The National Institute of Metrology (NIM, China) proposed a joule balance method to measure the Planck constant in 2006, and built the first prototype NIM-1 to verify its principle with a relative uncertainty of 8.9 × 10 -6 by 2013. Since 2013, a new joule balance NIM-2 has been designed, with a series of improvements to reduce the measurement uncertainty. By April 2017, NIM-2 has been constructed and can be employed to measure the Planck constant in vacuum. A first measurement on NIM-2 yields a determination of the Planck constant is 6.626 069 2(16) × 10 -34 Js with a relative uncertainty of 2.4 × 10 -7 . The determination differs in relative terms by −1.27 × 10 -7 from the CODATA 2014 value. Further improvement of NIM-2 is still in progress towards 10 -8 level uncertainty in the future.
-Permanent magnets with yokes are widely used in the watt and joule balances to measure the Planck constant for the forthcoming redefinition of the unit of mass, the kilogram. Recently, a permanent magnet system has been in consideration for a further practice of NIM-2, the generalized joule balance. In this paper, an analytical model to design the permanent magnet system is presented. The presented model can be solved to obtain the preliminary parameters and then is used as guidance for FEA software to optimize the parameters of such magnetic system. As a instance for the application of the designing model, the design of the permanent magnet system for NIM-2 is described and the special design of opening shape makes the misalign of the top and middle yokes has little influence on the vertical component of the magnetic field.Index Terms -Analytical model, watt balance, joule balance, permanent magnet.
The first determination of the Planck constant with the second generation of the joule balance, NIM-2, was completed in 2017 with an uncertainty of 2.4 × 10 −7 . Due to the movement of the magnet during the measurement process, the effect of the external field is a critical problem in NIM-2. At present, the electromagnet system is used in NIM-2. By taking the average of the results with positive and negative exciting currents, the uncertainty from the external field is reduced to 1.7 × 10 −7 , which is still the largest source in the uncertainty budget as all the other items are less than 1 × 10 −7 . In the near future, a permanent magnet system will be applied in NIM-2 and the main field cannot be reversed. Although the coupling of the external magnetic field in the permanent magnet system is about 40 times less than that in the electromagnet system, further reduction of this effect is still required in the permanent magnet system. In this paper, the effect of the external field is analyzed in both an electromagnet system and a permanent magnet system based on simulations and experiments. Then, the methods of magnetic shielding and compensation coils are proposed and simulated in the permanent magnet system. The results show that it may be possible to reduce the uncertainty of the external field to less than 2 × 10 −8 in the permanent magnet system by employing the two methods.
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