Abstract
In this chapter, the evolution of coherences of uncoupled spins in inhomogeneous magnetic fields is treated. The attenuation of echo signals by irreversible effects such as relaxation or translational diffusion is not yet considered, but will be discussed in detail in Part II.
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If the magnetic field is particularly homogeneous so that coherences exist for a relatively long time without getting spoiled by inhomogeneities, so-called “radiation damping” [1, 45] comes into play as a third sort of irreversible attenuation mechanisms: Coherences manifest themselves as a precessing magnetization which again produces a rotating magnetic field. Hence, an oscillating voltage is induced in the pick-up RF coil. The corresponding current in the resonance circuit causes a secondary oscillating magnetic field which tends to drive the magnetization vector towards the z direction. The term “damping” is justified because Zeeman energy is dissipated in the resistive elements of the probehead circuit. One should, however, bear in mind that the magnitude of the magnetization is not changed, and the transverse component may even rise if the initial flip angle was greater than 90°. It is also known that in probeheads with high quality factor Q, back action of the coil on the evolution of spin coherences can arise [310] leading to “artifacts” in high-field high-resolution NMR. An operational remedy is the application of dephasing/rephasing field-gradient pairs in the non-acquisition intervals of the RF pulse sequence so that coherences are spoiled when not needed for acquisition. Other possibilities are (i) gated tuning of the probehead during the RF pulses and acquisition only [307]; (ii) feedback suppression of high currents in the RF coil except during the excitation pulses [64]; (iii) the use of composite RF pulses [504].
Such pulses are usually designated as “hard.”
Instants just before and immediately after an RF pulse are specified by the time at which the pulse occurs supplemented by — and + signs, respectively.
Note that we comply with Hahn’s original definition of the stimulated echo [186] which refers to isolated spins in inhomogeneous magnetic fields. Coherence-transfer or spin-order transfer effects generated in coupled spin systems are therefore considered as phenomena of a different physical origin even if the echo-time schedules coincide (see Sect. 7.2, for instance). In order to avoid confusion, the term “stimulated echo” should therefore not be used under such circumstances.
This does not mean that a net z magnetization arises!
That is, the sign of the Hamiltonian is reversed, whereas with the Hahn-echo pulse sequences the coherences and their phases are changed.
We are dealing here with two-pulse sequences. Recently three-pulse echo phenomena also related to the demagnetizing field, namely the multiple nonlinear stimulated echoes (NOSE) were discovered [12].
The demagnetization factor of a long cylinder with the axis aligned along B0 vanishes; that of a thin slab to which B0 is normal takes the value 4π.
Note that the spatial modulation of the z magnetization obviously disappears if the flip angle of the second pulse is β = 180°, but is maximal for β = 90°.
Recall that Ωδ is a nonlinear function of ΩG. This is represented here by the Fourier expansion in harmonics of ΩG.
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© 1997 Springer-Verlag Berlin Heidelberg
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Kimmich, R. (1997). Isolated Spins in Inhomogeneous Fields. In: NMR. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60582-6_2
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DOI: https://doi.org/10.1007/978-3-642-60582-6_2
Publisher Name: Springer, Berlin, Heidelberg
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