Synchrotron radiation collimation

[TheDestroyer]

Can someone please explain why the synchrotron radiation is very collimated? not only with equations and not only with words, both please. But anyway any efforts is really appreciated :)

Thank you

 

[Bob S]

Hi destroyer-
Synchrotron radiation comes from very high energy electrons (over 1 GeV) in strong magnetic fields. Because the total electron energy is at least 2000 times the electron rest mass (0.511 MeV), the opening angle of synchrotron radiation is about 1/2000 (0.511/1000) radians.
[Added] More specifically, the transverse momentum (momentum transfer) needed to produce a synchrotron radiation photon is very small relative to the longitudinal momentum of a 1 GeV electron.
Bob S

 

[TheDestroyer]

In your first paragraph, what's the relation between the angle and energy in general?

and also I heard that it has something to do with Doppler effect, do you have an explanation related to that?

Thanks :)

 

[Born2bwire]

I do not think that the collimation or tight beamwidth has anything to do with the Doppler effect. The Doppler effect would affect the observed frequency of the radiation. What happens is that if the electrons are moving at near relativistic speeds or greater, then the emitted radiation is sent out in within a small angle, like a spot light, along the electron's velocity vector. Jackson's Classical Electrodynamics text (which I do not have in front of me at home) has a section that deals with this. In fact, if you were to watch a synchrotron from the side, you would see a flash of light/radiation as the electron's beam swept your eye. The faster the electron travels, the tighter the beam becomes. At slower speeds, the beam splits into two beams that emit at an angle away from the electron's velocity vector. Without having Jackson with me to refresh your memory I cannot go into the exact details though.

 

[TheDestroyer]

Thank you :), can anyone give me some mathematical treatment for this? I would like to understand what equation describes the angle.

 

[Bob S]

hello Destroyer-
The synchrotron radiation beam size should also include electron beam size and divergence in the vertical plane, and in addition beam momentum spread and dipole magnet bending angle in the horizontal plane, all convoluted.
The best description is in "Handbook of Accelerator Physics" by Tigner and Chao.
Bob S

 

[TheDestroyer]

Thank you guys :)

 

[Born2bwire]

Ahh crap, I just got back from the office and completely forgot to grab my copy of Jackson.

 

[TheDestroyer]

Don't bother so much pal, my exam is tomorrow :) hehehehehe