You can't do any real research into high impulse current without one. All I have is one of those freon filled probes but its useless if I keep picking up the voltage signal with my current probe.
I also thought a good method for starting would be to take your ring, glue it to a spin indexer, and make some kind of fixed pivot with a knife edge on it for initial marking, so you rotate it in your spindexer and peck at it with your fixed edge, or even mount a contoured pattern instead of a knife edge so you can scribe your follow line on the core.
You can make a contour pattern by drilling a hole the same diameter as your inner core, cutting it roughly in half, then filing it exactly in half, to make a semicircle, but instead of cutting it in half you would cut it along the axis between two opposite designated points and then file it on a flat. This way you don't really need machine tools.
Trying to think about how to get past the need for a spinindexer though. If its large enough it might be possible to make a precision rotational table using a fixed magnifier, a computer printed diagram and a round, I am wondering if you can use a sheet of glass cut with a glass hole scriber, then cut teeth in the glass using a diamond knife file (very fine for a very fine metric screw), you would need a very perfect circle, I don't think something generated by a hole saw is going to work good enough with how precise everyone wants this thing.
I would have to inspect some common round low thickness objects for roundness. What comes to mind is old CDROMS (they might be well regulated) that are glued together, old record player, or I think for a hobbiest the most accessible accurately sized and bearinged material would be to use an old hard drive, then glue a bunch of spindles together lined up on an axis, print out a marked strip (like for an encoder, glue it to the outside edge, then use a fine point file to make teeth that can interface with a lead screw (now getting the dimension of the tooth groove is difficult, its like making your own gears, I need to research this more... but you can also do something with brass), not sure how to do this again without a broach an a spindxer, all I can say is you need to be a competent and careful with filing and visual inspection, you might need some kind of a go/no go gauge too
But, if your lead screw is plastic or long enough to flex a bit without warping the table, it will act as a break and greatly reduce the amount of precision you need your gear teeth to have, since your optically aligning it like a caliper and you don't need high linearity.
Since your just using it for marking, backlash does not matter, only how ridgid it is, so your top computer printed scale would have to line up with some kind of overlay
This procedure would produce a little table that is capable of very fine rotation if you do it right, by adjustment of a lead screw, so you can mark sub degrees of your torroidal ring very accurately. I would recommend making fixed optical magnifiers so all the work during rotational marking is done under magnification (I plan on using a bench magnifier).
I hope that this will allow for enough symmetry that you get high CMRR without the shield, so you can make a useful measurement on a spark, after you shield it
Figuring out how to do the shield well is the next part.