I have never had any problem coiling gold tube, Silver, 9 ct or 18
ct providing the wall thickness is about 0.5+ mm for about 2,5mm. By
the way how long are the lengths? The longer the better.
Find a piece of pipe, or steel just a bit smaller than the diameter
of the ID of the rings you need to make.
Make a piece of copper wire to fit tightly just into the end of the
tube, perhaps slightly taper with a file.
As you say, first anneal the tube and test a bit, if it does not
collapse then your in business.
Insert into the tube about 15 mm and carefully bend that end around
the mandril set vertically in a vice.
Prepare a second piece of copper wire to go into the other end of
the tube. Start bending the wire and the tube. Get a friend to hold
the bent end as you carefully coil the rest of the length around the
mandril, when you reach the end just continue to coil the copper a
bit. Remove copper.
You should have a perfect coil, you may need to adjust the size a
bit, mark and cut. I use a piercing saw blade with the teeth facing
forward (as with a hack saw) cutting against the bench pin.
You can also draw down aluminium wire (welding rod) to just fit in
to the tube, all the way through, cut your rings and put in sodium
hydroxide which will eat out the aluminium.
Takeing Great Care!