Cherenkov radiation

Physical origin

While electrodynamics holds that the speed of light in a vacuum is a universal constant (c), the speed at which light propagates in a material may be significantly less than c. For example, the speed of the propagation of light in water is only 0.75c. Matter can be accelerated beyond this speed (although still to less than c) during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (electrically polarizable) medium with a speed greater than that at which light propagates in the same medium.

Moreover, 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 employing 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 (whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity).

As a charged particle travels, it disrupts the local electromagnetic field in its medium. In particular, the medium becomes electrically polarized by the particle's electric field. If the particle travels slowly then the disturbance elastically relaxes back to mechanical equilibrium as the particle passes. When the particle is traveling fast enough, however, the limited response speed of the medium means that a disturbance is left in the wake of the particle, and the energy contained in this disturbance radiates as a coherent shockwave.

A common analogy is the sonic boom of a supersonic aircraft or bullet. The sound waves generated by the supersonic body propagate at the speed of sound itself; as such, the waves travel slower than the speeding object and cannot propagate forward from the body, instead forming a shock front. In a similar way, a charged particle can generate a light shock wave as it travels through an insulator.

In the figure, the particle (red arrow) travels in a medium with speed v p such that c / n < v p < c , where c is speed of light in vacuum, and n is the refractive index of the medium. (If the medium is water, the condition is 0.75 c < v p < c , since n = 1.33 for water at 20 °C.)

We define the ratio between the speed of the particle and the speed of light as β = v p / c . The emitted light waves (blue arrows) travel at speed v em = 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

whereas the emitted electromagnetic waves are constricted to travel the distance

So:

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.

Reverse Cherenkov effect

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, 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 will emit 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). 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).

Arbitrary Cherenkov emission angle

Cherenkov radiation can also radiate in an arbitrary direction using a properly engineered one dimensional metamaterials. The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle ( d ϕ / d x ), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation:

Characteristics

The frequency spectrum of Cherenkov radiation by a particle is given by the Frank–Tamm formula. 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 cos ⁡ θ = 1 / ( n β ) can no longer be satisfied. The refractive index n varies with frequency (and hence with wavelength) in such a way that the intensity cannot continue to increase at ever shorter wavelengths, even for very relativistic particles (where v/c is close to 1). At X-ray frequencies, the refractive index becomes less than unity (note that in media the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below the frequencies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonant frequency (see Kramers-Kronig relation and anomalous dispersion).

As in sonic booms and bow shocks, the angle of the shock cone is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge.

Cherenkov radiation can be generated in the eye by charged particles hitting the vitreous humour, giving the impression of flashes, as in cosmic ray visual phenomena and possibly some observations of criticality accidents.

Detection of labelled biomolecules

Cherenkov radiation is widely used to facilitate the detection of small amounts and low concentrations of biomolecules. Radioactive atoms such as phosphorus-32 are readily introduced into biomolecules by enzymatic and synthetic means and subsequently may be easily detected in small quantities for the purpose of elucidating biological pathways and in characterizing the interaction of biological molecules such as affinity constants and dissociation rates.

Medical Imaging of Radioisotopes & External Beam Radiotherapy

More recently, Cherenkov light has been used to image substances in the body. These discoveries have led to intense interest around the idea of using this light signal to quantify and/or detect radiation in the body, either from internal sources such as injected radiopharmaceuticals or from external beam radiotherapy in oncology. Radioisotopes such as the Beta emitters 18-F and 13-N or positron emitters 32-P or 90-Y have measurable Cherenkov emission and isotopes 18-F and 131-I have been imaged in humans for diagnostic value demonstration. External beam radiation therapy has been shown to induce a substantial amount of Cherenkov light in the tissue being treated, due to the photon beam energy levels used in the 6 MV to 18 MV ranges. The secondary electrons induced by these high energy x-rays result in the Cherenkov light emission, where the detected signal can be imaged at the entry and exit surfaces of the tissue.

Nuclear reactors

Cherenkov radiation is used to detect high-energy charged particles. In pool-type nuclear reactors, beta particles (high-energy electrons) are released as the fission products decay. The glow continues after the chain reaction stops, dimming as the shorter-lived products decay. Similarly, Cherenkov radiation can characterize the remaining radioactivity of spent fuel rods.

Astrophysics experiments

When a high-energy (TeV) gamma photon or cosmic ray interacts with the Earth's atmosphere, it may produce an electron-positron pair with enormous velocities. The Cherenkov radiation emitted in the atmosphere by these charged particles is used to determine the direction and energy of the cosmic ray or gamma ray, which is used for example in the Imaging Atmospheric Cherenkov Technique (IACT), by experiments such as VERITAS, H.E.S.S., MAGIC. Cherenkov radiation emitted in tanks filled with water by those charged particles reaching earth is used for the same goal by the Extensive Air Shower experiment HAWC, the Pierre Auger Observatory and other projects. Similar methods are used in very large neutrino detectors, such as the Super-Kamiokande, the Sudbury Neutrino Observatory (SNO) and IceCube. Other projects operated in the past applying related techniques, such as STACEE, a former solar tower refurbished to work as a non-imaging Cherenkov observatory, which was located in New Mexico.

Astrophysics observatories using the Cherenkov technique to measure air showers are key to determine the properties of astronomical objects that emit Very High Energy gamma rays, such as supernova remnants and blazars.

Particle physics experiments

Cherenkov radiation is commonly used in experimental particle physics for particle identification. One could measure (or put limits on) the velocity of an electrically charged elementary particle by the properties of the Cherenkov light it emits in a certain medium. If the momentum of the particle is measured independently, one could compute the mass of the particle by its momentum and velocity (see four-momentum), and hence identify the particle.

The simplest type of particle identification device based on a Cherenkov radiation technique is the threshold counter, which gives an answer as to whether the velocity of a charged particle is lower or higher than a certain value ( v 0 = c / n , where c is the speed of light, and n is the refractive index of the medium) by looking at whether this particle does or does not emit Cherenkov light in a certain medium. Knowing particle momentum, one can separate particles lighter than a certain threshold from those heavier than the threshold.

The most advanced type of a detector is the RICH, or Ring-imaging Cherenkov detector, developed in the 1980s. In a RICH detector, a cone of Cherenkov light is produced when a high speed charged particle traverses a suitable medium, often called radiator. This light cone is detected on a position sensitive planar photon detector, which allows reconstructing a ring or disc, the radius of which is a measure for the Cherenkov emission angle. Both focusing and proximity-focusing detectors are in use. In a focusing RICH detector, the photons are collected by a spherical mirror and focused onto the photon detector placed at the focal plane. The result is a circle with a radius independent of the emission point along the particle track. This scheme is suitable for low refractive index radiators—i.e. gases—due to the larger radiator length needed to create enough photons. In the more compact proximity-focusing design, a thin radiator volume emits a cone of Cherenkov light which traverses a small distance—the proximity gap—and is detected on the photon detector plane. The image is a ring of light, the radius of which is defined by the Cherenkov emission angle and the proximity gap. The ring thickness is determined by the thickness of the radiator. An example of a proximity gap RICH detector is the High Momentum Particle Identification Detector (HMPID), a detector currently under construction for ALICE (A Large Ion Collider Experiment), one of the six experiments at the LHC (Large Hadron Collider) at CERN.

In popular culture

The blue color of Doctor Manhattan in Watchmen may have been inspired by Cherenkov radiation. (In contrast, the typical depiction of radioactive materials as glowing green, as for example in The Simpsons, is most likely inspired by radium paint.)

The 'Cherenkov Effect' is mentioned in the Fabulous Furry Freak Brothers story "Burned Again" in Issue 7 of the eponymous comic book series written by Gilbert Shelton. When a canister of discarded plutonium is discovered, the Freak Brothers attempt to sell it for personal gain, however during a mix-up near an ice cream parlour, the agents trying to recover the plutonium discover a canister containing melted ice cream. The resultant misunderstanding leads a government agent to yell 'It's all melted and purple! We're seeing the Cherenkov Effect!'

Vacuum Cherenkov radiation

The Cherenkov effect can occur in vacuum. In a slow-wave structure, the phase velocity decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than 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 p = ℏ β ( β is phase constant) rather than the de Broglie relation p = ℏ k . This type of radiation(VCR) is used to generate high power microwaves.