The KRISS Kibble balance realized the kilogram for the first time in 2019–2020 at a combined relative standard uncertainty of 1.2×10−71.2\times10^{-7} (k=1k=1, i.e. a one-standard-deviation coverage factor), with alignment-related effects — weighing-mode force bias, moving-mode parasitic voltages, Abbe offset and laser-beam verticality — forming the largest block of the uncertainty budget, and with further type-B reduction projected toward a target of 1×10−81\times10^{-8} for national realization and dissemination. The open problem is the practical and metrological route by which this apparatus, or its successor KRISS Kibble balance II (KB-2), can suppress those alignment-dominated systematics — together with the accompanying reductions in the remaining uncertainty components — far enough to reach a reproducible 10−810^{-8}-level realization, and whether that is achievable: which specific alignment terms, mechanical couplings and correction strategies ultimately limit or enable the improvement. The successor instrument remains at the prototype stage, and no improved KRISS realization and no further comparison entry has been published since 2019, so the question remains open.

Background

In the revised International System of Units (SI), in force since 20 May 2019, the kilogram is defined by fixing the numerical value of the Planck constant hh, and national metrology institutes realize the unit by experiments that link mass to hh. The two principal routes are the Kibble balance and the X-ray crystal density (XRCD) method, which determines the mass of a highly enriched silicon sphere from its lattice spacing, isotopic composition and volume. A Kibble balance (formerly called a watt balance) is an electromechanical instrument operated in two modes. In the weighing mode, the weight mgmg of a test mass is balanced by the Lorentz force BLIBLI on a current II flowing in a coil of effective length LL in a magnetic field BB. In the moving mode, the same coil is moved vertically at velocity vv, inducing a voltage U=BLvU=BLv. Equating the two expressions for BLBL eliminates the coil–magnet properties and yields the virtual-power relation mgv=UImgv=UI; when UU is measured against a Josephson voltage standard (a superconducting circuit whose output voltage is tied to hh and the elementary charge) and II is measured via a resistor calibrated against the quantum Hall resistance (a resistance standard based on the quantized Hall resistance of a two-dimensional electron gas), the mass value becomes traceable to hh through the second and the metre.

The balance relation holds exactly only when the coil moves along the direction of gravity and the electromagnetic and gravitational forces acting on the mass comparator are collinear. Residual misalignment enters as type-B uncertainty — uncertainty evaluated by means other than the statistical scatter of repeated observations (which is type A). The main alignment terms are: force biases in the weighing mode, arising when the electromagnetic force is not exactly vertical and anti-parallel to gravity; parasitic voltages in the moving mode, induced by velocity components of the coil in undesired horizontal directions within the magnetic-field gradient; the Abbe offset, the distance between the interferometer's measurement axis and the point at which the mass and force act, which converts angular errors of the moving stage into length (velocity) errors; and non-verticality of the interferometer laser beam, which biases the measured velocity. Alignment suppression is a generic difficulty of the method, treated classically for the Mark II balance of the NPL (National Physical Laboratory, UK) and the balance of the NRC (National Research Council of Canada).

The Korea Research Institute of Standards and Science (KRISS) completed its first kilogram realization with its Kibble balance (KB-1) between December 2019 and January 2020, measuring a platinum–iridium artefact (No. 111) and a stainless-steel artefact under vacuum at a combined relative standard uncertainty of 1.2×10−71.2\times10^{-7}, consistent with the values inherited from the international prototype of the kilogram. In the itemized budget of the source work [1] the alignment category (about 101×10−9101\times10^{-9} of the 120×10−9120\times10^{-9} combined value, with the weighing-mode force bias its largest sub-term at about 64×10−964\times10^{-9}) is the dominant block, and the reduction of type-B uncertainties toward a target relative uncertainty of 1×10−81\times10^{-8} for realization and dissemination is reported as the paper's stated forward path; the combined value of 120×10−9120\times10^{-9} is confirmed by the CCM.M-K8.2019 key comparison [2].

That target is metrologically motivated: the leading Kibble balances already operate at or near this level — NIST-4 (the fourth-generation balance of the National Institute of Standards and Technology, USA) determined hh with a relative standard uncertainty of 34×10−934\times10^{-9} in 2016, and the LNE (Laboratoire national de métrologie et d'essais, France) Kibble balance calibrated 500 g standards with relative standard uncertainties of 3.1×10−83.1\times10^{-8} in 2024 — and the Consultative Committee for Mass (CCM) runs periodic key comparisons (formal inter-laboratory comparisons of national measurement standards) of kilogram realizations whose results feed an international "consensus value" used for coordinated dissemination of the kilogram until the realization experiments agree sufficiently. KRISS's balance took part in the first such comparison (CCM.M-K8.2019) but not in the second (CCM.M-K8.2021). The unresolved question is therefore: whether, and by which apparatus refinements, alignment diagnostics and correction strategies, the alignment-dominated type-B block of this specific instrument (or its successor) can be measured and suppressed so that a reproducible, dissemination-grade realization at the 10−810^{-8} level is achieved, and which terms will ultimately bind.

Problem Statement

Determine whether, and if so by what practical and metrological route, the KRISS Kibble balance — the present instrument (KB-1) or its successor (KB-2) — can suppress the alignment-related type-B uncertainties that dominate its realized uncertainty budget, namely the weighing-mode force bias from imperfect collinearity of the electromagnetic and gravitational forces, the moving-mode parasitic voltages generated by horizontal coil motion, the Abbe offset between the interferometer axis and the coil/mass centre, and the non-verticality of the laser beam, so that the kilogram is realized reproducibly with a combined relative standard uncertainty of 1×10−81\times10^{-8} (coverage factor k=1k=1, i.e. one standard uncertainty) at dissemination grade? The answer should identify which specific alignment terms, mechanical couplings and correction strategies ultimately limit or enable the improvement from the realized 1.2×10−71.2\times10^{-7} (120×10−9120\times10^{-9}) baseline. A constructive route to that target is complete when it names the controlling alignment terms, the corrective mechanical and optical strategies, and a quantitative budget showing both the residual alignment contribution and the resulting combined relative standard uncertainty (coverage factor k=1k=1) at or below 1×10−81\times10^{-8}; a well-argued negative verdict also resolves the task when it demonstrates, with the same term-by-term budget, that no such route exists for KB-1 or KB-2 and identifies the term that binds first. 'dissemination grade' here means a realization usable for calibrating transfer standards at that uncertainty level and entering the CCM key comparisons of kilogram realizations, and 'reproducibly' means reproduction of the value across independent realizations — several artefacts and measurement campaigns — rather than within a single weighing series.

References

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