# Can Cherenkov radiation be a color other than blue?

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?

### 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.

• If the material strongly absorbs blue light you might see a green glow as well... – Floris Mar 12 '16 at 21:45
• Because I'm interested in using the effect to build detectors the idea of intentionally absorbing any of those precious, precious photons simply hadn't occurred to me. But I suppose that such a material would likely have rapidly changing optical parameter in that regime, so I probably get away with this answer. – dmckee Mar 12 '16 at 21:47
• Fair point. I know all about "frantically preserving photons". One can get myopic. :-) – Floris Mar 12 '16 at 22:07
• @dmckee I'm still a bit confused. Would this equation make it possible to find out how to get a glow of a certain color? Would it be possible to get something like green Cherenkov radiation through air? – FeatAnalyzer Mar 13 '16 at 20:25
• The index of refraction and permeability of air vary little in the optical so you'll see blue. – dmckee Mar 13 '16 at 20:49