Most people don't seem to realize the 22 Mag ammo is copper jacketed, and tend to just use a regular cleaning solvent. It doesn't even amaze me anymore when I buy a used 22 Mag, and clean it thorougly with Shooters Choice bore solvent, that the first patch comes out cobalt blue from the disolved copper. Treat a 22 Mag like a centerfire, and use a good copper solvent every time you do clean it.
Sincerely,
Garry