Gas damping force noise on a macroscopic test body in an infinite gas reservoir

Abstract

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 against 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 accurate 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.

Absolute pressure and gas species identification with an optically levitated rotor

“…The torsional drag β rot has been shown to scale inversely to the thermal velocity and thus β rot ∝ m 1/2 0 , with m 0 the molecular mass, validating the rotational dynamics presented here and in Ref. [13], and opening the possibility to measure the effective molecular mass of a mixture of gases without ionization, and directly in moderate vacuum.…”

“…By comparison, spinning-rotor gauges measure the torsional drag induced by residual gas on a macroscopic rotor (an idea originally proposed by Maxwell [9]) which in existing devices is generally magnetically levitated. At high vacuum, in the molecular flow regime, such drag can be simply related to the pressure [10][11][12][13], resulting in an absolute calibration. The minimum measurable pressure, approximately 5 × 10 −7 mbar, is usually limited * cblakemo@stanford.edu † Now at SRI International, Boulder, Colorado 80302 by systematic uncertainties or the required integration times [12,14,15].…”

Sensitivity of the Advanced LIGO detectors at the beginning of gravitational wave astronomy

“…This noise is amplified by a factor of ∼10 below 100 Hz due to the small gap of 5 mm between the end test and reaction masses [63] (the top view of a test mass and its surroundings is shown in Fig. 7).…”

Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics

“…The effective frequencies w m,eff and w f,eff and damping constants g m,eff and f D ,eff introduced in table 1 take the following form The damping constants g m and f D can be expressed in terms of the parameters of the system [56] g p p p p = + + where P is the pressure of the surrounding gas of particles of mass m gas . For the vibrational motion along the symmetry axis the damping rate g m must be substituted by the following expression [56]…”

“…In general a shear force component will appear in addition to the normal component. Detailed calculations have been carried out analytically for a gas of particles within an infinite volume [56]. For a cube it is found that the ratio of rotational to vibrational noise is a a > ¥  -0.226 gas CSL .…”