This follows on from the introductory NMR material on the introductory page. In all of the following animations, the blue arrow corresponds to the effective magnetic field, while the pink arrow is the magnetization vector, \(\mathbf{M}\).
To recap, excitation can be viewed either in the lab frame:
or in a rotating reference frame:
This frame can be moving at the local resonance frequency, the RF frequency (these could be different), or indeed any other frequency. More on that in the lecture notes.
RF pulses can be shaped, and this usually helps improve their selectivity in frequency (or space via an applied gradient). On resonance, slice selective pulses simply tip \(\mathbf{M}\) back and forth. Here is a long sinc pulse
and a heavily truncated one:
A time-resolved view of slice selection (here we see just the transverse magnetisation):
A k-space view of slice selection:
Frequency-swept pulses are frquently used to invert magnetization. Their properties differ quite a lot from the simple pulses shown above. Here is the magnetization trajectory from a simple pulse whose frequency is swept linearly, and whose magnitude is modified to maintain constant effective magnetic field strength in the rotating frame of the magnetization:
The dynamics are confusing to look at, but it is clear that \(\mathbf{M}\) does end up being inverted by this pulse. The picture would be simpler if we transform to the rotating frame moving at the instantaneous frequency of the RF pulse, rather than the resonance frequency of the magnetization. We can achieve this in part by making the camera move at the right speed:
Notice how the camera changes direction half way through - this is because of the frequency offset changing sign. Now the dynamics looks simpler, but the trails we have drawn are hard to interpret. Finally, we can do a better job by simulating directly in the rotating frame of the RF pulse:
The magnetization precesses around the effective magnetic field, which is swept down as the frequency of the pulse is swept. As long as the sweep is done slowly compared to the speed of rotation of \(\mathbf{M}\) about \(\mathbf{B_{eff}}\), \(\mathbf{M}\) remains locked-in and an inversion is achieved.
This analysis shows how adiabatic pulses work, however constant sweeps like this are not commonly used. An improved version is the Adiabatic Full Passage (AFP) which uses a time-variable frequency sweep that is designed to effectively invert \(\mathbf{M}\). Here we see it in the magnetization frame of reference:
Switching to the FM reference frame we see that the effective magnetic field is swept such that \(\mathbf{M}\) follows it closely:
This type of pulse can also be stopped half way, to make a \(\frac{\pi}{2}\) rotation, called an Adiabatic Half Passage (AHP):
In practical terms, the most popular type of adiabatic pulse is the hyperbolic secant pulse, which can achieve nice slice selectivity (and can be used as a refocusing pulse). Here is an example of the dynamics of \(\mathbf{M}\) in the rotating frame of the magnetization:
and in the frame of the pulse:
(c) Shaihan Malik 2017