- Frank-Tamm formula
The Frank-Tamm formula yields the amount of
Cherenkov radiation emitted as a charge particle moves through a medium at superluminal velocity.When a charged particle moves faster than the
speed of light in a medium, it can emit aphoton while conservingenergy andmomentum , this process can be viewed as a decay.Equation
The
Energy emitted per unit length (travelled by the particle) per unit frequency is::dE = frac{mu(omega) q^2} {4 pi} omega (1 - frac{c^2} {v^2 n(omega)^2}) dx domega,
where mu and n(omega) are the permeability and
index of refraction of the medium, q is theelectric charge of the particle, v is the speed of the particle, c is thespeed of light in vacuum, and omega is the angular frequency of radiation.The total amounted of energy radiated per unit length is:
:frac{dE}{dx} = frac{q^2}{4 pi} int_{v>c/n(omega)} mu(omega) omega (1 - frac{c^2} {v^2 n(omega)^2}) domega
This integral is done over the frequencies which the particle's speed v is greater than speed of light of the media frac{c}{n(omega)}.
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