Cherenkov radiation

Čerenkov radiation glowing in the core of a TRIGA reactor

Čerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than the speed of light in that medium. The characteristic "blue glow" of nuclear reactors is due to Čerenkov radiation. It is named after Russian scientist Pavel Alekseyevich Čerenkov, the 1958 Nobel Prize winner who was the first to rigorously characterize it.

Physical origin

While relativity 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 during nuclear reactions and in particle accelerators. Čerenkov radiation results when a charged particle, most commonly an electron, exceeds the speed at which light is propagating in a dielectric (electrically insulating) medium through which it passes.

Moreover, the velocity that must be exceeded is the phase velocity rather than the group velocity. The phase velocity can be altered dramatically by employing a periodic medium, and in that case one can even achieve Čerenkov 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 Čerenkov effects, such as radiation in a backwards direction (whereas ordinary Čerenkov radiation forms an acute angle with the particle velocity).

As a charged particle travels, it disrupts the local electromagnetic field (EM) in its medium. Electrons in the atoms of the medium will be displaced and polarized by the passing EM field of a charged particle. Photons are emitted as an insulator's electrons restore themselves to equilibrium after the disruption has passed. (In a conductor, the EM disruption can be restored without emitting a photon.) In normal circumstances, these photons destructively interfere with each other and no radiation is detected. However, when the disruption travels faster than light is propagating through the medium, the photons constructively interfere and intensify the observed radiation.

It is important to note, however, that the speed at which the photons travel is always the same. That is, the speed of light, commonly designated as c, does not change. The light appears to travel more slowly while traversing a medium due to the frequent interactions of the photons with matter. This is similar to a train that, while moving, travels at a constant velocity. If such a train were to travel on a set of tracks with many stops it would appear to be moving more slowly overall; i.e., have a lower average velocity, despite having a constant higher velocity while moving.

The geometry of the Čerenkov radiation.

A common analogy is the sonic boom of a supersonic aircraft or bullet. The sound waves generated by the supersonic body do not move fast enough to get out of the way of the body itself. Hence, the waves "stack up" and form a shock front.

In a similar way, a charged particle can generate a photonic shock wave as it travels through an insulator.

In the figure, the particle (red arrow) travels with speed $v_{p}$ and we define $\beta =v_{p}/c$ where $c$ is speed of light. n is the refractive index of the medium and so the photons (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

$x_{p}=v_{p}t=\beta \,ct$

whereas the electromagnetic waves are constricted to travel

$x_{em}=v_{em}t={\frac {c}{n}}t$

So:

$\cos \theta ={\frac {1}{n\beta }}$

Note that since this ratio is independent of time, one can take arbitrary time periods and achieve similar triangles. The angle remains unchanged, 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.

Characteristics

Intuitively, the overall intensity of Čerenkov radiation is proportional to the velocity of the inciting charged particle and to the number of such particles. Unlike fluorescence or emission spectra that have characteristic spectral peaks, Čerenkov radiation is continuous. Around the visible spectrum, the relative intensity of one frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Čerenkov radiation. This is why visible Čerenkov radiation is observed to be brilliant blue. In fact, most Čerenkov 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 for which the equation above cannot be satisfied. Since the refractive index is a function of frequency (and hence wavelength), the intensity doesn't continue increasing at ever shorter wavelengths even for ultra-relativistic particles (where v/c approaches 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 energies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 at these energies.

As in sonic booms and bow shocks, the angle of the shock cone is directly related to the velocity of the disruption. The Cerenkov angle is zero at the threshold velocity for the emission of Cerenkov 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 Čerenkov radiation-producing charge.

Uses

Detection of labeled biomolecules

Čerenkov 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.

Nuclear reactors

Čerenkov radiation is used to detect high-energy charged particles. In pool-type nuclear reactors, the intensity of Čerenkov radiation is related to the frequency of the fission events that produce high-energy electrons, and hence is a measure of the intensity of the reaction. Čerenkov radiation is also used to characterize the remaining radioactivity of spent fuel rods.

Astrophysics experiments

When a high-energy cosmic ray interacts with the Earth's atmosphere, it may produce an electron-positron pair with enormous velocities. The Čerenkov radiation from these charged particles is used to determine the source and intensity of the cosmic ray, which is used for example in the Imaging Atmospheric Čerenkov Technique (IACT), by experiments such as VERITAS, H.E.S.S., and MAGIC. Similar methods are used in very large neutrino detectors, such as the Super-Kamiokande, the Sudbury Neutrino Observatory (SNO) and IceCube.

Čerenkov radiation can also be used to determine properties of high-energy astronomical objects that emit gamma rays, such as supernova remnants and blazars. This is done by projects such as STACEE, a gamma ray detector in New Mexico.

Particle physics experiments

Čerenkov 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 Čerenkov 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 Čerenkov 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 by looking at whether this particle does or does not emit Čerenkov 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 Čerenkov detector, developed in 1980s. In a RICH detector, a cone of Čerenkov light is produced when a high speed charged particle traverses a suitable gaseous or liquid 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 Čerenkov 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 Čerenkov 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 Čerenkov 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 (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.

Uses in Fiction

Mass Effect

The codex, Mass Effect's in-game encyclopedia, mentions Cerenkov radiation when describing faster than light travel. FTL travel in the game depends on creating a field that lowers the mass of the ship in order to accelerate it quickly. According to the codex, "If the field collapses while the ship is moving at faster-tan-light speed, the effects are catastrophic. The ship is snapped back to sublight velocity, the enormous excess energy shed in the form of lethal Cerenkov radiation."

Halo

Čerenkov radiation is mentioned several times in the Fall of Reach, First Strike and Ghosts of Onyx. It refers to a burst of radiation given off when fissile materials (such as those in nuclear weapons) return to normal space from a faster-than-light dimension.

Fiasco

In Hermes' journey to Quinta in Fiasco, light from Čerenkov radiation is described as the only light in the ship while the crew is in stasis.

Starship Troopers

In the novel Starship Troopers there is a reference to spaceships using "Cherenkov drive" as a means of travelling between star systems in the war against the "bugs" in that novel. There is also a reference to the "blue glow" of Cherenkov radiation being visible through windows in the spaceship hull.

Olympos

In "Olympos" first the human Harman, then the two moravecs Mahnmut and Orphu enter a wrecked submarine (the Global Caliphate submarine "The Sword of Allah") with many black hole warheads and see a bluish glow due to the Čerenkov radiation.

See also

• Bremsstrahlung
• List of light sources
• Frank-Tamm formula

References

• L. D. Landau, E. M. Liftshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon: New York, 1984).
• J. V. Jelley, Cerenkov Radiation and Its Applications (Pergamon: London, 1958).
• S. J. Smith and E. M. Purcell, Phys. Rev. 92, 1069 (1953).
• Chiyan Luo, Mihai Ibanescu, Steven G. Johnson, and J. D. Joannopoulos, "Cerenkov Radiation in Photonic Crystals," Science 299, 368–371 (2003).

External links

• Hyperphysics on Čerenkov radiation