Cerenkov Radiation.

Cerenkov radiation is the term used to describe radiation produced when fast moving particles or cosmic rays pass through a transparent medium. When high-energy g rays pass through such a medium pair production may result. The speed of light in the medium is retarded to c/m , where m is the refractive index of the medium. Cerenkov radiation is emitted as particles pass the atoms in the medium. A cone of radiation is produced trailing the motion of the particle as seen in figure 1.

 

The half angle of the cone being given by:

q =tan-1[(m v2V2/C2-1)]

Where m v is the refractive index

V is the velocity of the particle where V >c/m v

The radiation is given by

Iv=e2v/2e oc2 (1-c2/m v2V2)

e o is the permittivity of free space

Cerenkov radiation was discovered in 1926 by Mallet. It was observed that the light had a continuous spectrum, having no "dark lines" characteristic of emission spectrum. The radiation was extensively studied between the years of 1934-1938 by Pavel Cerenkov (1904-1990). During his research Cerenkov found that the radiation was not a fluorescence effect and that the light was partially polarised. Cerenkov succeeded in speeding particles up over 230,000,000 ms-1. As can be seen from below this results in radiation moving faster than light. Particulate matter is often less susceptible to retardation than radiation such as visible light. Light is slowed in denser mediums and its velocity can be expressed as:

v= c/n

where v is the observed velocity

c is the speed of light in a vacuum 299, 792, 500 ms-1

n is the refractive index of the material.

The actual velocity one may expect to observe is discussed at length below.

It has been noted that the number of photons at a particular frequency or wavelength, as it turns out, is proportional to 1/l 2. Therefore, the smaller the wavelength (or conversely, the higher the frequency), the more photons arriving

 

As can be seen in figure two in the visible range, blue light predominates. The blue glow that can be seen associated with water in which highly radioactive nuclear reactor fuel rods are stored is caused by the Cerenkov effect.

University of Pennsylvania Web site

Though light in a vacuum travels at approximately 299, 792, 500 ms-1, this velocity is retarded by the density of the medium through which the light propagates as discussed previously. If we describe the density according to its refractive index, the ri being measured from Snell’s law:

According to Snell’s law

Refractive index n = sin i / sin r

However for ease of use if we assume an ri of 1.3 for water, then according to our equation:

v= c/n

velocity of light in water = 299, 792, 500 ms-1/1.3

velocity of light in water = 230,609,615 ms-1 to nearest integer

Pavel Cerenkov had succeeded in speeding electrons up to 257,500,000 ms-1 by 1934 thus sending particles at speeds greater than light. Beta particles with kinetic energies of 0.26 MeV will travel at speeds in excess of 230 thousand m/s in a dense medium such as water. Work was also conducted by Frank and Tamm in 1937 and the three shared the 1958 Nobel prize for their work in this area.

http://www.ne.uiuc.edu/Research/cerenkov.html 

When a fast moving charged particle moves through a medium such as water the effect is to polarise the water molecules in a direction adjacent to its path thus causing distortions in the electrical charge. In the wake of the particle, the molecules attempt to revert to their previous orientation. A pulse of electromagnetic radiation in the form of blue light is emitted as a result of this "reorientation." If the velocity of the particle is very much less than the speed of light a process of destructive interference tends to cancel the flash; however when the speed of the beta particle is greater than the speed, the light pulses are "amplified" through constructive interference.

The American Nuclear Society

The use of Cerenkov radiation is that the measurement of the trajectory of the pairs, both an electron and positron from a single gamma ray, we can determine the momentum, direction and magnitude, of the gamma ray itself.

As described above when a high-energy g rays pass through a medium, pair production may result. However, cosmic rays may also contain particles of relatively large size. If the initial cosmic ray was a nucleus there will also be muons in the showers. Muons are heavy electrons that have great penetrating power. Unfortunately, many particles have insufficient energy to reach the surface. However, the Cerenkov light generated will reach the ground, unfortunately this light will be very dim.

Though the light spreads out in a cone the size of this shape when observed at the surface is only around a couple of hundred metres across. Given the speed of light, that means that all of the Cerenkov light comes in about 10 nanoseconds. While this light comes too fast and is too dim to be viewed with the naked eye, large telescopes can focus the light onto an array of light sensitive detectors (known as photomultiplier tubes).

The Whipple collaboration, which pioneered the Atmospheric Cerenkov Technique for the detection of VHE gamma rays, is based at the F.L.Whipple Observatory in Southern Arizona, in the United States.

Sinnis Web Site Relating to the Milagro Telescope


 

Particles Produced By Astronomical Events and the Uses of Cerenkov Radiation

High energy particles and gamma rays are believed to be generated in a number of ways. One of these generators currently under study are Active Galactic Nuclei. The term AGN covers a variety of energetic types of galaxy. The most likely method for the generation of such high energy levels is a singularity at the centre upon which matter is accreting, at the rate of 1 or 2 solar masses a day in the more energetic cases. The central black hole is thought to have a mass of up to 108 solar masses. Energy from the central source is beamed away from the "poles" of the black hole. The energy is blocked by the accretion disk and radiates along discrete lines.

There are two forms of gas emitted "cool" moving at around 1% c and hot that moves very rapidly at relativistic velocities. These are referred to as astrophysical jets. Quite often what is observed is the energy given off by electrons via the synchotron effect caused by the leptons spiralling in a magnetic field.

University of Leeds Web Site

Another use would be to monitor gamma ray bursts from primordial black holes As gravity draws matter together, macrospcopically along the cosmic seeds, evidence of which was confirmed by COBE in 1992, so too would this affect small singularities. Although primordial black holes are rare, their actual density around other forms of matter may be higher than would be expected. We know from studying the gamma ray background that there can be no more than 300 per cubic light-year, however the observed density within the galaxy may be very different.

Even so the likelihood of detecting a black hole with a telescope is remote. The only chance really exists at the end of a black holes "life" when it effectively explodes. However as primordial black holes must have been around for 12 billion years even if they are reaching the end of their lives the margin of error may be thousands if not millions of years. Therefore the likelihood of detecting a nearby quantum singularity exploding is small. Thus we need to expand the search but in doing so we need a larger telescope than we can easily build.

Hawking 1988

The largest apparatus available is the atmosphere of the Earth. When a high-energy gamma ray hits the atoms in our atmosphere, it creates pairs of electrons and positrons. These create other collisions creating yet more virtual particles in a manner referred to as an electron shower. Unfortunately these showers are incredibly short lived and most likely occur in the high exosphere making them almost undetectable

However, there is one thing in our favour; these flashes of energy known as Cerenkov radiation travel extremely fast; at speeds approaching c, the speed of light in a vacuum. The result of this is that there is an intense time dilation, where by the particles experience time slower than we do. This is exactly the same as the proverbial "twins paradox". In the twins paradox two people, twins, are separated one remains on Earth while the other experiences travel at speeds approaching c. After a given length of time as measured by the Earth bound twin, the two people are reunited. However, the length of time the twin moving with velocity tending towards c is always less than the earth bound twin. We can calculate this using the Lorentz Fitzgerald contraction. The one we are interested in is time.

T=To/ 1-(v2/c2)

A discussion of the derivation of the Lorentz transformations and the affects of motion on mass and length can be found on the main site and in the glossary.

Cerenkov radiation is also produced when neutrinos strike the atmosphere. Neutrinos are very common particles and on average six hundred billion pass every square centimeter of atmosphere every 24 hours. These neutrinos very rarely interact and can travel over a tenth of the diameter of the galaxy before interacting with any matter. However, sometimes neutrino densities are even higher. Specifically when the light from a supernova reaches the earth. Strictly speaking, a neutrino burst hits around 3 hours prior to the light burst.

Supernova 1987 A, was the first visible supernova from Earth with the naked eye since Kepler’s observations in 1604. The star was previously known as -69 202. The neutrino burst detected was instrumental in the development of neutrino astronomy. Neutrino astronomy began in the 1960’s when theorsit John Bachall and experimenter Ray Davis in developed a chlorine tank for detecting neutrino collisions.

Neutrinos were first postulated in 1930 by Wolfgang Pauli to explain the movement of particles in radioactive decay and to make sure the conservation of momentum was observed. Basically in neutron decay a proton and electron are produced, also with the emission of a gamma ray. As there are only two particles microreversibility states that the sun of their paths should bring you back to the initial state:

Gribbin (1996)

By conservation of linear momentum

Mass * velocity before = mass * velocity after

\ Neutron mass 1.7*10-27kg * neutron velocity

= (Proton mass 1.7*10-27kg * proton velocity) + (electron mass 9.1*10-31kg * electron velocity)

There fore one might expect to see the two particle move away at 180 to one another with the electrons velocity high enough to cancel the mass of the proton, or with any angle whereby the two velocities are adjusted for the protons mass. One would not expect to find the two particles heading in a similar direction.

However, Pauli noticed these momentums suggesting something else was contributing to the momentum. As it could not be observed, its mass must have been small. In turn to take up such high momentum on its own, its velocity must have been incredibly high. That is very close to c. If the velocity equaled c, though, that meant its mass had to be zero and for a long time the existence of the particles was debated.

Today neutrinos are detected using large vats of chlorine, these baths are buried deep underground so as to avoid back ground noise and work by the equation

V+3717Cl 3718Ar+e-.

One such detector is located in the Homestake Gold Mine in South Dakota.

Since Pauli’s theory in 1930 they have subsequently been observed but never in the abundance predicted. It must be remembered it is a triumph that the elusive particles were seen at all.

Roy and Clarke 1988 (a)