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Current into a low-resistance "heater" element is used to produce the heat required for Thermionic Emission [0] in a vacuum tube. You only need the heater/emitter to be hot, and insulating the tubes would just spread the heat around to everything inside of it — at some extreme, making everything into an emitter, instead of elements that control the emission.

[0] https://en.wikipedia.org/wiki/Thermionic_emission

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This is not really accurate. To get meaningful emissions from normal electrodes, you need to heat them up to about 2000 °C. Vacuum tubes operate at 700 °C or something like that. The trick is that one electrode is doped with special rare-earth additives that greatly increase electron emissions. The same treatment isn't applied to the rest of the device. So, even if all internal components have the same temperature, a vacuum tube can still work (to some extent).

100% correct and I appreciate the additional details! I couldn't come up with a good analogy to explain you want the emitter as a separate and unique element from everything else involved in a tube — oversimplified in the process.

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