Recently, I asked a question about the plausibility of green superheated plasma (like the green plasma blasts in many video games) in real life. I actually found a post in the SciFi Stack Exchange asking a similar question about green plasma in Star Trek and noticed that one of the comments brought up Cherenkov radiation. After looking it up, I found that Cherenkov radiation is the blue glow around underwater nuclear generators caused by particles moving faster than the phase velocity of light in water.
My question is, can Cherenkov radiation be a different color than blue? Would the medium through which the particles are traversing, say air as opposed to water, have an effect on the color?
Best Answer
General Considerations
The place to start is with the Frank-Tamm formula for the quantity and spectrum of Cerenkov light. $$ \frac{\mathrm{d} E}{\mathrm{d}x\,\mathrm{d}\omega} = \frac{q^2}{4 \pi} \mu(\omega) \omega \left(1 - \frac{c^2}{v^2 n^2(\omega)} \right) \,, $$ where $v$ is the particle's speed, $q$ it's charge, and $\mu(\omega)$ and $n(\omega)$ are the frequency dependent permeability and index of refraction of the material respectively.
This depends on both the speed of the charged particles and the radiating material, but the explicit linear dependence on $\omega$ means that it tends to be brighter at higher frequency, leading to the characteristic blue appearance.
To find a material in which it had a different appearance would require seeking one for which $\mu$ or $n$ were strong functions of frequency in the higher frequency half of the human visual spectrum.
A Couple of Asides
Cerenkov radiation occurs whenever a charged particle passes through a medium at speeds faster than the $c/n$. There is nothing special about electron, water or nuclear reactors in that regard; those are just one of the very few situations in which you can see the light with the unaided eye.
The correct Anglicanism of the name is a matter of occasional debate. I had a Russian professor in grad school who preferred "Cerenkov" and I follow his lead.