The data are stored, so it's not a live-feed problem. It is an inordinate amount of data that's stored though. I don't actually understand this well enough to explain it well, so I'm going to quote from a book [1]. Apologies for wall of text.

"Serial femtosecond crystallography [(SFX)] experiments produce mountains of data that require [Free Electron Laser (FEL)] facilities to provide many petabytes of storage space and large compute clusters for timely processing of user data. The route to reach the summit of the data mountain requires peak finding, indexing, integration, refinement, and phasing." [...]

"The main reason for [steep increase in data volumes] is simple statistics. Systematic rotation of a single crystal allows all the Bragg peaks, required for structure determination, to be swept through and recorded. Serial collection is a rather inefficient way of measuring all these Bragg peak intensities because each snapshot is from a randomly oriented crystal, and there are no systematic relationships between successive crystal orientations. [...]

Consider a game of picking a card from a deck of all 52 cards until all the cards in the deck have been seen. The rotation method could be considered as analogous to picking a card from the top of the deck, looking at it and then throwing it away before picking the next, i.e., sampling without replacement. In this analogy, the faces of the cards represent crystal orientations or Bragg reflections. Only 52 turns are required to see all the cards in this case. Serial collection is akin to randomly picking a card and then putting the card back in the deck before choosing the next card, i.e., sampling with replacement (Fig. 7.1 bottom). How many cards are needed to be drawn before all 52 have been seen? Intuitively, we can see that there is no guarantee that all cards will ever be observed. However, statistically speaking, the expected number of turns to complete the task, c, is given by: where n is the total number of cards. For large n, c converges to n*log(n). That is, for n = 52, it can reasonably be expected that all 52 cards will be observed only after about 236 turns! The problem is further exacerbated because a fraction of the images obtained in an SFX experiment will be blank because the X-ray pulse did not hit a crystal. This fraction varies depending on the sample preparation and delivery methods (see Chaps. 3–5), but is often higher than 60%. The random orientation of crystals and the random picking of this orientation on every measurement represent the primary reasons why SFX data volumes are inherently larger than rotation series data.

The second reason why SFX data volumes are so high is the high variability of many experimental parameters. [There is some randomness in the X-ray pulses themselves]. There may also be a wide variability in the crystals: their size, shape, crystalline order, and even their crystal structure. In effect, each frame in an SFX experiment is from a completely separate experiment to the others."

"The Realities of Experimental Data" "The aim of hit finding in SFX is to determine whether the snapshot contains Bragg spots or not. All the later processing stages are based on Bragg spots, and so frames which do not contain any of them are useless, at least as far as crystallographic data processing is concerned. Conceptually, hit finding seems trivial. However, in practice it can be challenging.

"In an ideal case shown in Fig. 7.5a, the peaks are intense and there is no background noise. In this case, even a simple thresholding algorithm can locate the peaks. Unfortunately, real life is not so simple"

It's very cool, I wish I knew more about this. A figure I found for approximate data rate is 5GB/s per instrument. I think that's for the European XFELS.

Citation: [1]: Yoon, C.H., White, T.A. (2018). Climbing the Data Mountain: Processing of SFX Data. In: Boutet, S., Fromme, P., Hunter, M. (eds) X-ray Free Electron Lasers. Springer, Cham. https://doi.org/10.1007/978-3-030-00551-1_7