This is not yet a problem of how to get the Gas Cylinder back onto the barrel but to analyse why it happened. There are threads on the Barrel near the muzzle that the Gas Cylinder Lock screws onto. The first thing I would check is that the threads on the Barrel and in the Gas Cylinder Lock are in good condition and proberly engage, that is the Gas Cylinder Lock actually "locks" to the barrel.

A visual inspection of the threads on the Barrel and inside the Gas Cylinder Lock is obvious. If either or both are damaged you need to replace the damaged part(s). If the threads appear to be in good condition assemble the Gas Cylinder to the Barrel. This should be checked without the Gas Cylinder in place. Screw he Gas Cylinder Lock onto the Barrel while observing and feeling for binding or loosness. Once started onto the Barrel the Gas Cylinder Lock should positively screw onto the Barrel threads. If the Gas Cylinder Lock fails to stop against the shoulder on the Barrel, the threads on the Barrel, Gas Cylinder Lock or both are unserviceable and you will need to replace the Barrel and/or the Gas Cylinder Lock.

When assembling the Gas Cylinder make sure the Upper Hand Guard is fully seated in the band. (Make sure the band is properly assembled to the barrel) Assemble the Gas Cylinder and Gas Cylinder Lock. Turn the Gas Cylinder Lock onto the barrel until it stops and then back it off to align with the Gas Cylinder. Assemble the Gas Cylinder Lock Screw and hand tighten. During the assembly of the Gas Cylinder Lock Screw the Gas Cylinder should be drawn snug against the Gas Cylinder Lock.

If the Gas Cylinder, Gas Cylinder Lock and Gas Cylinder Lock Screw (the "gas plug" for all you that hate proper nomenclature here) were properly assembled you should not have had any problem with the Gas Cylinder as you described. I can only surmise that the Gas Cylinder lock was only partially assembled to the Barrel and I would suspect that you may have lost a turn or two of the threads on your Barrel and/or Gas Cylinder Lock.

If the rifle was properly assembled you probably have a dangerous condition that will need a competent gunsmith to diagnose and repair, most likely by replacement of the Barrel and/or Gas Cylinder Lock.

Your comments and images in post #6 seem to indicate you're assembling the Gas Cylinder, Gas Cylinder Lock and Gas Cylinder Lock Screw as a single unit to the Barrel. These three parts have to be taken apart and separately assembled to the rifle. Did you at any time disassemble this rifle, specifically the Gas Cylinder, or did there just come a day the Gas Cylinder assembly blew off the gun? I gather from your comments and images that you did not disassemble these parts and if that is the case I highly recommend that you take the rifle as it is and the ammunition you were using to a gun smith.

If you disasembled the Gas Cylinder then there is a good chance you merely reassembled it improperly and the following may be of use to you in properly assembling the Gas cylinder and componet parts to the rifle. If you improperly assembled the rifle there is a possiblity that the Operating Rod was damaged at the time your rifle malfunctioned as it probably struck the rear edge of the Gas Cylinder. In any case the rifle should be completely disassembled and inspected for damage.

Disassemble the Gas Cylinder Lock Screw from the Gas Cylinder and the Gas Cylinder Lock will then be separate components. Slide the Gas Cylinder onto the Barrel aligning the splines inside the Gas Cylinder with the grooves in the Barrel. Next assemble the Gas Cylinder Lock by aligning the threads inside the upper opening to the threads on the Barrel and screw the Gas Cylinder Lock onto the barrel as far as it will go. Back the lower opening in the Gas Cylinder Lock to align with the Gas Cylinder. Assemble the Gas Cylinder Lock Screw and tighten. (See my previous entry for more specific instructions regarding the inspection procedure of assembling these parts without the upper hand guard in place)

In one image the threads on the Barrel appear a little flat to me and in another image the threads appear OK. If you have been driving the Gas Cylinder, Gas Cylinder Lock and Gas cylinder Lock Screw onto the barrel as an assembly, as you show in your images, you had to have damaged the threads on the Barrel and/or the Gas Cylinder Lock. If you never disassembled the Gas Cylinder from the Barrel then there is a good chance the threads on the Barrel and/or inside the Gas Cylinder Lock were damaged at the time of the accident. In either case I hope only the threads inside the Gas Cylinder Lock were damaged because it will be considerably less expensive to replace than the Barrel.