Conditions for Cherenkov Radiation

In summary, Cherenkov radiation occurs when a charged particle travels through a medium at a greater phase velocity than the speed of light in that medium, causing the molecules to polarize and emit radiation. The particle will continue to polarize molecules until it loses energy and its velocity falls below the speed of light in the medium. Capture processes for high-energetic particles are rare. The group velocity of a particle is related to its velocity, and the phase velocity of massive particles always exceeds the speed of light in vacuum. Cherenkov radiation cannot occur in a vacuum as the velocity of the particle cannot exceed the speed of light. This is one of the arguments for why nothing can exceed the speed of light in a vacuum.
  • #1
Messiri
9
0
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.]
 
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  • #2
Messiri said:
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.
 
  • #3
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:

mfb said:
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)?
 
  • #4
Messiri said:
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.
 
  • #5
mfb said:
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.
 

Related to Conditions for Cherenkov Radiation

What is Cherenkov radiation?

Cherenkov radiation is a type of electromagnetic radiation that is emitted when a charged particle, such as an electron, travels through a medium at a speed greater than the speed of light in that medium.

What conditions are necessary for Cherenkov radiation to occur?

Cherenkov radiation can occur when a charged particle travels through a medium with a refractive index greater than 1 at a speed greater than the speed of light in that medium.

What is the relationship between the angle of Cherenkov radiation and the speed of the charged particle?

The angle of Cherenkov radiation is directly proportional to the speed of the charged particle. As the speed increases, the angle of Cherenkov radiation also increases.

What factors affect the intensity of Cherenkov radiation?

The intensity of Cherenkov radiation is affected by the speed of the charged particle, the refractive index of the medium, and the distance traveled by the particle through the medium.

What are the applications of Cherenkov radiation?

Cherenkov radiation has a wide range of applications in various fields such as particle physics, medical imaging, and nuclear engineering. It is also used in specialized detectors to identify high-energy particles and in radiation therapy to target cancer cells.

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