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Some NMR experiments can be halted partway through the acquisition and still give perfectly valid results: The traditional 1H experiment for example. Others, like a Saturation Transfer Difference Spectrum will have errors in the magnitude of the peaks in it if it is halted, due to the fact it uses groups of pulses and takes the difference of between them.
Can the standard proton-proton NOESY pulse sequence be halted halfway through and give a usable spectrum, or will this introduce artifacts?
There are two big differences between the STD experiment and a NOESY that matter when aborting the experiment early. The STD is usually run as a 1D experiment, and it's using the phase cycle to substract the on- and off-resonance spectra from each other.
When you acquire a 1D spectrum with multiple scans, the scans are not saved individually but directly added up to one FID, at least on Bruker spectrometers. So if you abort a 1D experiment (you need to execute tr to do that in most cases, as the FID is only written to disk after all scans are finished in most pulse sequences), you can't just throw away the last incomplete phasy cycle. And with experiments like the STD, your actual signal is the difference of two larger signals, so one incomplete substraction can ruin your spectrum.
In a 2D spectrum the increments for the indirect dimension are measured and written to disk sequentially, so you can throw away the last incomplete increment if you would need to. In most cases the incomplete increment will not be saved at all to disk, so you'll end up with one less data point in the indirect dimension, but no incomplete ones that were aborted in the middle of the phase cycle. This depends on how exactly the pulse program is written, but I suspect that most standard sequences handle it this way.
I've stopped HSQC and NOESY spectra before they were finished pretty often, and never observed any artifacts that could be traced to the abortion of the experiment.
Very late answer, but well, maybe it will help someone else who reads this.
halted halfway through
2D experiments are acquired as a series of increments where $t_1$ is changed in order to generate the indirect frequency dimension ($F_1$).
On Bruker spectrometers, 2D pulse programmes are always written so that each increment is saved to disk as soon as it has been recorded. So, if you were running an experiment with 256 increments and you stop acquisition halfway you will still have 128 increments saved to disk; there is no need to use the tr command. Furthermore, since $t_1$ increments are usually acquired in a regular, uniform manner, this truncated data will still be suitable for Fourier transformation.* This is already pointed out in Mad Scientist's answer.
However, it omits one salient point: if you record only half of the increments for a 2D experiment, then the resolution in the indirect dimension will be decreased by a corresponding amount. Depending on the processing being used you may also find that there are truncation artefacts, which appear as 'wiggles' around the peak in the indirect dimension (although processing parameters are often chosen to minimise these anyway).
Whether that is 'usable' enough will vary depending on your use case. If you are looking for NOEs between two peaks that are quite close to one another, it's possible that it's not good enough. On the other hand, HSQC spectra are very sparse and you can often get away with it.
If you're unsure, you can test this out by processing the 2D data during acquisition, i.e. before stopping it. Just do xfb (Fourier transform), and if necessary apk2d (phase correction), plus whatever other processing you would normally do. TopSpin will process the data which have been acquired so far. If the results are good enough, you can stop the experiment. If they aren't good enough, don't stop it.
* Off-hand, I'm not sure what happens with NUS spectra, but I expect that it can still be processed as usual (you'll just end up with a lower NUS sampling percentage than what you initially keyed in). Note that using a very low NUS sampling percentage can—and will—introduce reconstruction artefacts.
