Thermal induced noise on test mass with copper alloy electrode housing for spaceborne gravitational wave detection

The temperature gradient effect (TGE) is an important disturbance source in the inertial sensor, the core payload of space gravitational wave detectors. The inertial sensor electrode, made of copper alloy with high thermal conductivity, is expected to achieve lower temperature gradient, but its outgassing characteristics need to be verified experimentally. In this work, we have developed a torsion pendulum and measured the TGE of the copper alloy electrode. The measurement results show that the upper limit of the outgassing effect of this copper alloy gravitational reference sensor is about $18.0\mathrm{pN}/\mathrm{K}$, and the total TGE is less than $30.2\mathrm{pN}/\mathrm{K}$ at 293 K, which can be ignored in the application of gravitational wave detection. Our work reveals key physical properties associated with TGE and provides a viable alternative for specialized equipment applications in spaceborne gravitational wave detection missions and beyond.

Figure 1

Two modes of action for the TGE. (a) Transverse mode. (b) Diagonal mode.

Figure 2

Ground measuring device for the TGE. (a) Schematic diagram of the torsion pendulum. The TM is represented by the middle yellow cube in the structural diagram, and just the $x$ axis is shown here around the surrounding electrodes. (b) The picture shows the way of installing the heater and temperature sensor. (c) Picture of the torsion pendulum used in this experiment.

Figure 3

(a) The temperature difference generated by modulation. (b) Adjusted pressure after changing the opening of the flapper valve every two hours. (c) The motion angle of torsion pendulum was measured by autocollimator. (d) The torque response of the torsion pendulum. As the pressure gradually decreases, the torque response gradually becomes smaller. The average temperature is 293.0(1) K.

Figure 4

Average value of modulate pressure and torque value per unit temperature difference. The average temperature is 293.0(1) K.

Figure 5

Modulation experiments are performed at six different average temperatures. The vertical axis is the total torque of the TGE with per unit temperature difference.

Figure 6

Experimental measurements, fitting curves, and numerical simulations of the radiometer effect. The blue dots are experimental measurements at different average temperatures. The shadowed orange line is the fitting curve with errors. The pink dotted line is the numerical simulations values based on the ${\gamma }_{\mathrm{RM}}$ at Table 1.

Figure 7

Intensity plots of the torque coefficient (a), (b) and the force coefficient (c), (d), normalized by the factor ($2\sigma /3\mathrm{c}$), for emitting points on the X and Y surfaces. The outline of the TM section is shown as a dashed line 50 mm square in each case. The reflection properties: absorption coefficient $a=5\%$, purely specular reflection ($d=0\%$). Legends for the intensity values are shown in the color bars on the right of each plot.

Figure 8

Experimental measurements and fitting curves of the outgassing effect. The blue dots are experimental measurements at different average temperatures. The shadowed orange line is the fitting curve with errors.