This phenomena, aside from providing the eerie lighting in this picture from Idaho National Lab, is a central tool for many particle physics experiments. Actually, it's so important, it won Chernkov the Noble prize in 1958. We recall that it's analogous to a sonic boom, but for light, and we can explain it in purely in terms of classical electrodynamics.
The derivation is in full in Jackson, but I'll sketch it here. We consider a charged particle moving through a medium, where all the distant interactions of the particle with the atoms in the material are represented by a macroscopic dielectric constant  "\inline \epsilon (\omega )")
. Taking the Fourier transforms of the E&M wave equations, we get the E and B fields as follows:
Then, after integrating in k and recognizing the modified Bessel function, we get three field components in terms of 
, in each direction, where here 1 is parallel to the particle's velocity. I'll skip straight to the limit where 
(a and b are impact parameters, and lambda is ] "\inline \lambda^2 = \frac{\omega^2}{v^2}[1- \beta^2\epsilon(\omega)]")
), which gives:
We integrate over frequency to get energy over distance 
, which has Jackson explains is done rather elegantly by finding the energy flow through a cylinder radius a. After this integration and applying our limit, we get an expression which is multiplied by:
If lambda has a positive real part, this vanishes at large distance as the energy is deposited near the path. If lambda is purely imaginary, the exponential is unity and the expression is independent of scattering distance a, so some of the energy escapes to infinity as radiation! When is lambda imaginary? When epsilon is real (there is little absorption) and
Or, the speed of the particle is greater than the phase velocity of the E&M fields in the material. That's it!
We've now seen that with the right circumstances, namely the speed of the particle is greater than the phase velocity in the material, some of the energy of the particle escapes as "Cherenkov" radiation. You can go on to calculate the angle of emission and the photon yields, but I'll leave that to another post in which I'll describe the practical applications of this effect.
Source: Jackson's Classical Electrodynamics
Source: Jackson's Classical Electrodynamics
such a cool effect! it's too bad my experiment doesn't take advantage of it.
ReplyDeletein undergrads I was told that astronauts were all like, "dude i'm seeing blue flashes in my eyeballs". and the physicists in Houston were all like, "Cerenkov time", can anyone back that up?
ReplyDeleteI haven't heard about astronauts, but I have heard that in the early days of particle accelerators they would put their eye in a low energy beam to locate it. Of course, they'd see beautiful blue flashed. And die of cancer 30 years later.
ReplyDeletei've heard that about astronauts too, mostly from when they are passing through the van allen belts on their way to the moon. i don't think it happens that much in low earth orbit, i.e. the space station
ReplyDeleteThis abstract seems to back up the claim: http://www.ncbi.nlm.nih.gov/pubmed/12678106
ReplyDelete