Determining AC Magnetic Susceptibility of Kilogram-Level Test Masses for TianQin

Abstract The effect from the interaction of the alternating current (AC) magnetic field with kilogram-level test mass (TM) limits the detectivity of the TianQin space-based gravitational wave detection. The quantified effect requires the determination of the AC magnetic susceptibility χ ( f ) of the TM. A torque method is proposed to measure the χ ( f ) of kg-level samples at the mHz band with a precision of 1 × 10 −7 . Combined with our previous work [ Phys. Rev. Appl. 18 044010 (2022) ], the general frequency-dependent susceptibility of the alloy cube with side length L and electrical conductivity σ is determined as χ ( f ) = χ 0 + (0.24 ± 0.01) σμ 0 L 2 f from 0.1 mHz to 1 Hz. The determination is helpful for the preliminary estimation of the in-band eddy current effect in the TianQin noise budget. The technique can be adopted to accurately measure χ ( f ) of the actual TM in other precision experiments, where the magnetic noise is a significant detection limit.