Cherenkov radiation
Cherenkov radiation (also
spelled Čerenkov) is electromagnetic
radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. The charged particles
polarize the molecules of that medium, which then turn back rapidly to their
ground state, emitting radiation in the process. The characteristic blue glow
of nuclear reactors is due to Cherenkov radiation.
It is named after Russian scientist Pavel
Alekseyevich Cherenkov, the 1958 Nobel Prize winner who was the
first to detect it experimentally.[1]
A theory of this effect was later developed within the framework of Einstein's special relativity theory by Igor Tamm
and Ilya
Frank, who also shared the Nobel Prize. Cherenkov radiation is sometimes
considered to have been predicted by the English polymath Oliver
Heaviside in papers published in 1888–1889, although Heaviside's prediction
considered particles hypothetically moving faster than light in vacuum, which
is impossible according to the modern theory of relativity.
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 would otherwise propagate 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 (EM) in its medium.
Electrons in the atoms
of the medium will be displaced, and the atoms become 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.) Under normal conditions, these photons
destructively interfere with each other and no
radiation is detected; however, when a disruption which travels faster than
light is propagating through the medium, the photons constructively interfere
and intensify the observed radiation.
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 photonic shock wave
as it travels through an insulator.
In the figure, the particle (red
arrow) travels in a medium with speed 
such that 
, where 
is speed
of light in vacuum,
and 
is the refractive
index of the medium. (If the medium is water, the condition is 
,
since 
for water at 20 °C.)
such that , where is speed
of light in vacuum,
and is the refractive
index of the medium. (If the medium is water, the condition is ,
since for water at 20 °C.)
We define the ratio between the
speed of the particle and the speed of light as 
. The emitted light waves (blue arrows) travel at speed
.
. The emitted light waves (blue arrows) travel at speed
.
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 speed of light in that medium, that particle will radiate from a cone
behind itself, 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).
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 
cannot
be satisfied. Since the refractive index is a function of
frequency (and hence wavelength), the intensity does not 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
frequencies just below those corresponding to core electronic transitions in a
material, as the index of refraction is often greater than 1 just below a
resonance frequency (see Kramers-Kronig relation and anomalous dispersion).
cannot
be satisfied. Since the refractive index is a function of
frequency (and hence wavelength), the intensity does not 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
frequencies just below those corresponding to core electronic transitions in a
material, as the index of refraction is often greater than 1 just below a
resonance 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,[4]
as in cosmic ray visual phenomena.
Uses
Detection of labeled 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.
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 from these charged particles is
used to determine the source and intensity 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.
and MAGIC. Similar methods are used in very
large neutrino
detectors, such as the Super-Kamiokande, the Sudbury Neutrino Observatory (SNO) and
IceCube. In
the Pierre Auger Observatory and other similar
projects tanks filled with water observe the Cherenkov radiation caused by muons, electrons and
positrons of particle showers which are caused by
cosmic rays.
Cherenkov 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
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 (
, where is the speed
of light, and 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.
, where is the speed
of light, and 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.
Vacuum Cherenkov radiation
Vacuum Cherenkov radiation is the conjectured phenomenon
which refers to the Cherenkov radiation of a charged particle propagating in
the physical vacuum.
The classical (non-quantum) theory of relativity clearly forbids
any superluminal
phenomena including this one because a particle with non-zero rest mass can
reach speed of light only at infinite energy (besides, the nontrivial vacuum
itself would create a preferred frame of reference, in violation of one of the
relativistic postulates). However, according to modern views coming from the quantum
theory, physical vacuum is a nontrivial medium which affects the particles
propagating through, and the magnitude of the effect increases with the
energies of the particles.[6]
As a result, an actual speed of a photon becomes energy-dependent and thus can
be less than the fundamental constant of speed
of light c=299,792,458 metres per second, such that sufficiently
fast particles can overcome it and start emitting Cherenkov radiation.
Other possibility arises in some Lorentz-violating theories
when a speed of a propagating particle becomes higher than c which turns
this particle into the tachyon. The tachyon with an electric charge would lose energy as Cherenkov radiation—just as ordinary charged
particles do when they exceed the local speed of light in a medium. A charged
tachyon traveling in a vacuum therefore undergoes a constant proper
time acceleration and, by necessity, its worldline
forms a hyperbola
in space-time.
