A bit has developed about the project in my mind over the last few days thinking about it. I think it lends itself well to a highly modular structure with 4 comprising the full thing: 1) a power supply, 2) the pulse generator (both the namesake and most trivial component), 3) an embedded µC-based timing unit, and 4) software for that timing unit to pipe data to on a PC.
1) Is straightforward, if I think one of the most useful bits of the project. Generating HV is useful for lots of things, but doing it in a comfortable fashion is tricky since, you know, it can kill you if you mess it up. Having banana leads clipped to mains floating around on the table is the easiest option, but also the most insane. I've been shocked going this route... well, we'll leave it there.
2) Because a high-bandwidth pulse is sort of the point.
3) it turns out, there are a lot of useful side-effects of the pulse generator circuit. Most obviously, its timing is non-deterministic, and the timing probability distribution is quite related to the charge voltage it's fed. I'm really interested in working with that both experimentally and as a random entropy generator. I need something with pretty high timing accuracy to actually listen to and log pulses.
4) Gotta get that data into the computer. I imagine I'll also set up some web server software, probably with a RasPi, to make the random output available online as well. Nothing cooler than entropy sources accessible via API!
Partly fleshed-out details and a video coming soon.