer pancake coil, which is one of the key components of the instrument. However, the nonlinear aspect of the pancake coil inductance with respect to the coil to test mass separation imposes one of the main constraints to achieve such sensitivity at low frequencies. In this paper, we investigate the causes of that nonlinearity by finite element method using COMSOL Multiphysics® simulation software. Inductances were measured with an experimental setup where a gap spacing, created by a pancake coil and a niobium plate, could be adjusted. The inductances computed with a 2D axis-symmetric model satisfactorily agreed with the experimental data. We extensively studied several mechanisms for cancelling the nonlinearity of the inductance. A solenoid next to the pancake coil is possibly the most effective and practical way to mitigate it. Our approach may also be useful for obtaining a simple and effective model to study magnetostatic problems in a superconductor.