I put together a Segment Stomper as per LLoyd Johnson (Woodturner Pro) and I do use it however; I sometimes just use this set up to stack segmented rings right on the lathe. After I mount the base of the item I am turning onto a glue block or simply chuck it directly, I set up the Longworth attachment on the tailstock using a Vicmarc collet chuck. The longworth attachment I have has a center hole (approx 13/16"). I turned a small dowel with one end to fit the collet chuck and the other end to fit through the centering hole of the Longworth. After positioning the ring in the Longworth and applying glue to the previously attached ring I will use the tailstock to apply pressure to the stack for a couple of minutes. I don't apply too much pressure so as not to crack the plates of the longworth. Once the ring has been set for a couple of minutes I back off the tailstock, remove the longworth and put a piece of plywood between the tailstock and newly applied ring. I can now apply a little more pressure. 
After having applied a few rings I true up the inside and outside of the stack then continue to apply rings. Though they are not the greatest quality, I have attached pics
After having applied a few rings I true up the inside and outside of the stack then continue to apply rings. Though they are not the greatest quality, I have attached pics