Just checking on the status of your project :) 

Core memory is reasonably low power; but takes high current at low voltage due to each core having 1-turn coils. High currents are not suitable for vacuum tubes, but gas discharge tubes can do it (neon lamps, flash tubes, etc.) So perhaps something like a neon lamp relaxation oscillator can generate a high enough current pulse to X-Y select the cores. I suspect it will take something bigger than an NE-2 to get a high enough peak current, though.

Neon tubes are too slow, you wouldn´t get more than 10kHz out of them.
I´ve done a tube synthesizer with them before, they are really only suitable for low frequencies - although they have nice side effects when pushing beyond the limits :)
I will wind pulse transformers to drive the memory instead.
Coincidently, there is one paper from the 50ies that refers to that problem and proposes the same solution. I dunno if it has ever been tried, though.
Power tubes "always" existed, and money was not the problem when building those computers. Winding transformers would have been probably more costly than buying off-the-shelf tubes back than.
My only concern is the loss of bandwidth in the transformers. I will perform the experiments maybe next weekend, when time allows.
I´ll use a similar setup that CuriousMarc had in his videos, having two pulse generators and a power supply amplifier. I´ll check the transformer solution with that before proceeding with a final tube driver circuit.
Ramping of the pulses is extremely important to avoid multiple signals on the sense wire.
X has to come up first, then Y (or vice versa) with relatively soft slopes.
I´ll figure out the optimal timings with the lab setup and will tune the tube circuit with delay lines and grid resistors to produce similar pulse shapes.
The transformer cores already arrived, I got some from AliExpress in two different sizes.
The tubes are rated for 15mA continuous current at 200V. As I´m using 48V, the tube limits out at 20mA anyways, ca. 12mA when it´s tuned to the sweet spot.
The transformer will have a ratio of 1:15 or 1:20 - that´s why I have concerns to achieve a bandwidth of 1MHz - but we´ll see in a couple of days.
If it doesn´t work, I´ll use power tubes for the driving stage to either reduce transformer windings or get rid of the transformers at all. The problem is the price of power tubes. They would cost 10-20x as much as the ones I got. I mean, the reason I´m building up this beast is the low cost of the tubes. I got them for 10% of the market price. I assume they come either from Russia or from Ukraine. Someone needed to get rid of new old stock. Despite beeing bought from a reseller, they are still cheap enough to make the project possible.

Paul, what about a small thyratron, like the 2D21? Datasheet is at tube-data.com/sheets/137/2/2D21.pdf. It switches on in 0.5uSec, off in 35uSec, has a peak current of 500ma and continuous average current of 100mA. Finding a few is easy, though finding a quantity of them would be difficult.

There are (or were) quite a few other gas trigger tube. Some are quite small; like a neon lamp with a 3rd control grid. I'm not sure which ones you can still find. Some of them were used in street lamp "starter" circuits, which were produced by the millions.

On transformers: You should have no trouble operating them at as high a frequency as you need. With the right core and winding technique, they work well into the UHF range!

Happy hacking! :-)

Thanx for the info on the 2D21. Switch time of 35µs is too slow, so I´ll probably stick with the transformers. But it might come handy for peripherals, like driving a loudspeaker or lamps.

"without having any obligations." The only way to enjoy a project.

It will be 1400-2000 tubes, depends if I can optimize a few more things.
I got them for dirt cheap, that´s why I decided to make a "big" computer. It will still be pricey, though. But it´s a 1-2 years project, so the budget can be stretched.
Each tube has a heat dissipation of 2W and will drive up to 1W max, less in average.

The building blocks will go into 19" racks, each one actively cooled. Got the racks already.
The project design is ongoing for two months now, but it was not ready for publishing until now.

I finished experiments with logic gates and got them working properly up to 5 MHz @ 48V after some tuning. Will make a video when assembling some bigger building blocks. There are cheap but powerful supplies available. The supplies of course have semiconductors in them, but I´ll make that compromise for now. They can still be replaced later with linear transformers.
The bottleneck for speed is the core memory and the gate propagation depth. To reliably use it, the clock frequency will be around 500kHz. The propagation time on falling edge might be significantly shorter, so I could speed it up by changing the duty cycle of the clock.

Do you have an estimate of the number of tubes required, the power to run them and the required cooling?