Electrostatically suspended torsion pendulum

A torsion pendulum without a torsion wire has been designed and realized, in order to measure very weak forces. The arm of this torsion pendulum (5.40 g, 1.32×10−6 kg m2 of inertia) is electrostatically suspended. Its 6 degrees of freedom are controlled thanks to electrostatic forces, and capacitive position sensing with a noise spectral density between 10−10 and 10−13 m/Hz. The torque noise spectral density is 1.3×10−14 Nm/Hz around 0.05 Hz with a 1/f increase at lower frequency, corresponding to 10−8 rad/s2/Hz, and 2×10−10 ms−2/Hz with a lever arm of 2 cm. The residual seismic noise limit the performances above 0.1 Hz. The free oscillating mode has a torsion stiffness of 5.14×10−8 Nm/rad and a Q of 217. This new instrument allows on ground experiments on very weak parasitic forces inside space accelerometers developed in ONERA, with a good representativeness. For example, it is possible to measure electrostatic stiffnesses with high resolution thanks to the low torque noise spectral density; the electrostatic damping phenomenon is also well seen as illustrated by the rather low Q. The instrument design and operation are described, the main performances are given, and the possibilities offered are discussed.