Equations of motion of the nuclear magnetization vector of a flowing liquid in a modulated magnetic field of a nutation coil

Abstract

At present, flowmeters based on nuclear magnetic resonance (NMR) are finding numerous applications in atomic power engineering (monitoring of cooling systems), in technologies employing aggressive chem ical media (e.g., acids and alkali) and biological solu tions (under sterile conditions), and in the petro chemical industry [1][2][3][4]. An important advantage of NMR flowmeters in comparison to other types con sists in the absence of a contact between the measuring system and flowing liquid. Another advantage is the possibility of measuring liquid flow rate q online. These devices require no preliminary calibration and ensure high precision of measurements (with errors within 0.3-0.4%) [1,[5][6][7]. The possibility of opera tion in the relaxometer mode, which is achieved by introducing additional electronics without changing the magnetic system design and flow circuit scheme, is an additional advantage. In this regime, it is possible to measure the relaxation constants of a flowing medium and, hence, to monitor changes in its state and/or physical conditions in the system (e.g., presence of impurities, temperature variations, etc.) [4][5][6]8].Instruments (magnetometers, spectrometers, flow meters, relaxometers, etc.) based on the phenomenon of NMR in flowing fluids employ the dependence of the measured response signal (nutation line) on amplitude H 1 and/or frequency ω n of the radio fre quency (RF) field in the nutation coil [4][5][6][7][8][9]. Once the mechanism of formation of the nutation line is known, it is possible to develop new measuring techniques and improve the design of instruments so as to increase their metrological characteristics.The aforementioned high precision of measuring flow rate q by NMR label flowmeters is achieved due to large slope S n of the nutation line [4][5][6][7][8][9]. However, rapid variation of q in the flowing liquid medium, especially in the case of a nutation line with large S n , can lead to changes in the amplitude and phase of the NMR response signal that will result in increasing error of measurement (in practice, up to 5%). This problem is especially topical in the case of measure ment of small flow rates q. We have solved this problem by arranging a nutation coil in the field between poles of a permanent magnet with induction B 0 = 0.038 T and inhomogeneity 1.4 × 10 -2 cm -1 , which was mod ulated by an RF magnetic field. Under the action of this modulating field, the nutation line exhibited broadening and acquired a comblike structure consist ing of satellite lines with various amplitudes and widths, which resembled the phenomenon of para metric resonance in optically oriented atoms [10][11][12][13]. By selecting proper parameters of the modulation field, it was possible to reduce the amplitude of satel lites down to a noise level. This result allowed the NMR label flowmeter to operate in a new regime of measurements from a preset U c to 0 (where U c is the amplitude of NMR signal at H 1 = 0, while "zero" in the inverted NMR signal corresponds to the labeled liquid)...