Radiation damping.

Definition:

Radiation damping is an affect on intense signals in high field NMR. It appears during our calibration experiments using the water peak. It occurs when the rotating transverse magnetization of the sample is intense enough to induce a rotating electromotive force in the RF coil strong enough to act significantly back on the sample. In other words, the amplitude and phase of the RF pulse is disturbed by feedback from the sample. As detailed below radiation damping causes peak broadening, peak asymmetry, phase shifting, and residual signals at 180 and 360 degrees in the flip cycle, all of which can interfere with accurate calibration. The effect becomes greater with greater field strength (ie. it's worse on the 600, and will presumably be even worse on the 700). It affects high power pulses more than low power pulses.

Apparently the extra field produces a magnetization vector in the rotating frame that lags 90 degrees behind the B₁ field vector of the applied pulse (defined as the x axis) for reasons that might be found in:

Bloom S. Effects of radiation damping on spin dynamics J. Appl Phys (1957) 28: 800-805.
Bloembergen N, Pound RV. Radiation damping in magnetic resonance experiments Phys. Rev. (1954) 95: 8-12.

Let's call the radiation damping field vector B_rd. The two vectors B₁ and B_rd act simultaneously, and so produce a composite vector which is actually affecting the nuclei. However, conceptually it is easier to picture what is happening if you think of giving a pure B₁ square pulse, sequentially with the B_rd pulse -90 degrees out of phase. You have to think of them both as being given starting from the +z state, since in fact they both are.

Distortion of the 180 degree signal:

The signal recovered after a 180 degree pulse most strongly reveals the nature of the radiation damping effect, since it can be conceptualized as giving a B_rd pulse followed by a B₁ pulse that causes no further signal.. If the signal is phased such that shorter B₁ pulses would give in-phase peaks, then the residual damping signal crudely appears as a dispersive signal. That is, its positive and negative intensity are equal. This is a reflection of B_rd being -90 degrees out of phase with B₁. However, changing the phase does not produce a Lorenzian peak. I'm guessing here, but I think the distorted look of this signal is because the radiation damping signal itself is not a square pulse. It is shaped in parallel to the rise and ebb of the transverse magnetization during the 180 degree pulse, producing a signal of mixed phase.

Tuning and peak width:

In the context of delivering a 90 degree square pulse, the distortion of the pulse is often described as broadening the water peak. One consequence of this is that if the probe is poorly tuned (therefore delivering less power and less damping), the water peak will appear sharper. The effect does not carry over to weaker signals (because they are not broadened in the first place), hence judging the signal to be of higher quality because the probe is poorly tuned is just wrong. The signal would just be weaker. The following web page posted at the UC Berkeley NMR facility has a discussion of intentionally detuning the probe to sharpen the water peak itself. The theme is whether or not this could be of benefit in suppressing the water peak.

http://www.cchem.berkeley.edu/nmr/apps/misc/radiation-damp.html

Distortion of 90 degree peak phase:

Since B₁ and B_rd are in different phases, the composite vector is shifted out of phase relative to the pure B₁ pulse. The phase of a hard water pulse is shifted relative to a soft water pulse. On the Avance600, if you measure the relative phase of a hard and soft water pulse at 90 degrees, and then measure it again at 1/4 90 degrees (where radiation damping is less of a factor), there is about a 4 degree discrepency. You may also notice an asymmetrical shape at the base of the 90 degree hard pulse water peak. For this reason, it is recommended to reduce the pulse time by 1/4 of the 90 degree time when trying to precisely calibrate phase, or to judge shimming by the line shape. The automatic phase correction on the avance instruments sets phases without the radiation damping effect. I have some confusion as to whether it would ever be superior to include the small shift from the radiation damping (for example by setting it with phcor21 in the HNCACBSE pulse program).

Note that the radiation damping effect continues to build as the flip cycle proceeds towards 180. So making the radiation damping effect small isn't a matter of making the recovered signal small; rather it's a matter of reducing the total damping radiation emitted during the pulse cycle. Since the damping signal feeds back during the pulse itself, it doesn't matter that the receiver hasn't been activated. One continues to accumulate damping signal till 180 degrees. So making the pulse time close to 180 rather than close to 0 would make the radiation damping effect worse.

Distortion of the 360 degree signal:

Proceeding through the second 180 degrees towards a 360 degree pulse, the tranverse magnetization produced is of opposite sign to that produced during the first 180 degrees. The perpendicular radiation damping magnetization produced is therefore also of opposite sign to that produced during the first 180 degrees. Hence the radiation damping component is progressively subtracted out. At 360, the radiation damping signal is essentially removed. There is a residual damping signal because of some T1 relaxation during the 360 pulse itself. Because of relaxation, the subtractive signal in the second 180 degrees is slightly less than the radiation damping signal accrued in the first 180 degrees. This leaves a very small positive residual radiation damping signature at 360.

Note that its not correct to think of the radiation damping signal reversing at 180 degrees as being related to reaching the 90 degree point of a flip cycle. It's more like the damping signal reaches some fraction of the way to a 90 degree flip and then is subtracted back towards zero.

Dealing with radiation damping during proton pulse calibration:

We use this information during hydrogen pulse calibration by zeroing the 360 signal rather than the 180 degree signal. Most relevant is that the residual damping signal is very small at 360, and might not even be noticed without expanding the scale. Secondly, for very precise calibration, the scale can be expanded and the residual damping signal at 360 can be observed. The phase should be adjusted so that a 90 degree signal (or better yet a 10-20 degree signal) is in phase. At 360, the damping signal will be a distorted dispersive signal (equal positive and negative intensity), whereas any residual signal along the y axis (from not being perfectly at 360) will perturb this symmetry.

Note that the radiation damping effect makes it totally impractical to judge the 90 degree pulse time by a maximal signal intensity. As the y axis signal starts to decline over 90 degrees, the dispersive damping signal is building at a maximal rate. This pushes the maximum composite signal intensity far in the the direction of the 180 degree pulse.

Questions remaining:

Is it ever right to include the B_rd phase shift in calibrating the pulse used in 2 and 3D pulse programs? If a hard and soft pulse are both applied to a weak signal, then radiation damping doesn't occur and to have this phase shift in would distort the result. But if they are both applied to the actual water peak for water suppression, it might be true that the water signal is first generated with the phase shift in and that the suppression mechanism would have to take that into account. I'd have to look at the mechanics of the water suppression routines being applied. I suspect that first some kind of presaturation is applied to water, so that when the 90 degree pulse is applied there isn't a big water signal to start with. In that case, any subsequent pulsed applied to further suppress the water signal should not have the B_rd shift in them. Empiracally, water suppression started working a lot better when I started calibrating phases at 22.5 degrees rather than 90 degrees, so I suspect that the B_rd shift is never right to include.
Empirically, I discovered that 22.5 degree pulses worked better than 90 degree pulses in terms of avoiding various peak shape disturbances, but I seem to remember some problem with peak shape in even shorter pulses. This should be re-explored now that I have a stronger understanding of the radiation damping effect.
So are the 180 and 360 signals really symmetrical? The B_rd shape is probably not exactly symmetrical because of T1 relaxtion affecting the 2nd quadrant and the damping effect itself affecting the 2nd quadrant. It would be possible to test whether the 180 time judged by making the residual signal symmetrical is exactly 1/2 the 360 time judged by making the residual signal symmetrical. The assumption is that assymmetry in the damping signal itself would more profoundly shift the apparent null of the B₁ signal at 180 because the damping signal is so much higher at 180. If there is an assymmetry at 180, then there might be one at 360 also. It's probably only an academic question, since the 360 times seem to be set close enough without even looking at the damping signal.