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

The measurement of ac susceptibility χ(ω) down to 0.10.2em0exmHz 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 χ(ω) of centimeter-scale test mass from 500.2em0exμHz to $80$ Hz. The measurement resolution can reach a level of 10^-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.