Temporal Extent of Surface Potentials between Closely Spaced Metals

Abstract

Variations in the electrostatic surface potential between the proof mass and electrode housing in the space-based gravitational wave mission Laser Interferometer Space Antenna (LISA) is one of the largest contributors of noise at frequencies below a few mHz. Torsion balances provide an ideal test bed for investigating these effects in conditions emulative of LISA. Our apparatus consists of a Au coated Cu plate brought near a Au coated Si plate pendulum suspended from a thin W wire. We have measured a white noise level of 30 microV/sqrt Hz above approximately 0.1 mHz, rising at lower frequencies, for the surface potential variations between these two closely spaced metals.

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

“…These arise in different exposed crystalline facets and surface contamination. Typical observed average potential differences between roughly centimeter-size regions of a gold surface are of order 10-100 mV [16][17][18][19].…”

“…[18] are readily applicable to the LISA geometry. To compare with ∆ x , which is normalized to the size of a single LISA X electrode, those results (for linear spectral noise density) must be multiplied by a factor 5-6 for any characteristic domain sizes up to the dimensions (≈ 2000 mm 2 ) of the surfaces measured.…”

“…This significantly improves upon previous upper limits with LISA prototype hardware, from roughly 1 mV/Hz 1/2 [17] to 80 µV/Hz 1/2 at 1 mHz. The limit is also below the 150-200 µV/Hz 1/2 deduced for S 1/2 ∆x at 1 mHz from observations of potential fluctuations between opposing goldcoated plates [18,32].…”

“…6), we want ∆ x < 10 mV. This will likely require in-flight measurement and compensation of intrinsic imbalances typically of order 100 mV, repeated periodically, given the slow drifts observed here and elsewhere [18]. Additionally, analysis and measurements indicate that errors associated with the Zmodulation technique may not allow 10 mV accuracy.…”

“…At right is the geometry of Ref. [18], in which an average potential difference is measured between one half of the suspended plate and a facing electrode plate of width L 2 = 57.2 mm and area A = 2180 mm 2 .…”