No need for that David. You need to melt the solder more slowly, using a gentle flame. Make sure the ends of the jump ring are in close contact, or they will shrivel apart.

For closing single jump rings, lay the join on a piece of solder and flux it. Then heat gently starting on the opposing side until the solder just flows.

For chain making, Thread on two closed ones adjust the open join and hold up with small fine tweezers, the join to be soldered at the top, and the finished joins at the bottom.
Add solder and flux. Move a slightly fiercer flame with a tentative action just above the new pallion of solder, and pull away when the solder melts. This could take 15 seconds or so.

Apply the flux and solder with a small natural artists brush, but do not burn the hairs. Dennis