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arXiv 1903.08006quant-ph
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含时磁场中CPMG序列的自旋动力学

Spin Dynamics of CPMG sequence in time-dependent magnetic fields

Martin D. Hürlimann, Shin Utsuzawa, Chang-Yu Hou

摘要:

我们分析了随时间变化的磁场和射频场对Carr-Purcell-Meiboom-Gill(CPMG)序列自旋动力学的影响。该分析是基于一个单一的重聚焦周期的传播的本征模的磁化分解。对于足够缓慢的变化,在外部领域,磁化遵循变化的本征模式。这导致回波幅度随时间显示出规则的调制。更快的场变化可以引起本征模之间的跃迁。这种非绝热行为优先发生在拉莫尔频率与RF频率的特定偏移处,其中本征模式变得几乎退化。我们引入了瞬时绝热参数${\cal A}(t)$,它准确地预测了从绝热到非绝热制度的交叉,并允许场波动的分类。${\cal A}(t)$仅由静态条件下的单个重聚焦循环的性质以及场偏移的瞬时值及其时间导数确定。分析结果与数值模拟进行了比较。

英文摘要:

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.

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