Interaction between Stray Electrostatic Fields and a Charged Free-Falling Test Mass

Abstract

We present an experimental analysis of force noise caused by stray electrostatic fields acting on a charged test mass inside a conducting enclosure, a key problem for precise gravitational experiments. Measurement of the average field that couples to test mass charge, and its fluctuations, is performed with two independent torsion pendulum techniques, including direct measurement of the forces caused by a change in electrostatic charge. We analyze the problem with an improved electrostatic model that, coupled with the experimental data, also indicates how to correctly measure and null the stray field that interacts with test mass charge. Our measurements allow a conservative upper limit on acceleration noise, of 2 fm/s 2 /Hz 1/2 for frequencies above 0.1 mHz, for the interaction between stray fields and charge in the LISA gravitational wave mission.

Charge-Induced Force Noise on Free-Falling Test Masses: Results from LISA Pathfinder

“…When considered with the uncompensated values measured for Δ x , roughly −20 mV and 0 mV for TM 1 and TM 2, the stray fields in the GRS would seem to be similar in magnitude to those observed in various measurements on GRS prototype hardware on ground [2,30,31]. Small but significant changes in Δ x are observed for the two TMs, consistent with drifts of slightly less than mV/month, roughly an order of magnitude below typical drift values observed, for a limited number of samples, on ground [2,32].…”

“…Δ x originates both from surface patch potentials within the sensor and the GRS electronics. Measurements with representative systems in laboratory tests have found static levels of up to 100 mV [2,[30][31][32]. Tests on a representative electronics unit measured S 1=2 Δ x coming from electrodevoltage fluctuations to be 30 μV Hz −1=2 at 1 mHz [19].…”

“…Electrostatic free charge and stray potentials introduce unwanted disturbances that can limit measurement precision. The effect is relevant for gravitational wave (GW) observatories both in space [1,2] and on-ground [3] tests of the equivalence principal [4] and measurements of relativistic effects on precessing gyroscopes [5].…”

“…We represent these by an effective potential difference between opposite sides of the TM, Δ x , the equivalent uniform single GRS x-electrode potential that would give the same average stray field along the x axis. The resulting force along the x axis, following the notation of [2], is…”

“…Following the method described in [2], it is possible to estimate ∂F x =∂q as a function of V COMP measuring the change in Δg as the charge of one test mass is increased in steps by photoemission under UV illumination. By choosing a value for V COMP that provides an equal and opposite potential difference to Δ x , we can cancel dF x =dq to first order.…”