If I connect a piece of heavy copper wire or copper rod to the antenna cap of a magnetron can I guide the current so that microwaves would be emitted further away ?
Yes, but at microwave frequencies most cable connections are lossy. So instead, a waveguide is used which is a hollow metal pipe that exhibits low losses, confines the microwaves, conducts them to where you want them, and beams them out into space through a special antenna called a feed horn.
Lots of info on waveguides and feed horns can be found on the amateur radio stack exchange, which is populated by very helpful people.
$\begingroup$ ah cool to see you again Niels. I am precisely trying to avoid the waveguide (with a 6x3cm cross section), I want something more compact in order to deliver the heat in food (microwave penetration not that good contrary to pop belief). I can machine and perhaps solder (it's copper on the tip, and welding/brazing too risky) whatever would be needed to get a good contact $\endgroup$ Feb 27, 2022 at 19:10
1$\begingroup$ Hi Manu, good to hear from you. Short sections of wire are used all the time in microwave systems, so do not fear. The other trick would be to design the structure so that the magnetron itself is as close as possible to the load, to minimize the wire run. Note that if the wire has no grounded shield, it will radiate like crazy all along its length which is hazardous! best regards, Niels $\endgroup$ Feb 27, 2022 at 19:27
$\begingroup$ I would need about 25 cm of wire $\endgroup$ Feb 27, 2022 at 19:44