Upon reading a bit more, I’ve noticed that sources mention using an elliptical mirror-which reflects waves from one focus to the other-instead of a parabola. This appears to mostly work, and I’ve looked into getting an elliptical chamber fabricated. The magnitude of the rarefaction behind the wavefront worries me a bit for some applications, but everything will change as more details are included.
The chamber will be open a bit before the focus so the waves can be applied to objects. The cords for the spark gap will go in the narrower hole in the back. I plan on doing more detailed simulation work before finalizing the chamber design and putting in an order.