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The BIPM Kibble balance (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, who passed away in 2016.

    The main distinctive feature of the BIPM Kibble balance is its implementation of a one-mode measurement scheme, in addition to the conventional two-mode approach. In the one-mode scheme, a current flows through one of the windings of a bifilar coil in both weighing and moving measurements. The scheme hence makes the experiment less sensitive to changes in the magnetic field which varies with the coil current and alignment as compared to a one-mode Kibble balance. In addition, a comparison of measurements carried out using the two schemes 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.

    General description

    The BIPM Kibble balance operates with the following parameters: a 0.5 T radial magnetic field, a 250 mm diameter and 1060 turns induction coil, a coil current of ±13 mA and a mass standard of 1 kg. The coil travels over 15mm at a velocity of about 1 mm s-1. The mechanical system, the magnet, the mass loading and exchanger system as well as the optical system are housed in a vacuum enclosure and the experiment is run under vacuum at approximately 0.03 Pa. The experiment is housed on a large concrete block in a closed cabinet inside a laboratory with an air conditioning system.

    The BIPM Kibble balance housed inside a vacuum enclosure

    Mechanical system

    A commercial weighing cell is mounted on a 2-axis translation stage which is fixed on top of a rigid support composed of three stages of symmetric pentapod structures. A complex mechanical ensemble is suspended from the weighing cell. It includes a mechanism which creates a vertical movement of the lower part of the suspension by varying its length using an electrostatic motor. The weighing pan receiving the mass standard and the moving coil assembly are independently connected to the lower suspension via gimbal devices.

    Optical system

    A 3-axis heterodyne Michelson interferometer measures the coil vertical displacement and velocity. The laser source is based on a commercial single frequency 532 nm Nd:YAG laser and frequency stabilized on a hyperfine transition of iodine by the technique of saturated absorption. The two incident beams are spatially separated and shifted in frequency. Six solid corner cubes are used as retroreflectors, three for the fixed reference arms and three for the measurement arms. The measurement corner cubes are equally spaced at 120℃ to each other and fixed on the top surface of the coil former. Three time interval analyzers measure the phases of the interferometric signals and the related time information.

    Optical systems based on position sensitive detectors (PSDs) are used to measure the coil displacement along the unwanted degrees of freedom (two horizontal translations and rotations around three axes).



    For further details see:

    1.  Robertsson L., Fang H., and Stock M., A new interferometer for the BIPM Watt Balance, Proc. CPEM 2014, 2014.
    2.  Bielsa F., Robertsson L., Lavergne T., Kiss A., Fang H., and Stock M., The new interferometer of the BIPM watt balance, Proc. CPEM 2016, 2016.
    BIPM watt balance: optical systems to measure coil displacements

    Electrical system

    A high precision and stable current source is used to drive a current through the inductive coil. The current is determined by measuring the voltage drop across a 100 Ω standard resistor connected in series with the coil. The standard resistor is periodically calibrated using a quantum Hall resistance standard. Two voltage reference systems based on 1.2 V and 2.5 V programmable Josephson arrays provided by NIST are available. They allow us to determine the voltage drop across the standard resistor and the induced voltage in the coil in direct opposition. They additionally allow the calibration of the precision commercial digital voltmeters which are employed as null detectors.



    For further details see:

    1.  Solve S., Chayramy R., and Stock M., A Bias Source for the Voltage Reference of the BIPM Watt Balance, IEEE Trans. Instrum. Meas., 2013, 62, 1594-1599.
    2.  Bielsa F., Rolland B., Solve S., Li S., Kiss A., and Fang H., A programmable bias source for the PJVS in the BIPM Kibble Balance, Proc. CPEM 2018, 2018 (to be published).

    The 2.5 V programmable Josephson voltage standard

    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

    Environment

    The BIPM Kibble balance experiment is housed on a large concrete block in a closed cabinet inside a laboratory with an air conditioning system. 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 1100 turn induction coil, a flowing current of ±13 mA and a test mass of 1 kg. Coil velocity is about 1 mm s–1 with typical excursion of 20 mm.

    The apparatus is fully operational in air and in vacuum. The relative type B uncertainty on the Planck constant determination is currently about 2 x 10–7. The type B uncertainty is dominated by the residual misalignment of the interferometer laser beam due to the limited mechanical stability of the interferometer mount. A novel interferometer mounted on a much more stable support is being designed with the objective to reduce the uncertainty within 1 x 10–7. The standard deviation on the mean value for one week of measurements is a few parts in 108.



    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.
    2.  H. Fang, F. Bielsa, S. Li, A. Kiss, and M. Stock, The BIPM Kibble Balance for the realization of the redefined kilogram, Proc. CPEM 2018, 2018.