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Interesting question! Cherenkov radiation would definitely be inefficient for illumination. You only get Cherenkov radiation from charged particles moving faster than the local speed of light in a medium. If you have a transparent medium with index of refraction $n=2$ and you're sending fast electrons through it, you'll only get Cherenkov radiation while ...


Quite aside from the issue of ionizing radiation, Cerenkov generating particles also lose energy by other processes and that ends up as heat. Moreover, all the kinetic energy of the particles once they drop below the Cerenkov threshold is lost in non-optical channels (i.e. more heat). So no, they could never be anywhere near as efficient as diode ...

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