Phase lag in the amplitude modulated magnetic resonance

Abstract

Response of a magnetic spin system to the amplitude modulated radiofrequency field is studied. Spin system is assumed to obey Bloch equations. For a spin system resonant at Larmor frequency ω 0 , calculations demonstrate how the phase lags Φ ⊥ and Φ z , of magnetization components M x , M y and M z occur and how sensitive they are to the relaxation properties of the system. Relative to Larmor frequency the angular frequency of the amplitude modulation, Ω⪡ω 0 , is very low, at the same time it is comparable to the relaxation rates of the spins. With reference to the analytical solution of a damped harmonic oscillator a simple formula tanΦ ⊥=T 2Ω describes the magnitude of the phase lag Φ ⊥ as a function of relaxation time T 2 .