Watt Balance Research Articles

The Kibble balance and the kilogram

Abstract Dr. Bryan Kibble invented the watt balance in 1975 to improve the realization of the unit for electrical current, the ampere. With the discovery of the Quantum Hall effect in 1980 by Dr. Klaus von Klitzing and in conjunction with the previously predicted Josephson effect, this mechanical apparatus could be used to measure the Planck constant h. Following a proposal by Quinn, Mills, Williams, Taylor, and Mohr, the Kibble balance can be used to realize the unit of mass, the kilogram, by fixing the numerical value of Planck's constant. In 2017, the watt balance was renamed to the Kibble balance to honor the inventor, who passed in 2016. This article explains the Kibble balance, its role in the redefinition of the unit of mass, and attempts an outlook of the future.

Ensuring the stability of primary mass standards during the implementation of the new definition of the kilogram

In November 2018 the General Conference on Weights and Measures (CGPM) will meet and are likely to ratify the revision of the international system of units (SI). This represents a major change to the way the base SI units are defined and realised, a major consequence being that the last of the definitions based on a material artefact, the international prototype of the kilogram, will be “retired” and the “new” kilogram will be realised in terms of the Planck constant via the Kibble balance or X-ray crystal density (XRCD) experiment. While the revision of the SI and the redefinition of the kilogram will almost certainly be endorsed by the CGPM there are issues around the current agreement of the Kibble balance and XRCD experiments. This will mean that in order to implement the kilogram redefinition a consensus value for the “new” kilogram will need to be adopted in order that a consistent value for the SI unit of mass be maintained. In order to maintain this consistency the storage, monitoring and use of current primary mass standards will be critical and this paper outlines ways in which the stability of artefact based mass standards can be optimised by careful storage and monitoring using surface analysis techniques and quartz crystal microbalance technology.

NPL Kibble balance bifilar coil design and evaluation. XXII IMEKO World Congress, Belfast, 3 - 6 September 2018

A novel design of Kibble (watt) balance has been designed and is being constructed at the National Physical Laboratory. Lheory predicts that this type of balance will be simpler to construct and operate due to the removal of many of the alignment sensitivities present in existing balances. The balance uses a compact twisted pair coil in both the weighing and moving modes. This paper describes the design and manufacture of the coil and presents results of outgassing measurements made on the coil using a vacuum mass comparator.

Reduction of Type A noise in the NIST magnetic suspension mass comparator

The magnetic suspension mass comparator at NIST will be used to facilitate the dissemination of the kilogram, realized in the NIST-4 Kibble balance, from vacuum to air. The type A uncertainty, that is, the variation of the mass reading over time, is influenced by several factors. Our goal has been to understand all sources of noise and to minimize them to reduce the type A noise uncertainty below 20 µg. Here, we discuss the MSMC in general terms and focus on several sources of noise that we have been able to greatly reduce.

A self-calibrating multicomponent force/torque measuring system

A multicomponent self-calibrating force and torque sensor is presented. In this system, the principle of a Kibble balance is adapted for the traceable force and torque measurement in three orthogonal directions. The system has two operating modes: the velocity mode and the force/torque sensing mode. In the velocity mode, the calibration of the sensor is performed, while in the force/torque sensing mode, forces and torques are measured by using the principle of the electromagnetic force compensation. Details about the system are provided, with the main components of the sensor and a description of the operational procedure. A prototype of the system is currently being implemented for measuring forces and torques in a range of ±2 N and ±0.1 N · m respectively. A maximal relative expanded measurement uncertainty (k = 2) of 1 · 10−4 is expected for the force and torque measurements.

A new magnet design for future Kibble balances

We propose a new permanent magnet system for Kibble balance experiments, which combines advantages of the magnet designs invented by the National Physical Laboratory (NPL) and by the Bureau International des Poids et Mesures (BIPM). The goal of the proposed magnet system is to minimize the coil-current effect and to optimize the shielding at the same time. In the proposed design, a permanent magnet system with two gaps, each housing a coil, is employed to minimize the coil current effect, by reducing the linear coil-current dependence reported for the single air gap design by at least one order of magnitude. Both air gaps of the magnet are completely surrounded by high-permeability material, and hence the coils are shielded from outside magnetic fields and no magnetic field leaks outside of the magnet system. An example of the new magnet system is given and the analysis shows that the magnetic field in the air gap can be optimized to meet the requirement to be used in Kibble balances.

Preliminary Planck constant measurements via UME oscillating magnet Kibble balance

The UME Kibble balance project was initiated in the second half of 2014. During this period we have studied the theoretical aspects of Kibble balances, in which an oscillating magnet generates AC Faraday’s voltage in a stationary coil, and constructed a trial version to implement this idea. The remarkable feature of this approach is that it can establish the link between the Planck constant and a macroscopic mass by one single experiment in the most natural way. Weak dependences on variations of environmental and experimental conditions, small size, and other useful features offered by this novel approach reduce the complexity of the experimental set-up. This paper describes the principles of the oscillating magnet Kibble balance and gives details of the preliminary Planck constant measurements. The value of the Planck constant determined with our apparatus is , with a relative standard uncertainty of 6 ppm.

Progress of joule balance and redifination of Kilogram

Kilogram, the unit of mass, is the last one of seven base units in International System of Units (SI) which is still defined and kept by a material artifact. 1 kg is defined as the mass of the International Prototype of the Kilogram (IPK) kept at the Bureau International des Poids et Mesures (BIPM) in Paris. One of the major disadvantages of this definition is the fact that the amount of material constituting the IPK changes with time. Because a more stable mass reference does not exist, the variation of IPK is completely unknown so far. The International Committee for Weights and Measures (CIPM) recommended redefining the kilogram by fixing the numerical value of the Planck constant h and called on every national metrology institute to study the measurement of the h. To avoid possible system errors from one method, more experiments especially based on different principles are expected and encouraged for the final determination of the Planck constant. The CCM required that at least three consistent results should be obtained before the redefinition. Since 1970 s, the Kibble balance (also known as the Kibble balance) experiment has been used by a number of national metrology institutes such as NPL, NIST, METAS, LNE and BIPM. The IAC including the PTB, NMIJ and NMIA used the XRCD method to measure the Avogadro constant. To make contribution to the redefinition of kilogram, the National Institute of Metrology of China (NIM) proposed a joule balance method in 2006, which is also an electrical way but different from the watt balance method in that the dynamic phase is replaced with a static phase to avoid the trouble in the dynamic measurement. The progress of these approaches and the current situation of the redefinition of the kilogram are presented in this paper. In 2013, a model apparatus was built to verify the principle of the joule balance. Then NIM started to build its new joule balance aiming to obtain an uncertainty of 10-8 level since 2013. In Dec. 2016, the new apparatus was built and could be used to measure the Planck constant h in vacuum. In May 2017, the measurement result was submitted to the Metrologia and accepted by the CODATA TGFC as the input data. However, the measurement result has an uncertainty bigger than 10-8 and was not used for the final determination of the h value. At present, the joule balance group of NIM, together with the Harbin Institute of Technology, Tsinghua University and China Jiliang University is still making great efforts to improve the joule balance apparatus. The uncertainty of 10-8 level is expected to be achieved in the next two years.

Coil-current effect in Kibble balances: analysis, measurement, and optimization

The Kibble balance is expected to become an important instrument in the near future for realizing the unit of mass, the kilogram, in the revised international system of units (SI). The Kibble balance assumes an equality of two magnetic profiles measured in the weighing and velocity phases. A recent study conducted in the Kibble balance group at the Bureau International des Poids et Mesures (BIPM) showed that the coil current could significantly affect the magnetic profile, which should be carefully taken into account in the Kibble balance experiment. This paper gives a deeper understanding and investigation of the effect, and discusses the magnetic profile change due to the coil current, for both the classical two-mode and the one-mode Kibble balances. The coil current effect has been theoretically and experimentally investigated based on a typical magnet design with an air gap. One important conclusion found in the one-mode Kibble balance is that the magnetic profile change measured in the velocity phase is twice the change in the weighing phase. A compensation suggestion, to minimize the profile change due to the coil current in a BIPM-type magnet, is presented.

A New Proposal to Redefine Kilogram by Measuring the Planck Constant Based on Inertial Mass

A novel method to measure the Planck constant based on inertial mass is proposed here, which is distinguished from the conventional Kibble balance experiment which is based on the gravitational mass. The kilogram unit is linked to the Planck constant by calculating the difference of the parameters, i.e. resistance, voltage, velocity and time, which is measured in a two-mode experiment, unloaded mass mode and the loaded mass mode. In principle, all parameters measured in this experiment can reach a high accuracy, as that in Kibble balance experiment. This method has an advantage that some systematic error can be eliminated in difference calculation of measurements. In addition, this method is insensitive to air buoyancy and the alignment work in this experiment is easy. At last, the initial design of the apparatus is presented.

A permanent magnet system for Kibble balances

The magnet is one of the fundamental elements in Kibble balances. The Kibble balance group at the Bureau International des Poids et Mesures (BIPM) proposed a permanent magnet with a radial field, which has been widely employed in other Kibble balance experiments. In this paper, we discuss a different method of operation for the BIPM-type magnet, i.e. only the lower half of the magnetic circuit is closed. The merit of such a magnet is its convenience for opening the air gap and adjusting the coil. A disadvantage is that it can yield a lower and sloped magnetic field profile with less shielding. In the approach described, high permeability yokes are used to flatten the magnetic profile, which has proven to be a novel and convenient approach for removing the nonuniformity of the magnetic profile due to magnet magnetization asymmetries. The performance of the half-closed BIPM magnet is evaluated using experimental measurements. The results show that the half-closed magnetic circuit retains most of the main features of the fully-closed magnet and is a good option for the early stages of Kibble balance operations. In addition, the profile change due to the coil current is predicted and experimentally verified with a bifilar coil. Related systematic effects are discussed for the Planck constant measurement.

Progress of the Inertial Mass Measurement Project at NIM**Supported by the National Natural Science Foundation of China under Grant Nos 51477160 and 91536224, and the National Key Research and Development Program of China under Grant No 2016YFF0200102.

An experiment is proposed to precisely measure the Planck constant. In this experiment, the Planck constant is measured based on the inertial mass measurement rather than the gravitational mass determinations in some other well-known experiments, e.g., the Kibble balance and counting atoms. We link the mechanical force to a quantum-traceable electrostatic force by a beam balance oscillator. After a 5-year continuous effort, the principle of the proposal is verified by a preliminary measurement with a relative uncertainty of . The proposal has the potential to achieve much higher measurement accuracy with further improvements.

Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017

Researchers at the National Institute of Standards and Technology (NIST) have measured the value of the Planck constant to be J s (relative standard uncertainty ). The result is based on over 10 000 weighings of masses with nominal values ranging from 0.5 kg to 2 kg with the Kibble balance NIST-4. The uncertainty has been reduced by more than twofold relative to a previous determination because of three factors: (1) a much larger data set than previously available, allowing a more realistic, and smaller, Type A evaluation; (2) a more comprehensive measurement of the back action of the weighing current on the magnet by weighing masses up to 2 kg, decreasing the uncertainty associated with magnet non-linearity; (3) a rigorous investigation of the dependence of the geometric factor on the coil velocity reducing the uncertainty assigned to time-dependent leakage of current in the coil.

Boltzmann and Planck constants remeasured

NIST has announced more accurate measurements of the Boltzmann and Planck constants. The new values will contribute to an international effort to move away from defining basic units using physical objects and instead, starting in 2019, derive them from seven fundamental constants of nature. The kelvin, for example, is currently defined by measuring the triple point of water in a sealed glass cell. Going forward, metrologists want to define the kelvin in terms of the Boltzmann constant, which NIST researchers determined to be 1.3806410 × 10–23 J/K by measuring the degree of random motion of electrons in a resistor (Metrologia 2017, DOI: 10.1088/1681-7575/aa7b3f). Meanwhile, the kilogram is currently defined as the mass of a plum-sized cylinder of platinum-iridium alloy. Instead, metrologists want to define the kilogram in terms of the Planck constant. NIST scientists have now measured that constant’s value as 6.626069934 × 10–34 kg·m2/second by using a Kibble balance,

A determination of the Planck constant using the LNE Kibble balance in air

A determination of the Planck constant h using the LNE Kibble balance in air was carried out in the spring of 2017. Substantial improvements since 2014, chiefly related to the mass standard, mechanical alignments, voltage measurements and type A evaluation uncertainties, leads to a h value of 6.626 070 41(38) × 10–34 J · s, with a relative standard uncertainty of 5.7 × 10–8.

Self-attraction mapping and an update on local gravitational acceleration measurement in BIPM Kibble balance

The self-attraction effect needs to be evaluated and corrected towards a 10−9 level absolute determination of the local gravitational acceleration g in Kibble balance experiments. In this paper, the self-attraction effect of the BIPM Kibble balance apparatus is modelled by linking the gravitational field to the electrical field based on an electrostatic finite element analysis. A mapping of the gravitational field with different construction segments of the apparatus is presented, yielding a total correction of Gal at the mean trajectory position. Experimental measurements are carried out to check the self-attraction model. Based on the obtained result and previous measurements, we updated the g determination along the measurement trajectory for the forthcoming Planck constant measurement.

A summary of the Planck constant determinations using the NRC Kibble balance

We present a summary of the Planck constant determinations using the NRC watt balance, now referred to as the NRC Kibble balance. The summary includes a reanalysis of the four determinations performed in late 2013, as well as three new determinations performed in 2016. We also present a number of improvements and modifications to the experiment resulting in lower noise and an improved uncertainty analysis. As well, we present a systematic error that had been previously unrecognized and we have quantified its correction. The seven determinations, using three different nominal masses and two different materials, are reanalysed in a manner consistent with that used by the CODATA Task Group on Fundamental Constants (TGFC) and includes a comprehensive assessment of correlations. The result is a Planck constant of 6.626 070 133(60) ×10−34 Js and an inferred value of the Avogadro constant of 6.022 140 772(55) ×1023 mol−1. These fractional uncertainties of less than 10−8 are the smallest published to date.

The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass

The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as the watt balance. Once the new definition has been adopted, the Kibble balance technique will permit the realisation of the mass unit over a range from milligrams to kilograms. We describe the theory underlying the Kibble balance and practical techniques required to construct such an instrument to relate a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at present, in the region of 2 parts in 108. A number of Kibble balances have either been built or are under construction and we compare the principal features of these balances.

Gravimetry for watt balance measurements

In a watt balance (WB) the gravity on a known mass is used in the determination of the value of the Planck constant with a precision of <2 × 10−41 J s. To attain this precision the gravity value at the centre of a mass within the WB must be known with a relative uncertainty of <1 × 10−8. This necessitates laboratory gravity mapping in three dimensions, the establishment close to the WB of a gravity reference station, and modelling of the ties to the centre-of-mass location. The self-gravity of the WB must be accounted for, and since WB measurements run over several weeks, corrections for tidal, polar motion and atmospheric effects must be included. We describe the gravimetry carried out at the National Research Council of Canada WB laboratory, and include a discussion of past gravity variations in the vicinity of the WB, which suggest that seasonal variation may be of sufficient magnitude to affect results obtained with the balance.

A 10 V programmable Josephson voltage standard and its applications for voltage metrology

The concept of a programmable Josephson voltage standard (PJVS) was first proposed in 1997. Since then a significant amount of research and development work has been devoted to the fabrication of the programmable Josephson junction array and its deployment in a voltage standard system. This paper reports the recent development of a 10 V PJVS system at the National Institute of Standards and Technology (NIST) and its voltage metrology applications. The superior stability of the voltage step of the new 10 V PJVS enables it to perform the same tasks as the conventional Josephson voltage standard (JVS) that uses hysteretic voltage steps and to improve the efficiency and effectiveness of a JVS direct comparison. For the first time, a comparison between a conventional JVS and the NIST 10 V PJVS was performed in order to verify the performance of the NIST 10 V PJVS. The mean difference between the two systems at 10 V was found to be −0.49 nV with a combined standard uncertainty of 1.32 nV (k = 1) or a relative combined standard uncertainty of 1.32 parts in 1010. Automatic comparisons between the 10 V PJVS and a 2.5 V PJVS at 1.018 V were performed to monitor the long term accuracy and stability of the 2.5 V PJVS and to support the NIST electronic kilogram experiment. By matching the voltages of the two PJVS systems during a comparison, the type B uncertainty can be minimized to a negligible level. The difference between the two PJVS at 1.018 V was found to be −0.38 nV with a combined standard uncertainty of 0.68 nV (k = 1) or a relative combined standard uncertainty of 6.7 parts in 1010. Issues encountered during the PJVS comparison and potential challenges for 10 V applications are also discussed.