arXiv subjects

Stephan Schlamminger

Publications and source records attributed to Stephan Schlamminger.

At least 19 recordsLinked to original sources

arXiv2025

Precision Control of Resistive Power in Kibble Balance Coils: An Advanced Method for Minimizing Temperature-Related Magnetic Errors

Temperature changes affect the coercivity of permanent magnets, thereby impacting the $Bl$ factor and potentially introducing systematic errors in Kibble balance measurements. While the thermal-magnetic effect is negligible in large magnet systems, it increases substantially as the magnet size decreases, posing an engineering difficulty for tabletop Kibble balance systems. We discuss the mechanism of thermal-magnetic effects through finite element analysis, which has not been sufficiently emphasized in previous studies. A bifilar-coil power regulator is proposed to eliminate thermal-magnetic errors in Kibble balances. The approach aims to keep the power of the internal heating source -- coil ohmic power -- constant over time, allowing the $Bl$ drift to be mitigated through ABA or ABBA measurement sequences. Experimental results validate the proposal, demonstrating that the thermal effect can be reduced by more than two orders of magnitude compared to the conventional two-mode, two-phase measurement scheme, and by about one order of magnitude compared to the one-mode, two-phase scheme. The proposed approach can eliminate the influence of thermal-magnetic effects on the measurement results, thus further breaking down the limitations on the minimum size of tabletop Kibble balances.

physics.ins-det↗

arXiv2024

A digital four-arm bridge for the comparison of resistance with capacitance

We have built and demonstrated a digital four-arm bridge for the comparison of resistance with capacitance. The digital four-arm bridge mimics the classical quad bridge in the digital domain with three balances: the source balance, the detector balance, as well as the main balance. Due to correlation, the required precision of the source voltages is only of the order of the square root of the ultimate bridge precision. For the comparison of a $100\,$k$\Omega$ resistor with a $1\,$nF capacitor near 1592 Hz, the combined standard uncertainty $(k = 1)$ is $5\times 10^{-9}$.

physics.ins-det↗

arXiv2024

Flexures for Kibble balances: Minimizing the effects of anelastic relaxation

We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e., bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields 1.2E-4. This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure's internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.

physics.class-ph↗

arXiv2022

Calculation of magnetic forces and torques on the Kibble coil

Analytically the forces and torques on a coil in a field of magnetic flux density can be calculated one of two ways. The line integral can be conducted along the coil's wire, summing up the differential force contribution. For each differential line segment, the force is obtained as a cross product with the magnetic flux density. Alternatively, the coil's energy in the field is the current times the flux threading the coil. Hence, the energy is obtained by executing a surface integral over the coil's open surface. Here, a dot product of the differential surface element with the magnetic flux density is executed under the integral sign. The forces and torques can then be obtained from the negative derivative of the energy with respect to the appropriate coordinate. For yoke-based Kibble balances, the latter method is much simpler since most of the flux is contained in the inner yoke of the magnet and can be written as a simple equation. Here, we use this method to provide simple equations and their results for finding the torques and forces that act on a coil in a yoke-based magnet system. We further introduce a simple method that allows the calculation of the position and orientation difference between the coil and the magnet from three measurements.

physics.ins-det↗

arXiv2022

Conception of an enhanced mechanism for a new Kibble balance directly traceable to the quantum SI

The ``Quantum Electro-Mechanical Metrology Suite'' (QEMMS) is being designed and built at the National Institute of Standards and Technology. It includes a Kibble balance, a Graphene quantum Hall resistance array and a Josephson voltage system, so that it is a new primary standard for the unit of mass, the kilogram, directly traceable to the International System of Units (SI) based on quantum constants. We are targeting a measurement range of 10 g to 200 g and optimize the design for a relative combined uncertainty of $2\times 10^{-8}$ for masses of 100 g. QEMMS will be developed as an open hardware and software design. In this article, we explain the design of the moving and weighing mechanism in the QEMMS.

physics.ins-det↗

arXiv2022

Magnetic Uncertainties for Compact Kibble Balances: An Investigation

The Kibble balance has become one of the major instruments for realizing the mass unit, the kilogram, in the revised international system of units (SI). Researchers at about a dozen national metrology institutes are actively working with Kibble balances that are capable of weighing masses with nominal values from 10g to 1kg. In the future, the design of smaller Kibble balances will play a more significant role. Smaller Kibble balances require smaller magnet systems, and here we investigate the scaling of systematic uncertainties with the size of the magnet system. We describe the size dependence of three magnetic effects: the coil-inductance effect, the yoke nonlinear effect, and the thermal effect. The analysis shows that the relative systematic effects become increasingly larger with smaller sizes. For small magnets the thermal effects become dominant and, hence, a good thermal design is imperative.

physics.ins-det↗

arXiv2022

Design of electrostatic feedback for an experiment to measure $G$

The torsion pendulum at the heart of the apparatus to measure the gravitational constant, $G$ at the Bureau International des Poids et Mesures (BIPM) is used to measure the gravitational torque between source and test-mass assemblies with two methods. In the Cavendish method, the pendulum moves freely. In the electrostatic-servo method, the pendulum is maintained at a constant angle by applying an electrostatic torque equal and opposite to any gravitational torque on the pendulum. The electrostatic torque is generated by a servo. This article describes the design and implementation of this servo at the National Institute of Standards and Technology. We use a digital servo loop with a Kalman filter to achieve measurement performance comparable to the one in an open loop. We show that it is possible to achieve small measurement uncertainty with an experiment that uses three electrodes for feedback control.

physics.class-ph↗

arXiv2022

The kilogram: inertial or gravitational mass?

With the redefinition of the international system of units, the value of the Planck constant was fixed, similarly to the values of the unperturbed ground state hyperfine transition frequency of the $^{133}$Cs atom, speed of light in vacuum. Theoretically and differently from the past, the kilogram is now explicitly defined as the unit of inertial mass. Experimentally, the kilogram is realized by atom count or the Kibble balance. We show that only the former method measures the inertial mass without assuming the universality of free fall. Therefore, the agreement between the two measures can be interpreted as a test of the equivalence principle.

physics.class-ph↗

arXiv2021

Nanoscale torsional dissipation dilution for quantum experiments and precision measurement

We show that torsion resonators can experience massive dissipation dilution due to nanoscale strain, and draw a connection to a century-old theory from the torsion balance community which suggests that a simple torsion ribbon is naturally soft-clamped. By disrupting a commonly held belief in the nanomechanics community, our findings invite a rethinking of strategies towards quantum experiments and precision measurement with nanomechanical resonators. For example, we revisit the optical lever technique for monitoring displacement, and find that the rotation of a strained nanobeam can be resolved with an imprecision smaller than the zero-point motion of its fundamental torsional mode, without the use of a cavity or interferometric stability. We also find that a strained torsion ribbon can be mass-loaded without changing its $Q$ factor. We use this strategy to engineer a chip-scale torsion balance whose resonance frequency is sensitive to micro-$g$ fluctuations of the local gravitational field. Enabling both these advances is the fabrication of high-stress Si$_3$N$_4$ nanobeams with width-to-thickness ratios of $10^4$ and the recognition that their torsional modes have $Q$ factors scaling as their width-to-thickness ratio squared, yielding $Q$ factors as high as $10^8$ and $Q$-frequency products as high as $10^{13}$ Hz.

cond-mat.mes-hall↗

arXiv2021

The irony of the magnet system for Kibble balances -- a review

The magnet system is an essential component of the Kibble balance, a device that is used to realize the unit of mass. It is the source of the magnetic flux, and its importance is captured in the geometric factor $Bl$. Ironically, the $Bl$ factor cancels out and does not appear in the final Kibble equation. Nevertheless, care must be taken to design and build the magnet system because the cancellation is perfect only if the $Bl$ is the same in both modes: the weighing and velocity mode. This review provides the knowledge necessary to build a magnetic circuit for the Kibble balance. In addition, this article discusses the design considerations, parameter optimizations, practical adjustments to the finished product, and an assessment of systematic uncertainties associated with the magnet system.

physics.ins-det↗

arXiv2021

Design of an electrostatic balance mechanism to measure optical power of 100 kW

A new instrument is required to accommodate the need for increased portability and accuracy in laser power measurement above 100 W. Reflection and absorption of laser light provide a measurable force from photon momentum exchange that is directly proportional to laser power, which can be measured with an electrostatic balance traceable to the SI. We aim for a relative uncertainty of $10^{-3}$ with coverage factor $k=2$. For this purpose, we have designed a monolithic parallelogram 4-bar linkage incorporating elastic circular notch flexure hinges. The design is optimized to address the main factors driving force measurement uncertainty from the balance mechanism: corner loading errors, balance stiffness, stress in the flexure hinges, sensitivity to vibration, and sensitivity to thermal gradients. Parasitic rotations in the free end of the 4-bar linkage during arcuate motion are constrained by machining tolerances. An analytical model shows this affects the force measurement less than 0.01 percent. Incorporating an inverted pendulum reduces the stiffness of the system without unduly increasing tilt sensitivity. Finite element modeling of the flexures is used to determine the hinge orientation that minimizes stress which is therefore expected to minimize hysteresis. Thermal effects are mitigated using an external enclosure to minimize temperature gradients, although a quantitative analysis of this effect is not carried out. These analyses show the optimized mechanism is expected to contribute less than $10^{-3}$ relative uncertainty in the final laser power measurement.

physics.ins-det↗

arXiv2021

Resolution of the paradox of the diamagnetic effect on the Kibble coil

Employing very simple electro-mechanical principles known from classical physics, the Kibble balance establishes a very precise and absolute link between quantum electrical standards and macroscopic mass or force measurements. The success of the Kibble balance, in both determining fundamental constants ($h$, $N_A$, $e$) and realizing a quasi-quantum mass in the 2019 newly revised International System of Units, relies on the perfection of Maxwell's equations and the symmetry they describe between Lorentz's force and Faraday's induction, a principle and a symmetry stunningly demonstrated in the weighing and velocity modes of Kibble balances to within $1\times10^{-8}$, with nothing but imperfect wires and magnets. However, recent advances in the understanding of the current effect in Kibble balances reveal a troubling paradox. A diamagnetic effect, a force that does not cancel between mass-on and mass-off measurement, is challenging balance maker's assumptions of symmetry at levels that are almost two orders of magnitude larger than the reported uncertainties. The diamagnetic effect, if it exists, shows up in weighing mode without a readily apparent reciprocal effect in the velocity mode, begging questions about systematic errors at the very foundation of the new measurement system. The hypothetical force is caused by the coil current changing the magnetic field, producing an unaccounted force that is systematically modulated with the weighing current. Here we show that this diamagnetic force exists, but the additional force does not change the equivalence between weighing and velocity measurements. We reveal the unexpected way that symmetry is preserved and show that for typical materials and geometries the total relative effect on the measurement is $\approx 1\times10^{-9}$.

physics.ins-det↗

arXiv2020

A Simple Improvement for Permanent Magnet Systems for Kibble Balances: More Flat Field at Almost No Cost

Permanent magnets together with yokes to concentrate the magnetic flux into a cylindrical air-gap are widely employed in Kibble balances. These experiments require a uniform magnetic flux density along a vertical path, typically a substantial fraction of the length of the air-gap. Fringe fields that are present at both ends of the air-gap limit the region where the flux density does not change more than a certain relative fraction (here: $5\times 10^{-4}$) of the flux density in the center of the magnet system. By simply adding an iron ring with a rectangular cross-section to the inner yoke at each end of the air gap, the effects of the fringe fields can be counteracted, and, hence, the length of the region, where the flux density remains within a given tolerance band is increased. Compared to the alternative, employing a taller magnet, the proposed method yields a magnet system with an extended region of a uniform field without significantly increasing the mass of the magnet system. Potential applications include compact and table-top Kibble balances. We investigate possible adverse effects on the performance of the magnet system caused by the additional rings: magnetic field strength, coil-current effect, and a dependence of the radial field on the radial position in the field. No substantial disadvantage was found. Instead, the method presented here outperformed previously suggested methods to improve the radial dependence of the radial field, e.g., shorter outer yoke. In summary, adding rings to the inner yoke improves the uniformity of the field without a detrimental effect to function, cost, and form factor of the magnet system.

physics.ins-det↗

arXiv2019

Magnet system for the Quantum Electro-Mechanical Metrology Suite

The design of the permanent magnet system for the new Quantum Electro-Mechanical Metrology Suite (QEMMS) is described. The QEMMS, developed at the National Institute of Standards and Technology (NIST), consists of a Kibble balance, a programmable Josephson voltage standard, and a quantum Hall resistance standard. It will be used to measure masses up to $100\,\mathrm{g}$ with relative uncertainties below $2\times 10^{-8}$. The magnet system is based on the design of the NIST-4 magnet system with significant changes to adopt to a smaller Kibble balance and to overcome known practical limitations. Analytical models are provided to describe the coil-current effect and model the forces required to split the magnet in two parts to install the coil. Both models are compared to simulation results obtained with finite element analysis and measurement results. Other aspects, such as the coil design and flatness of $Bl$ profile are considered.

physics.ins-det↗

arXiv2019

The Performance of the KIBB-g1 Tabletop Kibble Balance at NIST

A tabletop-sized Kibble balance (KIBB-g1) designed to directly realize mass at the gram-level range with uncertainties on the order of parts in 10$^6$ has been developed at the National Institute of Standards and Technology (NIST). The masses of a nominally 5\,g and 1\,g weight were determined with 1-$σ$ standard uncertainties of 9.0\,$\upmu$g and 6.7\,$\upmu$g, respectively. The corresponding relative uncertainties are $1.8\times 10^{-6}$ and $6.3\times 10^{-6}$. The construction of the instrument, capabilities, and full uncertainty budgets are presented in this manuscript.

physics.ins-det↗

arXiv2019

Closed form expressions for gravitational multipole moments of elementary solids

Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape this shape can be rotated, translated, and even converted to an outer multipole with well established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three dimensional numerical integration of complex functions. Previous work has produced expressions for the low degree inner multipoles for certain elementary solids. This work goes further by presenting closed form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.

gr-qc↗

arXiv2019

Shades of Dark Uncertainty and Consensus Value for the Newtonian Constant of Gravitation

The Newtonian constant of gravitation, $G$, stands out in the landscape of the most common fundamental constants owing to its surprisingly large relative uncertainty, which is attributable mostly to the dispersion of the values measured for it in different experiments. This study focuses on a set of measurements of $G$ that are mutually inconsistent, in the sense that the dispersion of the measured values is significantly larger than what their reported uncertainties suggest that it should be. Furthermore, there is a loosely defined group of measured values that lie fairly close to a consensus value that may be derived from all the measurement results, and then there are one or more groups with measured values farther away from the consensus value, some higher, others lower. This same general pattern is often observed in many interlaboratory studies and meta-analyses. In the conventional treatments of such data, the mutual inconsistency is addressed by inflating the reported uncertainties, either multiplicatively, or by the addition of random effects, both reflecting the presence of dark uncertainty. The former approach is often used by CODATA and by the Particle Data Group, and the latter is common in medical meta-analysis and in metrology. We propose a new procedure for consensus building that models the results using latent clusters with different shades of dark uncertainty, which assigns a customized amount of dark uncertainty to each measured value, as a mixture of those shades, and does so taking into account both the placement of the measured values relative to the consensus value, and the reported uncertainties. We demonstrate this procedure by deriving a new estimate for $G$, as a consensus value $G = 6.67408 \times 10^{-11} \,\text{m}^{-3} \, \text{kg}^{-1} \, \text{s}^{-2}$, with $u(G) = 0.00024 \times 10^{-11} \,\text{m}^{-3} \, \text{kg}^{-1} \, \text{s}^{-2}$.

physics.data-an↗

arXiv2014

Construction, Measurement, Shimming, and Performance of the NIST-4 Magnet System

The magnet system is one of the key elements of a watt balance. For the new watt balance currently under construction at the National Institute of Standards and Technology, a permanent magnet system was chosen. We describe the detailed construction of the magnet system, first measurements of the field profile, and shimming techniques that were used to achieve a flat field profile. The relative change of the radial magnetic flux density is less than $10^{-4}$ over a range of 5 cm. We further characterize the most important aspects of the magnet and give order of magnitude estimates for several systematic effects that originate from the magnet system.

physics.ins-det↗