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$^2$rthz for frequencies above 0.1 mHz, for the interaction between stray fields and charge in the LISA gravitational wave mission.
We present an analysis of Brownian force noise from residual gas damping of reference test masses as a fundamental sensitivity limit in small force experiments. The resulting acceleration noise increases significantly when the distance of the test ma
ss to the surrounding experimental apparatus is smaller than the dimension of the test mass itself. For the Advanced LIGO interferometric gravitational wave observatory, where the relevant test mass is a suspended 340 mm diameter cylindrical end mirror, the force noise power is increased by roughly a factor 40 by the presence of a similarly shaped reaction mass at a nominal separation of 5 mm. The force noise, of order 20 fNrthz for $2 times 10^{-6}$ Pa of residual H$_2$ gas, rivals quantum optical fluctuations as the dominant noise source between 10 and 30 Hz. We present here a numerical and analytical analysis for the gas damping force noise for Advanced LIGO, backed up by experimental evidence from several recent measurements. Finally, we discuss the impact of residual gas damping on the gravitational wave sensitivity and possible mitigation strategies.
We present a simple analysis of the force noise associated with the mechanical damping of the motion of a test body surrounded by a large volume of rarefied gas. The calculation is performed considering the momentum imparted by inelastic collisions a
gainst the sides of a cubic test mass, and for other geometries for which the force noise could be an experimental limitation. In addition to arriving at an accurated estimate, by two alternative methods, we discuss the limits of the applicability of this analysis to realistic experimental configurations in which a test body is surrounded by residual gas inside an enclosure that is only slightly larger than the test body itself.
