Brass tube was fitted inside the original barrel and the another brass tube was slide over that to give the right outside diameter. The muzzle brake was scavenged off of something, but it was not a purpose built piece. I noticed it and said, "hey that would make a great Pershing muzzle brake": Sorry I can't remember exactly what it came off . Might have been a piece out of an old hair dryer or something
I cover the barrel in a coat of auto body spot filler, and once dry, chuck it in my drill and sand it all smooth..