# Spin Dynamics of CPMG sequence in time-dependent magnetic fields

## TL;DR

This paper investigates how time-dependent magnetic fields affect the spin dynamics of the CPMG sequence, revealing conditions for adiabatic and non-adiabatic behavior and introducing an adiabaticity parameter to predict these regimes.

## Contribution

It introduces an analytical framework and an adiabaticity parameter to predict spin behavior under dynamic magnetic fields in CPMG sequences, extending understanding of spin dynamics.

## Key findings

- Adiabatic following occurs with slow field changes, leading to regular echo modulations.
- Fast field changes cause transitions between eigenmodes, especially near degeneracies.
- The adiabaticity parameter ${
m A}(t)$ accurately predicts the transition between regimes.

## Abstract

We analyze the effects of time dependent magnetic and RF fields on the spin dynamics of the Carr-Purcell-Meiboom-Gill (CPMG) 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 non-adiabatic 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 ${\cal A}(t)$ that accurately predicts the crossover from the adiabatic to the non-adiabatic regime and allows the classification of field fluctuations. ${\cal A}(t)$ 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.