Cherenkov radiation - phase velocity not group velocity

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Discussion Overview

The discussion centers on the conditions under which Cherenkov radiation occurs, specifically addressing why a charged particle must travel faster than the phase velocity of light rather than the group velocity. Participants explore the relationship between phase velocity, group velocity, and concepts such as refraction and Mach cones.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why the relevant speed for Cherenkov radiation is the phase velocity of light (v=c/n) instead of the group velocity.
  • Another participant explains that Cherenkov radiation occurs when the phase of light cannot keep up with the particle, preventing a static field from forming around it.
  • A further inquiry is made into understanding qualitatively why phase velocity is the critical factor, drawing parallels to the refraction of light.
  • One participant suggests that the phenomenon is more akin to the Mach cone associated with supersonic sound, particularly in the context of relativistic light propagation.
  • A reference to classical theoretical physics textbooks is provided as a resource for further understanding the calculations related to Cherenkov radiation.

Areas of Agreement / Disagreement

Participants express differing views on the analogy between Cherenkov radiation and refraction, with some emphasizing the similarities while others suggest a more appropriate comparison to Mach cones. The discussion remains unresolved regarding the qualitative understanding of why phase velocity is the relevant speed.

Contextual Notes

Participants do not fully resolve the assumptions underlying the definitions of phase and group velocities, nor do they clarify the implications of these definitions in the context of Cherenkov radiation.

JoePhysicsNut
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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!
 
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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.
 
mfb said:
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?

mfb said:
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.
 
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 :-).
 

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