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This article concerns the physical phenomenon of synchrotron radiation. For details on the production of this radiation and applications in laboratories, see Synchrotron light source.

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

emitted when charged particles are accelerated radially () is called synchrotron radiation. It is produced in synchrotrons
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

using bending magnets, undulators
Undulator
An undulator is an insertion device from high-energy physics and usually part of a largerinstallation, a synchrotron storage ring. It consists of a periodic structure of dipole magnets . The static magnetic field is alternating along the length of the undulator with a wavelength \lambda_u...

and/or wigglers. It is similar to cyclotron radiation
Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that...

except that is generated by the acceleration of ultrarelativistic
Ultrarelativistic limit
In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light c.Max Planck showed that the relativistic expression for the energy of a particle whose rest mass is m and momentum is p is given by E^2 = m^2 c^4 + p^2 c^2...

(moving near the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

) charged particles through magnetic fields.
This may be achieved artificially in synchrotron or storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...

s, or naturally by fast electrons moving through magnetic fields in space.
The radiation produced in this way has a characteristic polarization and can range over the entire electromagnetic spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

.

## History

Synchrotron radiation was named after its discovery in a General Electric
General Electric
General Electric Company , or GE, is an American multinational conglomerate corporation incorporated in Schenectady, New York and headquartered in Fairfield, Connecticut, United States...

synchrotron accelerator built in 1946 and announced in May 1947 by Frank Elder, Anatole Gurewitsch, Robert Langmuir, and Herb Pollock in a letter entitled "Radiation from Electrons in a Synchrotron". Pollock recounts:
"On April 24, Langmuir and I were running the machine and as usual were trying to push the electron gun and its associated pulse transformer to the limit. Some intermittent sparking had occurred and we asked the technician to observe with a mirror around the protective concrete wall. He immediately signaled to turn off the synchrotron as "he saw an arc in the tube." The vacuum was still excellent, so Langmuir and I came to the end of the wall and observed. At first we thought it might be due to Cherenkov radiation
Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...

, but it soon became clearer that we were seeing Ivanenko
Dmitri Ivanenko
Dmitri Ivanenko , Professor of Moscow State University , made a great contribution to the physical science of the twentieth century, especially to nuclear physics, field theory , and gravitation theory.His outstanding achievements include:* the Fock-Ivanenko coefficients of parallel...

and Pomeranchuk
Isaak Pomeranchuk
Isaak Yakovlevich Pomeranchuk was a Soviet physicist, who was the founder and first head of the theory division at ITEP. The particle pomeron is named in his honour. For his work, Pomeranchuk was twice awarded Stalin Prize .-External links:**...

## Properties of synchrotron radiation

1. Broad Spectrum (which covers from microwaves to hard X-rays): the users can select the wavelength required for their experiment.
2. High Flux: high intensity photon beam allows rapid experiments or use of weakly scattering crystals.
3. High Brilliance: highly collimated photon beam generated by a small divergence and small size source (spatial coherence)
4. High Stability: submicron source stability
5. Polarization: both linear and circular
6. Pulsed Time Structure: pulsed length down to tens of picoseconds allows the resolution of process on the same time scale.

## Emission mechanism

When high-energy particles are in rapid motion, including electrons forced to travel in a curved path by a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

, synchrotron radiation is produced. This is similar to a radio antenna, but with the difference that, in theory, the relativistic speed will change the observed frequency due to the Doppler effect by the Lorentz factor
Lorentz factor
The Lorentz factor or Lorentz term appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula. Because of its ubiquity, physicists generally represent it with the shorthand symbol γ . It gets its name from its earlier...

, .
Relativistic time contraction then bumps the frequency observed in the lab by another factor of , thus multiplying the GHz frequency of the resonant cavity that accelerates the electrons into the X-ray range. The radiated power is given by the relativistic Larmor formula while the force on the emitting electron is given by the Abraham-Lorentz-Dirac force.
The radiation pattern can be distorted from an isotropic dipole pattern into an extremely forward-pointing cone of radiation. Synchrotron radiation is the brightest artificial source of X-rays.
The planar acceleration geometry appears to make the radiation linearly polarized when observed in the orbital plane, and circularly polarized when observed at a small angle to that plane. Amplitude and frequency are however focussed to the polar ecliptic.

### Liénard–Wiechert Field

where

which is the unit vector between the observation point and the position of the charge at the retarded time, and is the retarded time.

In equation (1), and (2), the first terms fall off as the inverse square of the distance from the particle, and this first term is called the generalized Coulomb field or velocity field. And the second terms fall off as the inverse first power of the distance from the source, and it is called the radiation field or acceleration field.
If we ignore the velocity field, the radial component of Poynting's Vector resulted from the Liénard–Wiechert field can be calculated to be

Note that
• The spatial relationship between and determines the detailed angular power distribution.
• The relativistic effect of transforming from the rest frame of the particle to the observer's frame manifests itself by the presence of the factors in the denominator of Eq. (3).
• For ultrarelativistic particles the latter effect dominates the whole angular distribution.

The energy radiated into per solid angle during a finite period of acceleration from to is

Integrating Eq. (4) over the all solid angles, we got relativistic generalization of Larmor's formula

However, this also can be derived by relativistic transformation of the 4-acceleration in Larmor's formula.

### Velocityacceleration: synchrotron radiation

When the charge is in instantaneous circular motion with its acceleration perpendicular to its velocity . Choosing a coordinate system such that instantaneously is in the z direction and is in the x direction. With the customary polar angles defining the direction of observation, the general formula Eq. (4) reduces to

In the relativistic limit , the angular distribution can be written approximately

The factors in the denominators tip the angular distribution forward into a narrow
cone like the beam of a headlight pointing ahead of the particle. The figure of the angular distribution (dP/d vs. plot) has a sharp peak around .
Integrating over the whole solid angle we obtain the total power radiated by one electron

Note that radiated power is proportional to , , and . Because of synchrotron radiation's high power, the surface of the vacuum chamber hit by synchrotron radiation must be cooled.

The energy received by an observer (per unit solid angle at the source) is

Using the Fourier Transformation we move to the frequency space

Angular and frequency distribution of the energy received by an observer (consider only the radiation field)

Therefore, if we know the particle's motion, cross products term, and phase factor, we could calculate the radiation integral. However, calculations are generally quite lengthy (even for simple cases as for the radiation emitted by an electron in a bending magnet, they require Airy function
Airy function
In the physical sciences, the Airy function Ai is a special function named after the British astronomer George Biddell Airy...

or the modified Bessel functions).

Trajectory of the arc of circumference is

In the limit of small angles we compute

Substituting into the radiation integral and introducing

,where the function is modified Bessel function
Bessel function
In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...

.

#### Frequency distribution of radiated energy

From the Eq.(10), we observe that the radiation intensity is negligible for .
Critical frequency is defined as the frequency when and 0. So,

,and critical angle is defined as

For frequencies much larger than the critical frequency and angles much larger than the critical angle, the synchrotron radiation emission is negligible.

Integrating on all angles, we get the frequency distribution of the energy radiated.

If we define

,where . Then,

Note that , if , and , if

Formula for spectral distribution of synchrotron radiation, given above, can be expressed in terms of rapidly coverged integral with no special functions involved (see also modified Bessel functions ) by means of the relation:

#### Synchrotron radiation emission as a function of the beam energy

First, define the critical photon energy as

Then, the relationship between radiated power and photon energy is shown in the graph on the rightside. The higher the critical energy, the more photons wih high energies are generated. Note that, there is no dependence on the energy at longer wavelength.

#### Polarization of synchrotron radiation

In Eq.(10), the first term is the radiation power with polarization in the orbit plane, and the second term is the polarization orthogonal to the orbit plane.
In the orbit plane , the polarization is purely horizontal.
Integrating on all frequencies, we get the angular distribution of the energy radiated

Integrating on all the angles, we find that seven times as much energy is radiated with parallel polarization as with perpendicular polarization. The radiation from a relativistically moving charge is very strongly, but not completely, polarized in the plane of motin.

#### Solution of equation of motion and undulator equation

Undulator
Undulator
An undulator is an insertion device from high-energy physics and usually part of a largerinstallation, a synchrotron storage ring. It consists of a periodic structure of dipole magnets . The static magnetic field is alternating along the length of the undulator with a wavelength \lambda_u...

is consist of periodic array of magnets, so that they provide a sinusoidal magnetic field.

Solution of equation of motion is

where,

, and

,and the parameter is called the undulator parameter.
Condition for the constructive interference of radiation emitted at different poles is

Therefore,

This equation is called the undulator equation.

#### Radiation from the undulator

Using the periodicity of the trajectory, we can split the radiation integral into a sum over terms.

, where

, and
,　　　,　　and

The radiation integral in an undulator can be written as

The sum of generates a series of sharp peaks in the frequency spectrum harmonics of fundamental wavelength

,and depends on the angles of observations and

On the axis(, ), the radiation integral becomes

and,

, where

Note that only odd harmonics are radiated on-axis, and as K increases higher harmonic becomes stronger.

## Synchrotron radiation from accelerators

Synchrotron radiation may occur in accelerators either as a nuisance, causing undesired energy loss in particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

contexts, or as a deliberately produced radiation source for numerous laboratory applications.
Electrons are accelerated to high speeds in several stages to achieve a final energy that is typically in the GeV range. In the LHC
The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....

proton bunches also produce the radiation at increasing amplitude and frequency as they accelerate with respect to the vacuum field, propagating photoelectrons, which in turn propagate secondary electrons from the pipe walls with increasing frequency and density up to 7x1010. Each proton may lose 6.7keV per turn due to this phenomenon.

## Synchrotron radiation in astronomy

Synchrotron radiation is also generated by astronomical objects, typically where relativistic electrons spiral (and hence change velocity) through magnetic fields.
Two of its characteristics include non-thermal power-law spectra, and polarization.

### History

It was first detected in a jet emitted by M87 in 1956 by Geoffrey R. Burbidge
Geoffrey Burbidge
Geoffrey Ronald Burbidge FRS was an English astronomy professor, most recently at the University of California, San Diego. He was married to astrophysicist Dr. Margaret Burbidge.-Education:...

, who saw it as confirmation of a prediction by Iosif S. Shklovsky in 1953, but it had been predicted several years earlier by Hannes Alfvén
Hannes Alfvén
Hannes Olof Gösta Alfvén was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics . He described the class of MHD waves now known as Alfvén waves...

and Nicolai Herlofson in 1950.

T. K. Breus noted that questions of priority on the history of astrophysical synchrotron radiation is quite complicated, writing:
"In particular, the Russian physicist V.L. Ginzburg
Vitaly Ginzburg
Vitaly Lazarevich Ginzburg ForMemRS was a Soviet theoretical physicist, astrophysicist, Nobel laureate, a member of the Russian Academy of Sciences and one of the fathers of Soviet hydrogen bomb...

broke his relationships with I.S. Shklovsky and did not speak with him for 18 years. In the West, Thomas Gold
Thomas Gold
Thomas Gold was an Austrian-born astrophysicist, a professor of astronomy at Cornell University, a member of the U.S. National Academy of Sciences, and a Fellow of the Royal Society . Gold was one of three young Cambridge scientists who in the 1950s proposed the now mostly abandoned 'steady...

and Sir Fred Hoyle
Fred Hoyle
Sir Fred Hoyle FRS was an English astronomer and mathematician noted primarily for his contribution to the theory of stellar nucleosynthesis and his often controversial stance on other cosmological and scientific matters—in particular his rejection of the "Big Bang" theory, a term originally...

were in dispute with H. Alfven
Hannes Alfvén
Hannes Olof Gösta Alfvén was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics . He described the class of MHD waves now known as Alfvén waves...

and N. Herlofson, while K.O. Kiepenheuer and G. Hutchinson were ignored by them."

Supermassive black hole
Supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...

s have been suggested for producing synchrotron radiation, by ejection of jets produced by gravitationally accelerating ions through the super contorted 'tubular' polar areas of magnetic fields. Such jets, the nearest being in Messier 87, have been confirmed by the Hubble telescope as apparently superluminal, travelling at 6×c (six times the speed of light) from our planetary frame. A number of inconsistent solutions have been offered but it is suggested by both the DFM (Discrete Field Model) and 'Einstein Aether theory' to be the columnar effect of charged particles following and travelling within previous 'tubes' of particles, all travelling at 'c' locally with respect to the previous particles. The observations are of change of position, with light from the observations arriving at 'c', so the second postulate of SR (invariance of speed of light) would not be violated.

### Pulsar wind nebulae

A class of astronomical sources where synchrotron emission is important is the pulsar wind nebula
Pulsar wind nebula
A pulsar wind nebula is a nebula powered by the pulsar wind of a pulsar. At the early stages of their evolution, pulsar wind nebulae are often found inside the shells of supernova remnants...

e, or plerions, of which the Crab nebula
Crab Nebula
The Crab Nebula  is a supernova remnant and pulsar wind nebula in the constellation of Taurus...

and its associated pulsar
Pulsar
A pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

are archetypal.
Pulsed emission gamma-ray radiation from the Crab has recently been observed up to ≥25 GeV, probably due to synchrotron emission by electrons trapped in the strong magnetic field around the pulsar.
Polarization in the Crab at energies from 0.1 to 1.0 MeV illustrates a typical synchrotron radiation.

• Synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...

for this type of particle accelerator
• Synchrotron light source for laboratory generation and applications of synchrotron radiation
Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that...

• Relativistic beaming
Relativistic beaming
Relativistic beaming is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light...