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The BIPM Kibble (watt) balance

    The BIPM Kibble (watt) balance: General concept

    The international metrology community renamed their moving-coil watt balances as 'Kibble balances' in honour of the pioneering work in this field by Dr Bryan Kibble, following his death in 2016.

    Most Kibble 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 Kibble 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 Kibble 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 Kibble (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 Kibble 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°.

    BIPM watt balance: weighing cell and electrostatic motor

    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.

    BIPM watt balance: optical systems to measure coil displacements

    Magnet

    A closed magnet circuit is employed. The circuit design includes two discs of Sm2Co17 magnets, magnetized in opposite directions, as the flux source. The yoke is made of a high permeability FeNi alloy which eliminates the non-uniformity of the magnetic flux density in the air gap, which would otherwise result from the small magnetization asymmetry of the two permanent magnet discs. The mean diameter of the circular air gap is 250 mm and the width is 13 mm. The magnetic field has radial symmetry and a magnetic flux density of about 0.5 T.

    Due to the geometry of the system, the magnets and the air gap are completely screened by the high permeability iron yoke. This considerably reduces 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. The uniformity of the vertical profile of the flux density in the air gap was measured to be below 1 × 10-4 within the working length of 40 mm.



    A theoretical and experimental study was conducted to investigate the influence of the coil-current on the magnetic field. The magnetic flux generated by the coil goes through the magnet and produces an additional contribution to the magnetic field at the coil position. It has been found that this mechanism leads to a significant slope of the vertical magnetic field profile. It has also been demonstrated that the effect on the magnetic field in the velocity measurement is twice that deduced from the weighing measurement. The exact size of the effect depends on the specific geometry and dimensions of each magnetic circuit, but in general has to be taken into account at the present level of uncertainty of Kibble balances.



    For further details see:

    1.  Li S., Bielsa F., Stock M., Kiss A., Fang H., A permanent magnet system for Kibble balances, Metrologia, 2017, 54, 775-783.
    2.  Li S., Bielsa F., Stock M., Kiss A., Fang H., Coil-current effect in Kibble balances: analysis, measurement, and optimization, Metrologia, 2018, 55, 75-83.

    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.



    For further details see:


    BIPM watt balance: Experimental set-up used for aligning the magnetic field

    Vibration isolation

    The Kibble balance laboratory has two concrete foundations – one for the Kibble balance (64 tonnes) and one for the gravimeter (10 tonnes). 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).

    BIPM watt balance: new laboratory showing concrete foundations for vibration isolation

    In Kibble balances, the absolute value of the local gravitational acceleration g at the mass weighing position should be determined at the 10−9 level, corresponding to a few µGal (1 µGal= 1 × 10−8 m/s2). The absolute value of g was measured in the BIPM Kibble balance laboratory during the 2009 International Comparison of Absolute Gravimeters (ICAG-2009), with a relative uncertainty of 4.2 µGal. The measurement result was obtained at the height of 1300 mm, horizontally centered with respect to the vacuum chamber.

    For the BIPM site, a number of comparison reference values (CRVs) of past international comparisons of absolute g measurements (ICAGs) are available. These can be used to estimate the long-term stability of absolute g values at the BIPM Kibble balance. The measurement results show that the g value change was within 1 µGal over 8 years. This might be verified again in the future.

    In Kibble balances, the g value has to be transferred from the measurement position to the mass weighing position, and hence the relative gravity changes in space, i.e. the horizontal gravity gradient (HGG) and the vertical gravity gradient (VGG), need to be known. The HGG and VGG at the BIPM were determined by a combination of the relative gravity mapping and the evaluation of the instrumental self-attraction.

    A 3-dimensional (3D) spatial array of g values was measured by a relative gravimeter inside the laboratory. Predictions were made from this 3D gravity map, which agreed to the off-grid experimental gravity measurement within 1 µGal.

    The self-attraction effect of the BIPM Kibble balance apparatus was modelled by using the mathematical analogy between the equations for the gravitational field and the electrical field based on an electrostatic finite element analysis (FEA). The gravitational field of individual construction segments of the BIPM Kibble balance was calculated and combined, yielding a total correction of (4.7 ± 0.5) µGal at the mean trajectory position.

    The time-varying contribution of g, known as the Earth tides, polar motion, and atmospheric mass redistribution, was modelled by a software package based on localized parameter determination. The long-term measurement showed that this calculation can achieve an uncertainty of about 1 µGal.

    The present uncertainty on the determination of the gravitational acceleration g at the location of the test mass is 4.6 µGal, which is not a limiting factor for a determination of the Planck constant at the 10−8 level.



    For further details see:

    1.  Jiang Z. et al., On the gravimetric contribution to watt balance experiments, Metrologia, 2013, 50, 452-471.
    2.  Li S., Bielsa F., Kiss A., Fang H., Self-attraction mapping and an update on local gravitational acceleration measurement in BIPM Kibble balance, Metrologia, 2017, 54, 445-453.

    Since 2005 the BIPM has been developing a Kibble balance as a means for the practical realization of the expected new definition of the kilogram in terms of the Planck constant. The BIPM Kibble 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.



    For further details see:

    1.  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.