Abstract
Abstract In space detection of gravitational waves (GWs), the presence of a low-frequency varying magnetic field will generate eddy currents in the test mass, resulting in a varying magnetic moment. This magnetic moment will couple with a constant magnetic field gradient, producing residual acceleration within the frequency band of GW detection, causing the test mass to deviate from the free-falling mode. However, this effect has not yet been studied clearly in the noise budget for TianQin and LISA Pathfinder since the constant DC magnetic susceptibility was applied to quantify the varying magnetic moment. This paper utilizes the parameter of alternating current (AC) magnetic susceptibility to define this process, and further analyzes and evaluates the effect. In a general magnetic field environment, the contribution of this effect to TianQin acceleration noise reaches 20\% from 0.1 mHz to 3 mHz. The contribution to LISA noise is less than 10\% from $10^{-4}$ to 0.1 Hz, and less than 10\% below $10^{-4}$ Hz. This effect does not have a potential limit on LISA low-frequency science down to 20 $\mu$Hz [Phys. Rev. Lett. 120, 061101 (2018)].
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