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What are the practical limits on generated wavelength in a Magnetron?

We know that Magnetrons could be used efficiently for generating microwaves for water heating, or for radar applications, but what are the achivable wavelength limits?

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Yeah, it would definitely help to put some more detail in. –  David Z Jan 11 '11 at 6:01
    
Wrote tiny clarification. –  BarsMonster Jan 11 '11 at 8:42
    
This seems like a question of searching the options in some vendor's catalogs, rather than a question about physics. –  Colin K Jan 14 '11 at 15:16
    
@Colin, I am wondering about theoretical limitations, not matter if there are practical/commercial implementations at the moment. –  BarsMonster Jan 14 '11 at 16:27

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To produce higher frequencies by a magnetron, one needs higher plate (anode) voltage and a stronger magnetic field, to keep the electrons within the central cavity. So, first limit is the magnet, if we exclude expensive solutions like superconductors. On the other hand, one could construct a wider central cavity, but remember, the cathode surface is the inner wall of it! This in turn would ask for a a lot of power to heat this cathode surface to yellow heat. Georg

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@Johannes: "resonance" of polar molecules in a liquid is impossible. The heating of bulk water in microwave ovens is due to relaxation of orientational polarisation. This errror is widespread. –  Georg Jan 16 '11 at 15:49

I interpret the question as "which frequencies/wavelengths can be generated by cavity magnetrons?" As far as the physics is concerned, I do not believe there are fundamental limits that constrain the frequencies generated. These frequencies are dictated by the cavity dimensions (see http://en.wikipedia.org/wiki/Cavity_magnetron). Now there are many practical engineering constraints (which brings the question outside the realm of physics) that render cavity magnetrons practical devices mostly for generating cm wavelength EM radiation. And of course as far as the heating of food is concerned, a magnetron needs to emit radiation that is in resonance with polar molecules. And that restricts magnetron wavelengths to cm scales.

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Mmm... Is it possible to generate 10nm deep UV light? Is it possible to build magnetron for 27Mhz radio? :-) –  BarsMonster Jan 16 '11 at 8:40
    
In principle (as far as the physics is concerned): yes. Generating 27 MHz radio waves would require a huge device, proper shielding, and would generate an abysmal efficiency. Going to higher frequencies you run into other engineering problems (like mentioned by Georg). –  Johannes Jan 16 '11 at 17:37
    
@Georg: well the word 'resonance' is wrong, but you get the point: the GHz frequencies are most efficient to heat up these polar molecules. –  Johannes Jan 16 '11 at 17:39

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