Cherenkov radiation (/tʃəˈrɛŋkɒf/^[1]) (also known as Čerenkov or Cerenkov radiation^[2]) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium (such as distilled water) at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium.^[3] A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov.

The radiation is named after the Soviet scientist Pavel Cherenkov, the 1958 Nobel Prize winner, who was the first to detect it experimentally under the supervision of Sergey Vavilov at the Lebedev Institute in 1934. Therefore, it is also known as Vavilov–Cherenkov radiation.^[4] Cherenkov saw a faint bluish light around a radioactive preparation in water during experiments. His doctorate thesis was on luminescence of uranium salt solutions that were excited by gamma rays instead of less energetic visible light, as done commonly. He discovered the anisotropy of the radiation and came to the conclusion that the bluish glow was not a fluorescent phenomenon.

A theory of this effect was later developed in 1937^[5] within the framework of Einstein's special relativity theory by Cherenkov's colleagues Igor Tamm and Ilya Frank, who also shared the 1958 Nobel Prize.

Cherenkov radiation as conical wavefronts had been theoretically predicted by the English polymath Oliver Heaviside in papers published between 1888 and 1889^[6] and by Arnold Sommerfeld in 1904,^[7] but both had been quickly dismissed following the relativity theory's restriction of superluminal particles until the 1970s.^[8] Marie Curie observed a pale blue light in a highly concentrated radium solution in 1910,^[9] but did not investigate its source. In 1926, the French radiotherapist Lucien Mallet described the luminous radiation of radium irradiating water having a continuous spectrum.^[10]

In 2019, a team of researchers from Dartmouth's and Dartmouth-Hitchcock's Norris Cotton Cancer Center discovered Cherenkov light being generated in the vitreous humor of patients undergoing radiotherapy. The light was observed using a camera imaging system called a CDose, which is specially designed to view light emissions from biological systems.^[11][12] For decades, patients had reported phenomena such as "flashes of bright or blue light"^[13] when receiving radiation treatments for brain cancer, but the effects had never been experimentally observed.^[12]

While the speed of light in vacuum is a universal constant (c = 299,792,458 m/s), the speed in a material may be significantly less, as it is perceived to be slowed by the medium. For example, in water it is only 0.75‍c. Matter can accelerate to a velocity higher than this (although still less than c, the speed of light in vacuum) during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (can be polarized electrically) medium with a speed greater than light's speed in that medium.

The effect can be intuitively described in the following way. From classical physics, it is known that accelerating charged particles emit EM waves and via Huygens' principle these waves will form spherical wavefronts which propagate with the phase velocity of that medium (i.e. the speed of light in that medium given by ${\displaystyle c/n}$, for ${\displaystyle n}$, the refractive index). When any charged particle passes through a medium, the particles of the medium will polarize around it in response. The charged particle excites the molecules in the polarizable medium and on returning to their ground state, the molecules re-emit the energy given to them to achieve excitation as photons. These photons form the spherical wavefronts which can be seen originating from the moving particle. If ${\displaystyle v_{\text{p}}<c/n}$, that is the velocity of the charged particle is less than that of the speed of light in the medium, then the polarization field which forms around the moving particle is usually symmetric. The corresponding emitted wavefronts may be bunched up, but they do not coincide or cross, and there are therefore no interference effects to consider. In the reverse situation, i.e. ${\displaystyle v_{\text{p}}>c/n}$, the polarization field is asymmetric along the direction of motion of the particle, as the particles of the medium do not have enough time to recover to their "normal" randomized states. This results in overlapping waveforms (as in the animation) and constructive interference leads to an observed cone-like light signal at a characteristic angle: Cherenkov light.

A common analogy is the sonic boom of a supersonic aircraft. The sound waves generated by the aircraft travel at the speed of sound, which is slower than the aircraft, and cannot propagate forward from the aircraft, instead forming a conical shock front. In a similar way, a charged particle can generate a "shock wave" of visible light as it travels through an insulator.

The velocity that must be exceeded is the phase velocity of light rather than the group velocity of light. The phase velocity can be altered dramatically by using a periodic medium, and in that case one can even achieve Cherenkov radiation with no minimum particle velocity, a phenomenon known as the Smith–Purcell effect. In a more complex periodic medium, such as a photonic crystal, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (see below) whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity.^[14]

In their original work on the theoretical foundations of Cherenkov radiation, Tamm and Frank wrote, "This peculiar radiation can evidently not be explained by any common mechanism such as the interaction of the fast electron with individual atom or as radiative scattering of electrons on atomic nuclei. On the other hand, the phenomenon can be explained both qualitatively and quantitatively if one takes into account the fact that an electron moving in a medium does radiate light even if it is moving uniformly provided that its velocity is greater than the velocity of light in the medium."^[15]

In the figure on the geometry, the particle (red arrow) travels in a medium with speed ${\displaystyle v_{\text{p}}}$ such that $${\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}$$ where ${\displaystyle c}$ is speed of light in vacuum, and ${\displaystyle n}$ is the refractive index of the medium. If the medium is water, the condition is ${\displaystyle 0.75c<v_{\text{p}}<c}$, since ${\displaystyle n\approx 1.33}$ for water at 20 °C.

We define the ratio between the speed of the particle and the speed of light as $${\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}$$ The emitted light waves (denoted by blue arrows) travel at speed $${\displaystyle v_{\text{em}}={\frac {c}{n}}.}$$

The left corner of the triangle represents the location of the superluminal particle at some initial moment (t = 0). The right corner of the triangle is the location of the particle at some later time t. In the given time t, the particle travels the distance $${\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}$$ whereas the emitted electromagnetic waves are constricted to travel the distance $${\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}$$

So the emission angle results in $${\displaystyle \cos \theta ={\frac {1}{n\beta }}}$$

Cherenkov radiation can also radiate in an arbitrary direction using properly engineered one dimensional metamaterials.^[16] The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle (${\displaystyle d\phi /dx}$), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation: $${\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}$$

Note that since this ratio is independent of time, one can take arbitrary times and achieve similar triangles. The angle stays the same, meaning that subsequent waves generated between the initial time t = 0 and final time t will form similar triangles with coinciding right endpoints to the one shown.

A reverse Cherenkov effect can be experienced using materials called negative-index metamaterials (materials with a subwavelength microstructure that gives them an effective "average" property very different from their constituent materials, in this case having negative permittivity and negative permeability). This means that, when a charged particle (usually electrons) passes through a medium at a speed greater than the phase velocity of light in that medium, that particle emits trailing radiation from its progress through the medium rather than in front of it (as is the case in normal materials with, both permittivity and permeability positive).^[17] One can also obtain such reverse-cone Cherenkov radiation in non-metamaterial periodic media where the periodic structure is on the same scale as the wavelength, so it cannot be treated as an effectively homogeneous metamaterial.^[14]

The Cherenkov effect can occur in vacuum.^[18] In a slow-wave structure, like in a traveling-wave tube (TWT), the phase velocity decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than ${\displaystyle c}$. In such a system, this effect can be derived from conservation of the energy and momentum where the momentum of a photon should be ${\displaystyle p=\hbar \beta }$ (${\displaystyle \beta }$ is phase constant)^[19] rather than the de Broglie relation ${\displaystyle p=\hbar k}$. This type of radiation (VCR) is used to generate high-power microwaves.^[20]

Radiation with the same properties of typical Cherenkov radiation can be created by structures of electric current that travel faster than light. ^[21] By manipulating density profiles in plasma acceleration setups, structures up to nanocoulombs of charge are created and may travel faster than the speed of light and emit optical shocks at the Cherenkov angle. Electrons are still subluminal, hence the electrons that compose the structure at a time t = t₀ are different from the electrons in the structure at a time t > t₀.

The frequency spectrum of Cherenkov radiation by a particle is given by the Frank–Tamm formula: $${\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}$$

The Frank–Tamm formula describes the amount of energy ${\displaystyle E}$ emitted from Cherenkov radiation, per unit length traveled ${\displaystyle x}$ and per frequency ${\displaystyle \omega }$. ${\displaystyle \mu (\omega )}$ is the permeability and ${\displaystyle n(\omega )}$ is the index of refraction of the material the charged particle moves through. ${\displaystyle q}$ is the electric charge of the particle, ${\displaystyle v}$ is the speed of the particle, and ${\displaystyle c}$ is the speed of light in vacuum.

Unlike fluorescence or emission spectra that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the ultraviolet spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum.

There is a cut-off frequency above which the equation ${\displaystyle \cos <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=1/(n\mathrm{\beta <!--\; \beta \; -->})}$Zdroj:https://en.wikipedia.org?pojem=Cherenkov_effect
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