The BIPM Kibble balance realizes the kilogram from the fixed numerical value of the Planck constant by comparing electrical and mechanical power in a one-mode, two-measurement-phase scheme using a bifilar coil. In 2020 its measurement of a 1 kg platinum–iridium (Pt-Ir) artefact in vacuum carried a combined relative standard uncertainty of 4.9×10−84.9\times10^{-8}, dominated by an alignment term of 33×10−933\times10^{-9} and a voltage-measurement term of about 30×10−930\times10^{-9}, with parasitic coil motion, possible current leakage and grounding issues, and BLBL magnet drift identified as the residual limitations. The open problem is to lower the combined uncertainty substantially below the 4.9×10−84.9\times10^{-8} level and to make the realization robust enough for routine dissemination of the kilogram and regular participation in Consultative Committee for Mass (CCM) key comparisons, by removing these identified limitations—controlling parasitic coil translations and rotations, hardening the electrical measurement chain, reducing Abbe-offset and laser-beam verticality errors through the air-to-vacuum transfer, and suppressing BLBL magnet drift. Work through 2024 (a new interferometer, a cryocooled Josephson voltage system, new beam mechanisms under development, and a 4.1×10−84.1\times10^{-8} result in the CCM.M-K8.2021 comparison) has lowered the uncertainty only modestly; the full programme remains open.

Background

Since 20 May 2019 the kilogram in the International System of Units (SI) is defined by fixing the numerical value of the Planck constant hh, so that a mass standard can only be 'realized' experimentally, i.e. measured directly in terms of hh. Two primary methods dominate: the X-ray crystal density (XRCD) method with silicon spheres, and the Kibble balance (formerly watt balance). A Kibble balance links mass to hh through a virtual comparison of electrical and mechanical power: in the weighing phase, a coil carrying current II in a magnetic flux-density field BB is held against the weight mgmg of a mass standard; in the moving phase, the same coil is moved vertically at velocity vv, inducing a voltage U=BLvU = BLv, where BLBL is the geometric flux linkage factor of the coil in the magnet. Electrical quantities are traceable to quantum standards—the programmable Josephson voltage system (PJVS), an array of superconducting Josephson junctions that generates a voltage linked to hh via the Josephson constant, combined with a quantum-Hall resistance standard—so that m=UI/(gv)m = UI/(gv) is expressed through hh alone. The International Bureau of Weights and Measures (BIPM) operates its own Kibble balance to realize the kilogram independently and to support international dissemination. Its distinctive feature is a one-mode, two-measurement-phase scheme: a single winding of a bifilar coil (two concentric windings on one former) carries current in both the weighing and moving phases, which reduces sensitivity to changes of the magnetic field and coil-current-dependent effects compared with the conventional two-mode scheme. In 2020 the BIPM team reported the apparatus's first complete kilogram realization: a 1 kg platinum–iridium (Pt-Ir) artefact was measured in vacuum with a combined relative standard uncertainty of 4.9×10−84.9\times10^{-8} (49 µg), differing by 15 µg from the value deduced from the calibration following the official dissemination process after the redefinition. The published uncertainty budget is dominated by alignment-related effects (33×10−933\times10^{-9}; e.g. Abbe offsets—the displacement-measurement axis being offset from the point where force acts—and laser-beam verticality as the beam passes the air-to-vacuum interface of the enclosure) and by the electrical measurement chain (about 30×10−930\times10^{-9}, attributed largely to possible current leakage and grounding). Further identified limitations are parasitic coil translations and rotations during the moving phase (at the level of tenths of a micrometre and tenths of a microradian, with five unconstrained degrees of freedom and no active damping) and drift of BLBL associated with magnet cooling and thermal gradients, currently treated by post-hoc drift interpolation. Progress on kilogram realizations is tracked internationally through the Consultative Committee for Mass (CCM) key comparisons of kilogram realizations (CCM.M-K8 series), whose results feed the 'consensus value' of the kilogram used for worldwide dissemination until independent realizations agree within their uncertainties; leading national realizations—the Kibble balances of the National Research Council of Canada (NRC) and the National Institute of Standards and Technology (NIST, USA), and the XRCD silicon-sphere realization of the Physikalisch-Technische Bundesanstalt (PTB, Germany)—currently operate at relative uncertainties of about 11–3×10−83\times10^{-8}. The BIPM Kibble balance, by contrast, entered the 2021 key comparison with an uncertainty several times larger than these leading realizations (41 µg versus 11 µg for NRC), and the BIPM authors themselves framed the further work needed: lowering the combined uncertainty substantially below the 4.9×10−84.9\times10^{-8} level and making the realization robust enough for routine dissemination and regular comparison participation.

Problem Statement

Advance the BIPM Kibble balance realization of the kilogram from its 2020 state—combined relative standard uncertainty 4.9×10−84.9\times10^{-8} on a 1 kg Pt-Ir artefact measured in vacuum—to a substantially lower, demonstrably robust uncertainty by removing the identified limiting factors: (1) parasitic coil displacements and rotations during the moving phase, presently at tenths of a micrometre and tenths of a microradian, with five unconstrained degrees of freedom and no active damping; (2) the voltage-related uncertainty of about 30×10−930\times10^{-9} attributed to possible current leakage and grounding issues in the electrical measurement chain; (3) the alignment uncertainty, presently the largest single term at 33×10−933\times10^{-9}, arising from Abbe offsets, laser-beam vertical alignment stability through the air-to-vacuum transfer, and torque around the vertical axis; and (4) drift of the flux linkage factor BLBL associated with magnet cooling and thermal gradients, currently handled by post-hoc drift interpolation. All four identified limiting factors (1)–(4) lie within the scope of this task: bringing the dominant alignment and voltage terms under control without addressing the parasitic-motion and BLBL-drift limitations does not resolve it. The target is an uncertainty budget for the BIPM balance with a substantially reduced combined uncertainty in which the dominant 2020 terms are demonstrably controlled, together with a realization reliable enough for routine dissemination of the kilogram and regular participation in CCM key comparisons of kilogram realizations. The deliverable is a design and analysis—the reduced uncertainty budget together with the design and procedural changes that produce it—rather than a physically demonstrated measurement. 'Substantially reduced' means reducing the combined relative standard uncertainty to at or below 2×10−82\times10^{-8}, the target set for the BIPM programme and a level within the 11–3×10−83\times10^{-8} range of the leading realizations. For robustness, the residual contributions of the identified limiting factors (1)–(4) must be shown to be controlled in the reduced uncertainty budget and to remain controlled under the operational variations the balance encounters.

References

  1. H. Fang, F. Bielsa, S. Li, A. Kiss, M. Stock, "The BIPM Kibble balance for realizing the kilogram definition", Metrologia 57 (2020) 045009. DOI: 10.1088/1681-7575/ab860c, https://doi.org/10.1088/1681-7575/ab860c
  2. M. Stock, P. Conceição, H. Fang, F. Bielsa, A. Kiss, L. Nielsen, et al., "Final report on the CCM key comparison of kilogram realizations CCM.M-K8.2021", Metrologia 60 (2023) 07003 (Technical Supplement). DOI: 10.1088/0026-1394/60/1A/07003, https://doi.org/10.1088/0026-1394/60/1A/07003 (final report PDF also at https://www.bipm.org/documents/20126/48150799/CCM.M-K8.2021.pdf/9a71fc63-fb10-614e-27df-727d3722ff52)
  3. M. Stock, P. Conceição, H. Fang, F. Bielsa, A. Kiss, L. Nielsen, et al., "Report on the CCM key comparison of kilogram realizations CCM.M-K8.2019", Metrologia 57 (2020) 07030 (Technical Supplement). DOI: 10.1088/0026-1394/57/1A/07030, https://doi.org/10.1088/0026-1394/57/1A/07030
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