Signal evolution in the local magnetic field of a capillary — analogy to the damped driven harmonic oscillator

The temporal behavior of the magnetization decay caused by the local inhomogeneous magnetic field of a capillary is analyzed. Respecting the diffusion of the spins surrounding the capillary and the strength of the susceptibility difference between the capillary and the surrounding medium, it is possible to distinguish different dephasing regimes. Each dephasing regime can be related to a certain characteristic form of the magnetization decay. If the influence of the diffusion dominates, the magnetization exhibits a monotonic decay. In the opposite case of dominating influence of the susceptibility effects, the magnetization shows an oscillating behavior. It can be shown that the dephasing process is closely related to the behavior of a damped driven harmonic oscillator.