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Spin Echoes

The vanishing of the transversal magnetization can not only be caused by incoherent dynamic processes, but also by static inhomogeneities. The apparent effect of these is the same as that of the spin-spin interaction. The relaxation resulting from them is usually denoted by $T_{2}'$, while the sum of the two phenomena is denoted by $T_{2}^{*}$.
However, an important difference is that while the coherence loss caused by the dynamic processes is final, the loss of coherence resulting from the static inhomogeneities of the static magnetic field is not. Due to the inhomogeneities, the phase of the local magnetization will differ in each position, but this does not mean that coherence is lost irreversibly. If the magnetization is rotated by 180° about the x axis by the exciting field, the phase of the local magnetizations, which precess slower, will be ahead, while the phase of the fast ones will stay behind. The local field, i.e. the local velocity of precession is not changed, thus the phase differences will decrease, the transversal magnetization will increase and an echo will be created.
At this point it is important to define what a “sequence” is. During MR studies radio pulses are emitted: gradients with different directions and magnitudes are switched on and measurements are performed periodically. Meanwhile, the spin system develops dynamically, so the succession and the precise timing of these steps are important. These parameters together are called the “sequence”, and they are usually described by diagrams similar to Figure 2.

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