soldering
I have to "fix" some 50 micron tungsten wire to copper/brass.
Note that this is on a scale that is too small for a mechanical connection to be used (screws, clamps, etc.)
In looking at your picture, I'd say it looks like to me that:
In general, I squeeze wire strippers on the insulated wire to cut through the insulation, then twist the cut end as I pull it off to get a tidy twisted end, like this (though that's a lot longer than I would generally ever expose)
Once that's done, I coat the neat wire end with a copious amount of flux, then get a gob of solder on the tip of the soldering iron, then lay the gob on the wire until the solder is wicked into the wire. No need to rub the iron on the wire, or press, or do anything else - it'll all get soaked up as soon as the wire gets hot enough.
Once that's done, keep adding solder until right at the point you can barely distinguish the original stranding. At this point, the wire's tinned. If you tin the pads with a **little* solder, then soldering the two parts together should just involve laying the soldering iron on the wire with the wire on the pad.
You shouldn't ever need to push or rub or poke with the iron. Be sure to clean the tip off with a damp sponge immediately before you do any work.
If you're looking to get a solder joint like the one below, check out this tutorial on tinning wires and this tutorial on soldering to LED strips.
The big difference between a soldering gun and a "regular" soldering iron is the former is only heated for a few seconds, while the latter usually stays on all the time during work.
Because of that, the gun already is more efficient than a "regular" soldering iron. Very few needs to further improve it.
Apart, from that, why not choose brass? Because brass is more rigid and likely to break. That's bad for a tool which is meant to be thrown into a tool bag.
Best Answer
Assuming you need a Tungsten wire for high temperature heating, then :
Use a tiny copper pipe, hose and crimp to the filament ends. Screw or solder the copper terminals to PCB or whatever you need. In such way you will have a good contact which won't excessively heat when the filament will be turned on. In place of copper pipe you can use also a wrapped copper foil, but firmly crimping the copper will give best performance.