Standard of Magnetic Flux Density

Magnetic flux density is the main quantity describing the magnetic field. Magnetic flux density is a vector quantity, its vector product with a current fiber element is equal to the force acting on this element. It is defined in terms of the magnetic flux quantity, which is the surface integral of magnetic flux density. The unit of magnetic flux density is tesla (T).

The main emphasis is placed on metrology of magnetic flux density of stationary (DC) magnetic field in vacuum or air. In vacuum, B = μ₀×H, where B is the magnetic flux density, H is the magnetic field strength, μ₀ = 1.256 637 062 12(19).10^-6 N×A^-2 [1] is the vacuum permeability (magnetic constant).

The realization of the Tesla (T) magnetic flux density unit is related to the realization of the magnetic field and at the highest national level is carried out in two ways, coil standards and standard devices using a suitable method of measuring magnetic flux density, usually some method of nuclear magnetic resonance (NMR).

The magnetic flux density to the electric current T×A^-1 (the constant K_B of the coil) is realized by coil standards and it is passed on or compared. Magnetic flux density is realized by passing current in the coil winding B = K_B×I. The permissible current through our national standard is up to 0.5 A, short-term up to 1 A. Values of up to 100 mT can be realized by the traceable secondary coil standards of magnetic flux density.

The Czech Metrology Institute produced a coil with one layer of winding wound in four sections into a cut groove on a frame made of quartz before 1984. The dimensions of the windings are chosen so that the homogeneity of magnetic flux density in the inner volume is as large as possible, it is the so-called Barker solenoid. This standard has been compared internationally several times and was after continuous monitoring and research declared in 1984 as Czechoslovakia national standard of magnetic flux density. After partial gradual modernization of the standard equipment, after improvements in the measurement methodology and after other comparisons, e.g. in VNIIM St. Petersburg and after the historically first comparison of magnetic quantities in Euromet Project No. 446 (PTB pilot laboratory), this standard was declared the Czech national standard of magnetic flux density in 2001. Our standard also participated in the subsequent key comparison of CCEM magnetic flux density. M.-K1 also with very good results.

For larger values of magnetic flux density, nuclear magnetic resonance (NMR) methods are usually used. The NMR standard method consists of measuring the frequency f_p resonance of protons in a magnetic field with magnetic flux density B. Magnetic flux density B is calculated from:

where gyromagnetic ratio of protons γ´_p is one of the most imporant fundamental physical constants and its recommended value is (CODATA 2018) 2.675153151(29) .10⁸ s^-1×T^-1 (1.1. 10^-8).

The device based on the NMR method of forced precession – precession of protons (hydrogen nuclei) or other atomic nuclei in a sample of water inserted into a stationary magnetic field with magnetic flux density B is another part of the national standard for magnetic flux density values of 0.02 T to 2 T. This method performs polarization of the nuclei of the working substance, the resonance effect and the indication of resonance in conjunction with frequency measurement in one and the same magnetic field.

The gap between the coil standard ranges and the forced precession NMR method is covered by another NMR method, the nutation method (NMR method with flowing water). It uses the resonance of protons in running water and the spatially separated magnetization of protons in a strong auxiliary field, the realization of the resonance effect in the measured field and the indication of resonance in another auxiliary field of a usually permanent magnet. The advantages of this method are significantly higher sensitivity, elimination of some effects of resonant frequency shift and less sensitivity to field inhomogeneity. The disadvantage is the greater complexity of the method and the incompactness of the device. We implemented the measuring equipment in-house between 1982 and 1984. The device includes a substantially redesigned NMR teslameter Sh1-1, redesigned for the NMR flow probe. It includes a running water circuit with a pump, an indicator permanent magnet of 0.2 T, coil probes of resonance with a digital programmable generator of electrical signal up to 500 kHz, a flow polarizer of water with an electromagnet and a Hewlet Packard counter. The original device is described in detail in [2], and was comprehensively published in [3]. In 2017, this method was modernised and improved [4]. As a national standard, it serves in the range of 0.1 mT to 200 mT.

International comparisons of these NMR methods in the range of 10 mT to 2 T have not yet been carried out in Europe and are not planned. For the time being, it is sufficient to rely on the knowledge of the γ ́p constant and relatively very accurate and commonly available frequency measurement.

[1] E. Tiesinga, P. J. Mohr, D. B. Newell and B. N. Taylor: „CODATA recommended values of the fundamental physical constants: 2018“, 2019. [Online]. Available:
https://physics.nist.gov/cuu/pdf/wallet_2018.pdf

[2] J. Kupec: „Etalony a vybrané metody měření magnetické indukce“, Kandidátská dizertační práce, Praha, 1984.

[3] J. Kupec, “Measurements of magnetic flux density with NMR methods using flowing water,” in Proc. BEMC, Teddington, U.K., Nov. 1997, pp. 44-1–44-4.

[4] M. Ulvr, J. Kupec: „Improvements to the NMR method with flowing water at CMI“, IEEE Transaction on Instrumentation and Measurement, vol. 67, No. 1, 2018, pp. 204-208.