N. A. Lockerbie

The STEP mission: principles and baseline design

The Satellite Test of the Equivalence Principle (STEP) will test the equality of fall of objects in Earth orbit to an accuracy approaching one part in 108 by measuring the difference in rate of fall of test cylinders in cryogenic differential accelerometers in a drag-free satellite. This paper describes the current baseline design and principles used in the design of the STEP mission.

Update on quadruple suspension design for Advanced LIGO

We describe the design of the suspension systems for the major optics for Advanced LIGO, the upgrade to LIGO—the Laser Interferometric Gravitational-Wave Observatory. The design is based on that used in GEO600—the German/UK interferometric gravitational wave detector, with further development to meet the more stringent noise requirements for Advanced LIGO. The test mass suspensions consist of a four-stage or quadruple pendulum for enhanced seismic isolation. To minimize suspension thermal noise, the final stage consists of a silica mirror, 40 kg in mass, suspended from another silica mass by four silica fibres welded to silica ears attached to the sides of the masses using hydroxide-catalysis bonding. The design is chosen to achieve a displacement noise level for each of the seismic and thermal noise contributions of 10^(−19) m/√Hz at 10 Hz, for each test mass. We discuss features of the design which has been developed as a result of experience with prototypes and associated investigations.

Sensors and actuators for the Advanced LIGO mirror suspensions

We have developed, produced and characterized integrated sensors, actuators and the related read-out and drive electronics that will be used for the control of the Advanced LIGO suspensions. The overall system consists of the BOSEMs (a displacement sensor with an integrated electromagnetic actuator), the satellite boxes (the BOSEM readout and interface electronics) and six different types of coil-driver units. In this paper, we present the design of this read-out and control system, we discuss the related performance relevant for the Advanced LIGO suspensions, and we report on the experimental activity finalized at the production of the instruments for the Advanced LIGO detectors.

Differential gravitational coupling between cylindrically-symmetric, concentric test masses and an arbitrary gravitational source: relevance to the STEP experiment

The gravitational interaction between a point mass and a finite, hollow, thick-walled cylinder is calculated, the axial force is derived, and the parametric form of the coupling coefficients k2p is presented. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, and an equation is derived for the differential gravitational coupling to these masses which is more than 105 times faster to compute than a Monte-Carlo integration of similar accuracy.

STEP: A Status Report

This paper presents an overview of the current technical status of STEP, the Satellite Test of the Equivalence Principle. STEP was originally presented as a candidate for ESA’s M2 mission as a joint mission with NASA, and has since been studied as an M3 candidate, and under NASA as QuickSTEP and MiniSTEP. Studies especially during the last two years have resolved some long standing issues such as control of helium tide, improved the mission definition and error analysis, and have resulted in an improved baseline design which should be capable of comparing rates of fall to an accuracy approaching 10-18.

Propagating phonons in liquid 4He

Phonon propagation in liquid 4He at T approximately=0.1 K is studied as a function of pressure input power and propagation distance. Using a superconducting tunnel junction detector it is found that a single injected pulse can form two propagating pulses at low pressures but only one at high pressures. It is shown that three-phonon scattering can explain this behaviour. At low pressures, one group of phonons propagates ballistically while another group consists of strongly interacting phonons which travel at the ultrasonic velocity.

Optimization of immunity to helium tidal influences for the STEP experiment test masses

This paper describes an optimization strategy for the design of the three pairs of test masses in the STEP (satellite test of the equivalence principle) experiment. Using these designs, the allowable helium tidal amplitude is calculated for a STEP accelerometer sensitivity of , based on a worst case distribution of the liquid helium in the satellites dewar. It is found that the hybrid belted/straight-cylinder geometry can be dimensioned such that the quadrupole moment and differential hexadecapole moment are identically zero. The resulting test mass designs are technically feasible. Some practical problems relating to their manufacture are discussed.

Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinders end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 104 times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies.

A 'Violin-Mode' shadow sensor for interferometric gravitational wave detectors

This paper describes a system of four novel shadow detectors having, collectively, a displacement sensitivity of (69 ± 13) picometres (rms) / √Hz, at 500 Hz, over a measuring span of ±0.1 mm. The detectors were designed to monitor the vibrations of the 600 mm long, 400 µm diameter, silica suspension fibres of the mirrors for the Advanced LIGO (Laser Interferometer Gravitational wave Observatory) gravitational wave detectors, at the resonances of the so-called Violin Modes (VM). The VM detection system described here had a target sensitivity of 100 pm (rms)/√Hz at 500 Hz, together with, ultimately, a required detection span of ±0.1 mm about the mean position of each fibre—in order to compensate for potential slow drift over time of fibre position, due to mechanical relaxation. The full sensor system, comprising emitters (sources of illumination) and shadow detectors, therefore met these specifications. Using these sensors, VM resonances having amplitudes of 1.2 nm (rms), were detected in the suspension fibres of an Advanced LIGO dummy test-mass. The VM bandwidth of the sensor, determined by its transimpedance amplifier, was 226 Hz–8.93 kHz at the —3 dB points. This paper focuses mainly on the detector side of the shadow-sensors. The emitters are described in an accompanying paper.

Gravitational quadrupolar coupling to equivalence principle test masses: the general case

This paper discusses the significance of the quadrupolar gravitational force in the context of test masses destined for use in equivalence principle (EP) experiments, such as STEP and MICROSCOPE. The relationship between quadrupolar gravity and rotational inertia for an arbitrary body is analysed, and the special, gravitational, role of a bodys principal axes of inertia is revealed. From these considerations the gravitational quadrupolar force acting on a cylindrically symmetrical body, due to a point-like attracting source mass, is derived in terms of the bodys mass quadrupole tensor. The result is shown to be in agreement with that obtained from MacCullaghs formula (as the starting point). The theory is then extended to cover the case of a completely arbitrary solid body, and a compact formulation for the quadrupolar force on such a body is derived. A numerical example of a dumb-bells attraction to a local point-like gravitational source is analysed using this theory. Close agreement is found between the resulting quadrupolar force on the body and the difference between the net and the monopolar forces acting on it, underscoring the utility of the approach. A dynamical technique for experimentally obtaining the mass quadrupole tensors of EP test masses is discussed, and a means of validating the results is noted.