Cherenkov radiation - phase velocity not group velocity

[JoePhysicsNut]

Why must the charged particle that leads to Cherenkov radiation travel faster than the phase velocity of light not the group velocity of light?

One of the sides of the triangle that is used to define cosθ is v=c/n i.e. the phase velocity. I don't see why it's one rather than the other.

Thanks!

 

[mfb]

Cherenkov radiation happens when the phase of the light cannot "keep up" with the particle, so you cannot get a static field around the particle (as seen by the particle).

One of the sides of the triangle that is used to define cosθ is v=c/n i.e. the phase velocity. I don't see why it's one rather than the other.

It is very similar to refraction of light.

 

[JoePhysicsNut]

Cherenkov radiation happens when the phase of the light cannot "keep up" with the particle, so you cannot get a static field around the particle (as seen by the particle).

Thanks for the reply! But again, is there a qualitative way of understanding why it's phase velocity not group velocity?

It is very similar to refraction of light.

True, refraction of light is also controlled by c/n - the phase velocity. Refraction can be understood from Fermat's principle, but again I don't know why it's one type of speed rather than the other.

 

[vanhees71]

It's not so much similar to the refraction of light but rather to the Mach cone of supersonic sound, here of course for the relativistic case of light propagation in a medium. You find the full calculation of the Cherenkov-radiation field in

A. Sommerfeld, Lectures on Theoretical Physics IV (Optics)

These are pretty old but very marvelous textbooks on classical theoretical physics. I really love those :-).