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A coupled resonator model of the detection of nuclear magnetic resonance: Radiation damping, frequency pushing, spin noise, and the signal‐to‐noise ratio
Author(s) -
Guéron M.
Publication year - 1991
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.1910190104
Subject(s) - physics , radiation damping , resonator , noise (video) , electromagnetic coil , spin (aerodynamics) , nuclear magnetic resonance , sensitivity (control systems) , noise temperature , spins , resonance (particle physics) , signal to noise ratio (imaging) , computational physics , acoustics , condensed matter physics , atomic physics , optics , phase noise , quantum mechanics , electronic engineering , computer science , engineering , artificial intelligence , image (mathematics) , thermodynamics
Magnetic resonance involves two coupled resonating systems: the spins and the tuned receiver coil. We simulate the spin system by an equivalent electrical resonator. An analysis of coupled resonators leads to a straightforward derivation of properties such as radiation damping, frequency pushing, and spin noise. The theory is applied to recent experiments (M. Guéron and J. L. Leroy, J. Magn. Reson. 85 , 209–215 (1989)). The sensitivity of the spin noise experiment is shown to be T 2 /τ 0 , where 1/τ 0 is the rate of radiation damping. This result leads directly to a fundamental formulation of the usual signal‐to‐noise ratio,\documentclass{article}\pagestyle{empty}\begin{document}$$({\rm SNR)}^{\rm 2} = (m_0 B/\tau _0)/(4Fk\theta \delta \nu),$$\end{document}where m 0 is the equilibrium magnetic moment, θ is the temperature, and F is the noise figure of the receiver. An equivalent electrical resonator can also be used to describe the active medium of masers. © 1991 Academic Press, Inc.