What is the mechanism behind transition radiation?

[JeffKoch]

We had a post-doctoral candidate interviewing this week who did his dissertation on OTR generated by relativistic electrons crossing a solid/vacuum interface. Unfortunately for him, he clearly didn't understand transition radiation, but it piqued the interest of the rest of us who interviewed him. Can anyone explain it? Links to explanations? Wiki is useless, and I couldn't find any good links on Google. For example, the candidate indicated that each electron generates a small fraction of a photon, which is nonsense and tells me it must be a collective effect of many charged particles with an associated current density threshold - why, and what determines the threshold?

 

[Klockan3]

Well, if you consider that dielectrics works as distance lengthener, meaning that the electric field looks like it comes from further away if you sit behind a dielectric. If you go on with that and have a particle moving with a constant velocity through a dielectric medium if you look at its field it looks like its moving faster, call that effective speed, and as such when it moves from one medium to another you alter the effective speed in terms of fields which can be seen as an acceleration which becomes electromagnetic radiation as we all know.

Now, I have never heard of this before but nothing I said was wrong so then I am right.

 

[Astronuc]

Applications of Electrodynamics in Theoretical Physics and Astrophysics: Electrodynamics with Applications to Astrophysics
By Vitaliĭ Lazarevich Ginzburg

Ginzburg has another book, Transition Radiation and Transition Scattering, but it seems to be out of print.
https://www.amazon.com/dp/0852740034/?tag=pfamazon01-20

The search for a standard model Higgs at the LHC and electron identification using transition radiation in the ATLAS tracker
http://www.hep.lu.se/atlas//thesis/egede/thesis.html
http://www.hep.lu.se/atlas//thesis/egede/thesis-node1.html (TOC)
http://www.hep.lu.se/atlas//thesis/egede/thesis-node30.html
http://www.hep.lu.se/atlas//thesis/egede/thesis-node31.html#SECTION00710000000000000000 Transition radiation from a single boundary

 

[Vanadium 50]

It's in Jackson - section 14.9 in the 2d edition.

The quick answer is that an electron traveling for a long distance in free space has a certain electromagnetic field configuration. An electron traveling for a long distance in a dielectric has a certain, but different, electromagnetic field configuration. If you have an electron crossing from free space to a medium (or one medium to another), at the boundary these two configurations have to match up. A consequence of this matching is that you get radiation - the easiest way to see that you do is to think about the multipole expansion at the point of transition.

 

[Bob S]

First, Cerenkov radiation is radiation generated by a charged particle traveling faster than c/n in a dielectric (e.g., glass or plexiglass) with index of refraction n, where c is the speed of light. The directional cone of the light inside the medium approaches a fixed angle as the particle velocity approaches the speed of light. This is derived in the Quantum Mechanics book by Schiff, and in Jackson (see above).

When a charged particle in a vacuum approaches a surface with n>1 at speed greater than c/n, the surface image charges (which represent an image charge inside the dielectric or a foil) move toward the point of impact at speeds greater than c/n. The light cone of radiation peaks in the forward (or backward) direction. The radiated field is called transition radiation. At high Lorentz factor gamma, the opening angle of the cone is very narrow (roughly 1/gamma).

 

[Vanadium 50]

Bob, Cerenkov radiation is not the same as transition radiation.

 

[JeffKoch]

O.K., I finally got around to reading the links. Jackson's book was actually the most helpful ( this is amusing for anyone who had to wade through the book in graduate E&M), but I couldn't find anything relevant in my copy of Schiff's book - his index is notoriously useless.

I'm still hung up on the quantum aspect of this. The candidate indicated that it takes many, many high-energy electrons to create one transition radiation photon, which (if true - perhaps he was just mistaken) would indicate that there is a current density threshold. I don't understand what would be responsible for this threshold - I think I understand the basics and the angular pattern, but I don't understand why there would be a threshold current.

 

[Vanadium 50]

There's no threshold. Classically, you have a low intensity of transition radiation. Quantum mechanically, you have a low probability of photon emission.

 

[Bob S]

The reference for Cerenkov Effect (note spelling) in Schiff (2nd Ed. 1955) is on pages 267 -271. The threshold for this radiation is velocity of particle > c/n where n is index of refraction of media.

Many years ago I had to build some Cerenkov detectors for an experiment to selectively detect K mesons (actually deselect pi mesons that were faster). I was told to use a special clear fluoocarbon liquid FC-75. The liquid was about twice a dense as water, so I thought the index of refraction should be high, like maybe 1.6. Actually n = 1.275 for FC-75 (compare to water at 1.33), probably one of the lowest of any liquid or solid.

 

[Vanadium 50]

Bob, I say again, Cerenkov radiation is not the same as transition radiation.

 

[Bob S]

There's no threshold. Classically, you have a low intensity of transition radiation. Quantum mechanically, you have a low probability of photon emission.

Vanadium 50 is correct. There is no threshold for transition radiation (unlike Cerenkov radiation). The attached plot shows the energy radiated between 400 nm and 800 nm per incident charged (Z=1) particle for 1 < gamma < 30. For an electron with gamma = 2 (kinetic energy = 0.5 MeV), it is about 0.01 eV.
Cerenkov radiation is a volume effect; Transition is a surface effect (transition from one media to another). For more detail, see http://beamdocs.fnal.gov/DocDB/0006/000652/001/note2003-03.pdf or search the web.

 

[JeffKoch]

Quantum mechanically, you have a low probability of photon emission.

That's how I interpreted his statement at first, but it's a bit troubling. That would imply that some electrons manage to get away with moving from one medium to another without anything happening - but they all have the same initial and final "states" (traveling at a high velocity in one medium or the other), so it seems a bit like an electron moving from an excited electronic level to a lower level without emitting a photon. Does something else happen when no transition radiation photon is emitted?

 

[Vanadium 50]

That's how I interpreted his statement at first, but it's a bit troubling. That would imply that some electrons manage to get away with moving from one medium to another without anything happening

Correct.

so it seems a bit like an electron moving from an excited electronic level to a lower level without emitting a photon.

Not really. In one case you have a 500 MeV electron, and in the other, a 499 MeV electron and a 1 MeV photon. It's more like perturbing an atom in an excited state. Sometimes it transitions down, and sometimes it doesn't.

 

[JeffKoch]

Correct.



Not really. In one case you have a 500 MeV electron, and in the other, a 499 MeV electron and a 1 MeV photon. It's more like perturbing an atom in an excited state. Sometimes it transitions down, and sometimes it doesn't.

O.K., thanks, I think I'm wrapping my head around this.

 

[Bob S]

The transition radiation (TR) photons are very soft, visible and maybe soft x-rays. For 1 million 25-MeV electrons, you will get about 60,000 TR photons between 400 and 800 nanometers (3 eV to 1.5 eV), into a 2 pi solid angle. The photons peak at either a forward or backward angle, and the peaking MAY be at an angle of 1/gamma. The photons are polarized. Look up Ralph Fiorito on the web 'Fiorito "transition radiation" ' He has done a lot of theoretical work on TR.