Light from Cherenkov radiation

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SUMMARY

Cherenkov radiation occurs when a charged particle travels through a medium at a speed greater than the speed of light in that medium, resulting in light emitted at a specific angle relative to the particle's trajectory. This phenomenon is due to the interference of light waves emitted at different points along the particle's path, creating a characteristic conical emission pattern. The discussion also raises questions about the behavior of uncharged particles, like neutrons, which are composed of charged constituents, and the mathematical principles governing the angle of emission based on the particle's speed.

PREREQUISITES
  • Understanding of Cherenkov radiation principles
  • Familiarity with electromagnetic theory
  • Basic knowledge of particle physics
  • Concept of refractive index in different media
NEXT STEPS
  • Study the mathematical derivation of Cherenkov radiation angles
  • Research the electromagnetic response of media to charged particles
  • Explore the behavior of neutrons in relation to Cherenkov radiation
  • Investigate the implications of superluminal speeds in particle physics
USEFUL FOR

Physicists, students of particle physics, and researchers interested in the properties of light and charged particles in various media will benefit from this discussion.

TheCanadian
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What exactly is the physical origin behind light produced by Cherenkov radiation having a non-zero angle with the trajectory of superluminal charged particle? Why is the light simply not allowed to go in any direction? Also, is Cherenkov radiation observed for "uncharged" particles (e.g. neutrons) that are still composed of charged constituents (e.g. quarks)?
 
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The point is that light waves emitted at different points along the path interfere so that the light rays seem to propagate normal to the cone.
 
DrDu said:
The point is that light waves emitted at different points along the path interfere so that the light rays seem to propagate normal to the cone.

That appears somewhat visually clear from the diagram, where it's akin to a change in index of refraction due to the displacement of charges/electromagnetic response from the medium), although is there perhaps a clearer mathematical explanation or resource that describes why the cone of that particular angle for a particular speed is the result?

I guess I'm interested in the mathematics behinds why this begins at the speed of light, and what limiting expression exists for even below the speed of light. For example, would not a charged particle simply even approaching superluminal speeds result in a non-zero similar effect (e.g. electromagnetic response from the medium) on the propagation of photons through the medium?
 

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