Conditions for Cherenkov Radiation

[Messiri]

As far as I know, Cherenkov radiation occurs when a charged particle travels through a medium at a greater phase velocity than the speed of light in that medium. Molecules in that medium are polarized and after de-excitation emit radiation.

But there are a couple of things about Cherenkov radiation that I don't understand:

1. Will the charged particle continue to polarize molecules until it loses energy and its speed falls below the speed of light in the medium?
2. If the charged particle is an electron, why isn't it simply captured by a molecule/atom? Why does it polarize molecules instead?

Looking forward to your responses and clarifications.

[This is my first post on PF, so if this thread is posted in the wrong section of the website, please inform me. Thank you.]

 

[mfb]

As far as I know, Cherenkov radiation occurs when a charged particle travels through a medium at a greater phase velocity than the speed of light in that medium.

Not like that.
Radiation occurs if [the actual motion of the particle*] exceeds [the phase velocity of light].

*in quantum mechanics, this is related to the group velocity. [The phase velocity of massive particles] always exceeds [the speed of light in vacuum].

The [ ] brackets are there to clarify the structure.

Will the charged particle continue to polarize molecules until it loses energy and its speed falls below the speed of light in the medium?

Yes. It loses energy via Cherenkov radiation, too.

If the charged particle is an electron, why isn't it simply captured by a molecule/atom? Why does it polarize molecules instead?

That can happen, but capture processes are usually rare for high-energetic particles.

 

[Messiri]

OK, so the charged particle will continue to polarize molecules until it loses energy and its velocity is at/below that of light in the medium and its energy is usually too high for it to be captured. Thanks mfb.

But I'm not sure I understand what you mean by:

Radiation occurs if [the actual motion of the particle*] exceeds [the phase velocity of light].

*in quantum mechanics, this is related to the group velocity. [The phase velocity of massive particles] always exceeds [the speed of light in vacuum].

The [ ] brackets are there to clarify the structure.

How is the group velocity related to a single charged particle's velocity, for example, an electron? Secondly, let's assume the medium is water for simplicity, I'm not sure about the implications of having the charged particle in a vacuum. Can we even have Cherenkov radiation in a vacuum (can the electron's velocity exceed c)?

 

[mfb]

How is the group velocity related to a single charged particle's velocity, for example, an electron?

If you express the electron as matter wave packet, the velocity of this packet is the group velocity.

Secondly, let's assume the medium is water for simplicity, I'm not sure about the implications of having the charged particle in a vacuum. Can we even have Cherenkov radiation in a vacuum (can the electron's velocity exceed c)?

We cannot have Cherenkov radiation in vacuum. The (group) velocity of the electron cannot exceed c.

 

[jlefevre76]

The (group) velocity of the electron cannot exceed c.

Actually, I thought this was one of the arguments for why, as far as we know, nothing can exceed the speed of light in a vacuum: because we have never witnessed something emit
Cherenkov radiation in a vacuum.