I have had this interesting idea for a very long time that I just remembered, so I will share it with you. The idea is as follows:

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A cathode ray tube constructed identically to a normal oscilloscope CRT, but with one key change. Instead of the screen being made of standard soda-lime glass coated with a layer of phosphor, make the screen out of uncoated uranium soda-lime glass. I know that from a glassworking perspective this sounds nearly impossible, so the whole entire tube might have to be made of uranium glass.

This will make a final product that has a completely transparent screen, making the electron gun (and deflection plates if present) visible, while still being able to illuminate the uranium glass screen green with the electron beam.

I think this floating image would look super super cool, and would be a nice demonstration as well. Maybe if using radioactive glass is a concern then terbium glass could be used, which is much more expensive but I hear has similar glowing properties.

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Does this seem possible at all?

Also, making a clear MV lamp out of uranium glass would be pretty cool, but that is unrelated to this idea.

The point of an instrument CRT is not to generate light, but to show well readable visual information. Without reflectrions, without any light spots from other bright object (glowing dathode visible through the clear front screen), or any other distraction.
So an uniform gray screen with a bright green pattern on it does the job,
just brightly lit pattern on transparent glass where the light going in back direction is reflecting from internal surfaces and where the cathode filament glow is visible will not make anything like well readable display.

@Medved
You are absolutely right, it would be very distracting and hard to see nicely. The point of this isn't to have a very readable/practical display, but to show the inner workings of a CRT while still getting to see an image.

You should note that not all phosphors are both sensitive to UVA and electron beam irradiation, and if something is bright under UVA it does not necessary mean it will be sensitive to cathode rays.

Though, it is known from the world of electron tubes, that the glass (lead glass I assume) often shows patterns of somewhat pretty blue glow, that definitely appears where some stray electrons from electrode system hit the tube's bulb. And at the same time lead glass is known to liminesce blue under UV. So there is a chance that uranium glass may behave in a same way.

Bottom line: I bet the same effect may be achieved with *much less effort* by scanning a thick piece of uranium glass with moderately powerful UVA or violet laser from a laser projector. 

That's a cool idea. I have an uranium glass vase with a flat bottom. Anyone experimenting with it should take good care that the beam itself is spread out enough to not risk eye damage, and that the beam is instantly shut off if the galvos or rotating mirrors stay stationary, if not all of the UVA light is absorbed or transformed by the uranium glass.

@RRK
I googled whether or not uranium glass would glow with an electron beam and got very few results, but the AI overview said that uranium glass should glow with an electron beam. I know that isn't the most accurate source of information, but maybe a similar effect could be had from lead glass like you mentioned or some other fluorescent glass types like terbium-doped glass if uranium glass won't work.

@Laurens
I saw a Youtube video of someone doing something similar except with a fluorescent plastic, and ended up making a sort-of usable monitor out of it.