Measuring ac Magnetic Susceptibility at Low Frequencies with a Torsion Pendulum for Gravitational-Wave Detection

Abstract

The measurement of ac susceptibility $\ensuremath{\chi}(\ensuremath{\omega})$ down to $0.1\phantom{\rule{0.2em}{0ex}}\mathrm{mHz}$ of test masses is vital for TianQin, a Chinese space-based gravitational-wave detection mission, since the magnetic induced disturbing force is one of the main contributors to residual acceleration noise of test masses. Here we report a method based on a torsion pendulum with dual magnetic field modulation to measure $\ensuremath{\chi}(\ensuremath{\omega})$ of centimeter-scale test mass from $50\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Hz}$ to $80$ Hz. The measurement resolution can reach a level of ${10}^{\ensuremath{-}8}$, meeting the requirements of TianQin. Meanwhile, this method also provides an important ground-validation approach for the down-converted effects [Phys. Rev. Lett. 120, 061101 (2018)] from ac magnetic fields, potentially reducing the risk of failure in space.