Copper can be tig'd or mig's, but the most common process for joing it is by
brazing. I have done mig welding of some very thick copper (4"x5" solid)
used as buss bars on a gantry crane. Mig copper is not particularly hard,
but its a very weird looking arc and takes quite some time to get used to
setting it up.
Silver solder it. Better than either welding or brazing, and it has by
far the best visual appearance / required skill level ratio.
Downsides are that the solder is expensive (affordable at this level
though) and that it needs a well-fitting joint. It flows by capillary
action, rather than manually building up a fillet.
Advantages are that it flows by capillary action. You get it clean,
well-fitting and hot, then it just "flashes" by itself. You can even do
it in an oven without needing to touch it. The toolign is also cheap -
a few firebricks and a natural draught propane torch are enough.
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