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 The BIPM watt balance

### The BIPM watt balance: General concept

Most watt balances operate in two distinct measurement phases – weighing and moving – so measurement accuracy could be limited by variations in the environmental and experimental conditions between the two phases. The main novelty of the BIPM watt balance is its implementation of simultaneous weighing and moving measurement phases, in addition to the conventional approach. The great advantage of this simultaneous measurement is to guarantee that the geometric properties of the coil, the coil orientation and the magnetic field, acting in both phases are strictly the same. The simultaneous method hence makes the experiment less sensitive to changes in magnetic field and alignment when compared to a two-phase watt balance. In addition, a comparison of measurements carried out using the conventional and the BIPM simultaneous approach may provide a better understanding of the limiting factors and possibly reveal some unexpected effects unique to each technique.

 The BIPM watt balance

### The principle of the watt balance

The concept of the moving coil watt balance was proposed by B. P. Kibble (NPL) in 1975. The experiment consists of two parts: the weighing and the moving experiments.

 Weighing experiment Moving experiment In the weighing experiment, a mass and a coil are suspended from a balance. The coil (wire length L) is placed in a magnetic field of flux density B. The gravitational force on the mass m is balanced by an equal and opposite electromagnetic force on the coil by sending a current I through it: m g = I L B In the moving experiment, the coil is moved at a vertical speed v through the magnetic field so that a voltage U is induced: U = B L v

If the properties of the coil and the magnetic field, L and B, and their alignment, do not change between the two experiments, they can be eliminated from both equations, which leads to the new equation

U I = m g v

which shows an electrical power on the left-hand side and a mechanical power on the right-hand side. This explains the name of the experiment, since the watt is the unit of power. It is important to understand that both types of power are only "virtual", in the sense that they do not appear in one of the single phases of the experiment. In the case of the electrical power, the voltage is measured in the moving experiment, and the current in the weighing experiment.

To establish a link between the macroscopic mass m and the Planck constant h, the electrical quantities voltage and current are measured by using two macroscopic quantum phenomena, the Josephson effect and the quantum Hall effect.

The Josephson effect allows us to determine an unknown voltage U as a dimensionless multiple u' of a combination of the Planck constant, the elementary charge and a precisely measurable frequency fJ:

 U = u' fJ h = u' fJ 2e KJ

The quantum Hall effect allows us to determine an unknown resistance R as a dimensionless multiple r' of a different combination of the Planck constant and the elementary charge:

 R = r' h = r' RK e2

The application of both effects on the measurement of the voltage and the current in the watt balance equation leads to:

 m = u1' u2' fJ,1 fJ,2 1 h r' g v 4

where the first component on the right-hand side shows the quantities related to the measurement of the voltage and the current using the macroscopic quantum effects, the second component shows the mechanical measurands gravitational acceleration g and velocity v, and the last term is the Planck constant. This equation establishes the link between the macroscopic mass m and the Planck constant h.

### Suspension

The moving coil hangs from the weighing cell via a variable-length suspension. An integrated electrostatic motor varies the length of the suspension and allows the coil to move (see image below). Force measurements are carried out using a 10 kg Sartorius weighing cell with 10 µg resolution.

The electrostatic motor is composed of three parallel plate electrodes (see image below). The central electrode is grounded and fixed. The upper and lower electrodes are mobile. By independently modulating the voltages on the two mobile electrodes, a net electrostatic force is obtained and the electrodes move. The movement of the mobile electrodes is transmitted to the lower part of the suspension via three levers separated by 120°.

 The BIPM watt balance

### Electrical system

The current source

A current of about 1 mA is injected into the moving coil by a bipolar current source built at the BIPM. Over 1 minute, the relative standard deviation of the current is about 4 × 10-7, with an integration time of 80 ms. The relative current drift is about 2 × 10-9 per minute.

Voltage reference

The correct operation of the core of the watt balance voltage reference, consisting of a dedicated programmable NIST SNS Josephson array, which was donated by the NIST to the BIPM, has been verified. This comprises a total of 33 705 Josephson junctions divided into 13 independent cells. In operation the voltage across the coil leads is tracked by the voltage produced by the array; the voltage difference is then within the selected range of an analogue detector. A bias current source which allows independent control of every cell in the array is under development.

### Optical system

Optical systems based on position sensitive detectors (PSDs) are used to measure the coil displacement for the unwanted degrees of freedom (2 translations and rotations around three axes). The vertical coil velocity is measured with a heterodyne interferometer. This measurement has recently been improved by replacing the one-axis with a three-axis interferometer.

Moving from a 1-axis to a 3-axis interferometer has improved the voltage to velocity signal-to-noise ratio by a factor of 10.

 (A): 3-axis interferometer; (B) Electrostatic damper

### Magnet

A new closed magnet circuit will be soon integrated into the experiment. The circuit design includes two discs of Sm2Co17 magnets, magnetized in opposite directions, as the flux source. The yoke is made of FeNi which has been selected for its high magnetic permeability and its mechanical stability at cryogenic temperatures. The mean diameter of the circular air gap is 250 mm and the width is 13 mm. The magnetic field will have radial symmetry and a magnetic flux density of about 0.5 T.

One of the properties of the system is that the magnets and the air gap are completely screened by a high permeability iron yoke. This should considerably reduce the level of external electromagnetic perturbations detected by the coil. The symmetry of the circuit with respect to the horizontal plane helps to improve the uniformity of the flux density in the air gap.

### Magnetic field alignment

An experimental procedure has been developed to accurately align the magnetic field of the circuit perpendicular to the direction defined by the local acceleration of gravity. The technique is based on a rotating Hall probe and a high-sensitive tiltmeter.

The magnetic plane at the central position inside the gap was aligned to better than 10 μrad with an uncertainty below 30 µrad. Constancy of the magnetic plane inclination was verified at the 30 µrad level over a length of 40 mm in the vertical direction. The geometry of the magnetic circuit was also characterized, confirming the suitability of the magnetic circuit for use in the BIPM watt balance at the 10–8 uncertainty level.

 Experimental set-up used for aligning the magnetic field.

### Vibration isolation

Two concrete foundations – one for the watt balance (64 tonnes) and one for the gravimeter (10 tonnes) – have been cast in the watt balance laboratory. Each is isolated from the main floor of the building but remains in lateral contact with the earth to avoid low-frequency swinging motions (excited by surface Rayleigh waves). The horizontal and vertical rms velocities due to ground vibrations are respectively 1 µm s-1 and 0.76 µm s-1 (for frequencies between 0.003 Hz and 100 Hz).

 The watt balance laboratory

The local gravitational acceleration g at any arbitrary location inside the dedicated watt balance laboratory can be evaluated. A 3-dimensional (3D) spatial array of g values was measured by a Scintrex CG5 relative gravimeter inside the laboratory. Measurements were made at three different heights from the ground floor covering the entire room. From these measurements a 3D gravity map has been produced using a 3D fit. Predictions from this 3D gravity map were compared with off-grid experimental gravity measurements. They agreed to within 1 µGal. The absolute value of g was measured in the watt balance laboratory during the 2009 International Comparison of Absolute Gravimeters (ICAG-2009).

In conclusion, the present uncertainty on the determination of the gravitational acceleration g at the location of the test mass is not a limiting factor for a determination of the Planck constant at the 10-8 level.

 White dots: 40 experimental gravity measurements taken in the watt balance laboratory at 1.7 m from the ground floor. Blue curved surface: 3D fit of 120 experimental points (measured at 3 different heights) evaluated at 1.7 m. The fit function contains 19 adjustable parameters. The observed spatial gravity gradient is due to a nearby hill.

Since 2005 the BIPM has been developing a watt balance as a means for the practical realization of the expected new definition of the kilogram in terms of the Planck constant. The BIPM watt balance operates using a 0.5 T radial magnetic field, a 250 mm diameter and 1160 turn induction coil, a flowing current of ±1 mA and a test mass of 100 g. Coil velocity is about 0.2 mm s–1 with typical excursion of 20 mm.

An improved version of the apparatus is fully assembled and operational in air. The relative uncertainty on the Planck constant determination is currently 3 x 10–6. The uncertainty is dominated by the residual misalignment of the electromagnetic force due to the limited mechanical stability of the suspension. Measurement in vacuum using a refined suspension is planned in spring 2017 with the objective to reduce the uncertainty to 1 x 10–7.

Reference: H. Fang, F. Bielsa, A. Kiss, T. Lavergne, Y. F. Lu, L. Robertsson, E. de Mirandés, S. Solve and M. Stock, Progress on the BIPM watt balance, Proc. CPEM 2016, 2016.