Cherenkov radiation is produced when a charged particle transmits through a material at a velocity greater than that at which light can travel through the material. This is analogous to the production of a
sonic boom when an airplane is traveling through the air faster than sound waves can move through the air. To create Cherenkov light, the charged particle must have a high enough velocity and therefore energy to meet the condition v> \frac{c}{n} or \beta > \frac{1}{n} where v, is the velocity of the particle, is greater than c, the speed of light in a vacuum divided by n, the
refractive index of the medium, or equivalently the with relativistic beta, \beta= \frac{v}{c}. The threshold condition can also be expressed in terms of the charge particle's energy through the
Frank–Tamm formula as E_{\text{th}} = \bigg( \frac{1}{\sqrt{1-\frac{1}{n^2}}} - 1 \bigg) m c^2. Thereby the incident particle must have above a specific energy in order create any Cherenkov radiation. This energy and velocity threshold relation is used as particle identification as a binary yes/no detection if any Cherenkov light is produced. The direction this light is emitted is on a cone about the direction the particle is moving, with the Cherenkov angle, \theta_c, having the relation \cos(\theta_c) = \frac{c}{n v} = \frac{1}{n \beta}. If the angle is measured, the particle velocity can be determined, with the resolution typically limited by chromatic error. The wavelength dependence from Cherenkov light is continuous and follows the Frank-Tamm formula \frac{d N_{\text{Cherenkov}}}{d \lambda} \approx \frac{ 2 \pi \alpha}{\lambda^2} \bigg(1 - \frac{1}{\beta^2 n(\lambda)^2} \bigg) (\Delta x) . Where the number of Cherenkov photons, N_{\text{Cherenkov}}, depends on constants like the fine structure constant, \alpha, and some path length \Delta x. Crucially, the frequency of Cherenkov photons follows a N_{\text{Cherenkov}} \propto \frac{1}{\lambda^2} wavelength dependence, which is unique compared to other types of emitted radiation like
bremsstrahlung,
line-emission or
scintillators. When one integrates this equation, the integration limits follow only to when the Cherenkov velocity conditions is met. With
dispersion in materials, this typically only goes up to a peak wavelength of ~200 nm, depending on the index of refraction dependence. Because of this, Cherenkov radiation is typically brightest in the UV/visible bands, 200 nm to 400 nm, which, for human eyes, gives its characteristic blue hue. However, Cherenkov radiation emits in any frequency range where the condition is met, i.e down to the radiofrequency range. Furthermore, the Cherenkov production method is extremely fast, to first order the transit time of a near-speed of light particle passing through a length through the material. Detailed calculations estimate Cherenkov pulses to vary ~1 to 100 femtoseconds, depending on details, and under specific conditions can be attosecond or shorter. In detectors, the temporal resolution of a Cherenkov detector depends more on the dispersion of the pulse or the speed of the amplification technique like a photomultipler. Other notable properties include that Cherenkov light is
coherent and
polarized. Most Cherenkov detectors aim at recording the Cherenkov light produced by a primary charged particle. Some sensor technologies explicitly aim at Cherenkov light produced (also) by secondary particles, be it incoherent emission as occurring in an electromagnetic
particle shower or by coherent emission, for example
Askaryan effect. ==Detector types==