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I've found an explanation on explainthatstuff.com. There are these electrons from the cathode that are going around in a circle (because of the magnetic field), passing next to the cavities.

Then it says:

As the electrons nip past the cavities, the cavities resonate and emit microwave radiation

I'm missing this piece, probably I'm not aware of the physics behind, and how does the radiation produced in one cavity go to the "main" cavity where the waveguide is placed?

Could you give me an explanation? Thank you!

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Here is a simple approximation to help.

Take a convenient bottle of dry-hopped IPA (or the soft drink of your choice) and drink off half of it. Now pucker up and blow air across the top of the bottle. You will notice this excites an acoustic resonance in the bottle, where the mass of the air entrained in the neck of the bottle bounces off the compliance of the air in the main part of the bottle. The beer bottle "cavity" is resonant at one fundamental frequency, and sound waves at that frequency fill the space surrounding the open end of the bottle.

At microwave frequencies, power is conducted not by currents flowing in a wire but by electromagnetic waves traveling down a hollow square tube, where their wavelength is of order ~the tube width. the tube exhibits a certain amount of microwave capacitance and inductance which depend on the shape of the tube which means you can then fashion yourself a resonant cavity for microwaves, in analogy with the beer bottle cavity resonator described above.

If you then whirl electrons around in a circle past the openings of a series of microwave cavity resonators, it is like blowing air across the top of the beer bottle resonator. The cavity resonators get excited at their fundamental frequency and flood the inside of the magnetron with microwaves of that frequency, which you can then conduct out of the magnetron through another hollow tube.

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  • $\begingroup$ Oh, ok thank you :) But I'm still missing one thing, how the radiation enters in the cavity. Is it because of bremsstrahlung? And since we want this effect is this the reason why we put the magnet? $\endgroup$ – Matte May 12 at 19:08
  • $\begingroup$ The magnet is there to force the electrons into a circular path. The central cavity starts off filled with EM radiation across a range of frequencies, caused by the electrons giving off synchrotron radiation (because they are traveling in circles). the capacitance and inductance of the side cavities make them resonant at the desired output frequency and EM radiation at that frequency exits the side chambers and floods the main cavity. $\endgroup$ – niels nielsen May 13 at 1:42

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