Cloud/Bubble Chamber As 3-D Display

Firstly I want to insert a disclaimer: I'm happy for any kind of particle detector to be used for this, but I don't think a spark chamber is useful, so it's cloud or bubble chambers.

Set up a cloud or bubble chamber in a transparent bottle. At one end, set up a particle accelerator to shoot subatomic particles into the chamber which can be steered using magnetic coils. This is a pretty similar situation to a CRT, which is more or less a particle accelerator with an evacuated glass bottle at one end, so it's not a stretch to imagine a device like this commercially available for an affordable price.

There are two alternatives here. One is to use short-lived charged particles such as muons to produce lines oriented three-dimensionally in the chamber like contrails, ending when the muon annihilates. The problem with this approach is that they will produce a streak going all the way from the start of the chamber to the point where they annihilate, which is hard to control. The other is to use a neutral particle whose half-life is long enough to get it all the way across the chamber but controlling its velocity so that it decays into charged particles at the appropriate position. The entire chamber is scanned like a three- dimensional version of a raster scan display. I haven't worked out how these particles would be steered.

That's one version of my idea. The second is less flexible and I have [beanangel] to thank for planting the seed. Swallowtail catastrophe graphs have more than three dimensions. Apparently three dimensional sections of a swallowtail catastrophe can be observed at the bottom of a curved, three-dimensional surface illuminated by a strong light source such as a tea cup in the sun, in the form of the caustic projected onto the bottom of the cup. The position of the section can be varied by moving the relative positions of the light source and the reflecting surface. My suggestion is this: provide a source of ionising radiation which can be reflected by a curved surface of electrodes of the opposite charge to the particles which can be modified in shape, and aim the radiation into a cloud or bubble chamber. The result should be, with appropriate curvature, a caustic representing a three-dimensional section of a swallowtail catastrophe in three dimensions, and different sections can be imaged by varying the direction of the beam of charged particles.

I don't know if this next bit is mathematically coherent. If a swallowtail catastrophe can be imaged in this way, perhaps the other catastrophe graphs with more than three dimensions can too, so hypothetically with variations in the shape of the deflecting surface it might be feasible to produce butterfly catastrophes and the three conic section umbilics.

There's still more!

There are variations of each catastrophe graph where the points of the discontinuity can be shifted away from the centre. If parts of the caustic remain visible in these circumstances, this gives us relatively flat surfaces of clouds and bubbles which could be used to construct more conventional three dimensional shapes.

What I don't know is considerable, but one item on that list is whether there is even an analogous effect to optical caustics among charged particles. It seems to me that they would tend to repel each other and in fact I don't understand how caustics are possible in the first place as they strike me as violating the laws of optics.

A little help with this possible pile of nonsense would be much appreciated.