Spin Dynamics of the Carr-Purcell-Meiboom-Gill Sequence in Time-Dependent Magnetic Fields

We analyze the effects of time-dependent magnetic and rf fields on the spin dynamics of the Carr-Purcell-Meiboom-Gill sequence. The analysis is based on the decomposition of the magnetization into the eigenmodes of the propagator of a single refocusing cycle. For sufficiently slow changes in the external fields, the magnetization follows the changing eigenmodes adiabatically. This results in echo amplitudes that show regular modulations with time. Faster field changes can induce transitions between the eigenmodes. Such nonadiabatic behavior occurs preferentially at particular offsets of the Larmor frequency from the rf frequency where the eigenmodes become nearly degenerate. We introduce the instantaneous adiabaticity parameter A(t) that accurately predicts the crossover from the adiabatic to the nonadiabatic regime and allows the classification of field fluctuations. A(t) is determined solely by the properties of a single refocusing cycle under static conditions and the instantaneous value of the field offset and its temporal derivative. The analytical results are compared with numerical simulations.