Cherenkov Radiation
When a charged particle moves faster than the phase velocity of light in a medium, it creates an electromagnetic shockwave — an optical Mach cone that glows characteristic blue. Seen in nuclear reactor pools worldwide.
n = —
cosθ: —
θC: —°
dE/dx: —
Threshold: —
Frank–Tamm Theory
Cherenkov radiation (1934, Nobel Prize 1958) occurs when a charged particle travels through a dielectric medium at a speed v > c/n, where c is the speed of light in vacuum and n is the refractive index. The threshold condition is βn = v·n/c > 1.
Like a sonic boom, the particle outruns its own electromagnetic field disturbances, which accumulate into a conical wavefront — the Cherenkov cone. The half-angle of this cone satisfies cosθC = 1/(nβ). At maximum speed (β→1), the cone angle approaches arccos(1/n).
The Frank–Tamm formula gives the energy radiated per unit path length per unit frequency: d²E/dx dω ∝ sin²θC. The spectrum is continuous and weighted toward higher frequencies (shorter wavelengths) — which is why the glow appears blue/violet. The total intensity scales as ω², meaning higher frequencies are more intense up to where the medium becomes absorbing.
This effect is used in Cherenkov detectors to measure particle velocities (knowing their momentum gives the mass). IceCube at the South Pole, Super-Kamiokande in Japan, and the ring-imaging Cherenkov counters (RICH) at CERN all rely on this principle. Nuclear reactor pools glow blue because fission products moving through water exceed the local speed of light there.