Solution of the Bloch Equations in Weak Fields for Rapid Monitoring

Expansion of the functionality of rapid monitoring into the state of condensed matter by nuclear magnetic resonance in weak fields was shown to require solving the Bloch equations considering the features of recording its signal during field modulation. New relationships were obtained for the absorption signal v and dispersion signal u, as well as the z component of the magnetization, which made it possible to obtain a new explicit dependence of the critical points of the absorption signal (for the other two quantities, these dependences are derived similarly) on the field parameters, the autodyne circuit, and the relaxation times T1 and T2 of the medium under study. Based on the analysis of the obtained relationships, a new expression using u and v was proposed to describe the recorded NMR signal using the modulation technique. The calculated NMR signal was compared with the experimental one. The necessity was substantiated for creating automatic adjustment of the modulating field amplitude in the design of a mobile NMR relaxometer to increase the signal-to-noise ratio and reduce the influence of modulation effects on the research results.