Jinxin Xu

A determination of the Planck constant by the generalized joule balance method with a permanent-magnet system at NIM

The joule balance experiment has been carried out at the National Institute of Metrology, China (NIM) since 2007. By the end of 2013 the first generation of the joule balance (NIM-1) achieved a measurement uncertainty of 7.2 × 10−6 (k = 1). To reduce the measurement uncertainty further, the next generation of the joule balance apparatus (NIM-2) system is under construction. A new coil system using ferromagnetic material is being adopted in NIM-2 to reduce self-heating in the coils. However, the effects on the measurement of the mutual inductance from the nonlinearity and hysteresis of the ferromagnetic material will bring a considerable measurement uncertainty. Inspired by the watt balance, the measurement of the mutual inductance is replaced by an equivalent measurement of the magnetic flux linkage difference. The nonlinearity and hysteresis will not be a problem in the measurement of the magnetic flux linkage difference. This technique comes from the watt balance method. It is called the generalized joule balance method, which is actually a modification of the watt balance method. However, it still represents a valid change that can reduce the difficulty of dynamic measurement experienced using the watt balance. Permanent magnets can also be adopted in the generalized joule balance. To check the feasibility of the generalized joule balance method, some preliminary experiments have been performed on NIM-1. A yokeless permanent magnet system has been designed and used to replace the exciting coils in NIM-1. In this paper, the structure of the yokeless permanent magnet system is introduced. Furthermore, a determination of the Planck constant with the permanent magnet system is presented. The value of the Planck constant h we obtained is 6.626 069(17) × 10−34 J s with a relative standard uncertainty of 2.6 × 10−6.

The Improvement of Joule Balance NIM-1 and the Design of New Joule Balance NIM-2

The development of the joule balance method to measure the Planck constant, in support of the redefinition of the kilogram, has been going on at the National Institute of Metrology of China (NIM) since 2007. The first prototype has been built to check the feasibility of the principle. In 2011, the relative uncertainty of the Planck constant measurement at NIM is 7.7 × 10-5. Self-heating and swing of the coils are the main uncertainty contributions. Since 2012, some improvements have been made to reduce these uncertainties. The relative uncertainty of the joule balance is reduced to 7.2 × 10-6 at present. The Planck constant measured with the joule balance is h = 6.6261041(470) × 10-34 Js. The relative difference between the determined h and the CODATA2010 recommendation value is 5×10-6. Further improvements are still being carried out on the NIM-1 apparatus. At the same time, the design and construction of a brand new and compact joule balance NIM-2 are also in progress and presented here.

Coils and the Electromagnet Used in the Joule Balance at the NIM

In the joule balance developed at National Institute of Metrology, the dynamic phase of a watt balance is replaced by the mutual inductance measurement in an attempt to provide an alternative method for the kilogram redefinition. However, for this method a rather large current in the exciting coil, is needed to offer the necessary magnetic field in the force weighing phase, and the coil heating becomes an important uncertainty source. To reduce coil heating, a new coil system, in which a ferromagnetic material is used to increase the magnetic field was designed recently. However, adopting the ferromagnetic material brings the difficulty from the nonlinear characteristic of material. This problem can be removed by measuring the magnetic flux linkage difference of the suspended coil at two vertical positions directly to replace the mutual inductance parameter. Some systematic effects of this magnet are discussed.

A proposal for absolute determination of inertial mass by measuring oscillation periods based on the quasi-elastic electrostatic force

A quasi-elastic electrostatic oscillation method is proposed for the absolute determination of inertial mass, which is distinguished from the gravitational mass measurement in the watt balance experiment. The value of the kilogram is determined by comparing oscillation periods of the quasi-elastic electrostatic oscillator with different test masses and applying different dc voltages on a symmetrical twin-Kelvin-capacitor system. The required measuring quantities for this method include the capacitance, voltage, vertical distance and oscillation periods, which in principle can be measured with high accuracy. In addition, this experiment is insensitive to the air buoyancy and the heating problem, and it can be operated in air. Both the theory and experimental verifications are presented. (Some figures may appear in colour only in the online journal)

Designing Model and Optimization of the Permanent Magnet for Joule Balance NIM-2

The permanent magnet with yokes is widely used in watt and joule balances to measure the Planck constant for the forthcoming redefinition of the unit of mass, the kilogram. Recently, the permanent magnet has been in consideration for a further practice of National Institute of Metrology (NIM)-2, the generalized joule balance. In this paper, an analytical model to design the permanent magnet system is proposed. This model can be solved to obtain the preliminary parameters and then used as guidance for the finite element analysis software to optimize the parameters of such a magnet system. As an instance of the application of this designing model, the permanent magnet system for NIM-2 is described. The special shape of the contact areas minimizes the effect of misalignment of the top and middle yokes on the vertical component of the magnetic field.

Uncertainty evaluation for ordinary least-square fitting with arbitrary order polynomial in joule balance method

The ordinary least-square fitting with polynomial is used in both the dynamic phase of the watt balance method and the weighting phase of joule balance method but few researches have been conducted to evaluate the uncertainty of the fitting data in the electrical balance methods. In this paper, a matrix-calculation method for evaluating the uncertainty of the polynomial fitting data is derived and the properties of this method are studied by simulation. Based on this, another two derived methods are proposed. One is used to find the optimal fitting order for the watt or joule balance methods. Accuracy and effective factors of this method are experimented with simulations. The other is used to evaluate the uncertainty of the integral of the fitting data for joule balance, which is demonstrated with an experiment from the NIM-1 joule balance.

Precision square waves synthesized by programmable Josephson voltage standards for induced voltage compensation in a Joule balance

A programmable Josephson voltage standard (PJVS) can be used to generate a precision square wave for induced voltage compensation to measure the mutual inductance between the coils in a joule balance. In this paper, the influence of the transitions between quantized voltages in the synthesized square waves is analyzed in detail. The ratio of the time-integrated value of the transitions to the total waveform is reduced to several parts in 104 to improve the measurement accuracy. The influence of different configurations of the integrating digitizer is discussed. The result shows that when the voltages are in a quantum state, the time-integrated agreement between the measured and theoretical differences for two PJVS systems is within 4 × 10−9 V s V−1 s−1. For the total time integration of a voltage waveform larger than 2 V s, the combined relative uncertainty is less than 5.9 × 10−8 V s V−1 s−1. The result confirms the capability of the PJVS to generate a precision square wave for the joule balance.

A magnetic damping device for watt and joule balances

Unwanted coil motions in watt and joule balances will introduce additional measurement uncertainty and systematic biases. In this summary, an active magnetic damping device is designed to suppress undesired coil motions, e.g., horizontal displacement and rational tilt. A merit of the designed damping device is that it can be used during the dynamic measurement mode of watt and joule balances. The initial analysis shows that the presented device can damp or control five degrees of freedom of the coil motion.

Preliminary result of accurate gravimetry at NIM Joule balance site

A new Joule balance is being set up at the National Institute of Metrology China (NIM) for realization of mass redefinition through the Planck constant. The relative uncertainty goal of the numerical value of the Planck constant required for the redefinition of kilogram should not exceed 2.0×10-8. To reach this goal using experiments based on the Joule balance, the precision gravity value at the centre of a mass on the Joule balance must be determined with a relative uncertainty of 1.0×10-8. In this paper, we describe the gravimetry carried out at Joule balance laboratory especially in terms of the accurate gravity network.

Absolute Position Sensing Based on a Robust Differential Capacitive Sensor with a Grounded Shield Window

A simple differential capacitive sensor is provided in this paper to measure the absolute positions of length measuring systems. By utilizing a shield window inside the differential capacitor, the measurement range and linearity range of the sensor can reach several millimeters. What is more interesting is that this differential capacitive sensor is only sensitive to one translational degree of freedom (DOF) movement, and immune to the vibration along the other two translational DOFs. In the experiment, we used a novel circuit based on an AC capacitance bridge to directly measure the differential capacitance value. The experimental result shows that this differential capacitive sensor has a sensitivity of 2 × 10−4 pF/μm with 0.08 μm resolution. The measurement range of this differential capacitive sensor is 6 mm, and the linearity error are less than 0.01% over the whole absolute position measurement range.