 Synchrotron radiation

 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.
The electromagnetic radiation emitted when charged particles are accelerated radially () is called synchrotron radiation. It is produced in synchrotrons using bending magnets, undulators and/or wigglers. It is similar to cyclotron radiation except that is generated by the acceleration of ultrarelativistic (moving near the speed of light) charged particles through magnetic fields. This may be achieved artificially in synchrotron or storage rings, 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.
History
Synchrotron radiation was named after its discovery in a General Electric 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".^{[1]} 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, but it soon became clearer that we were seeing Ivanenko and Pomeranchuk radiation."^{[2]}
Properties of synchrotron radiation
 Broad Spectrum (which covers from microwaves to hard Xrays): the users can select the wavelength required for their experiment.
 High Flux: high intensity photon beam allows rapid experiments or use of weakly scattering crystals.
 High Brilliance: highly collimated photon beam generated by a small divergence and small size source (spatial coherence)
 High Stability: submicron source stability
 Polarization: both linear and circular
 Pulsed Time Structure: pulsed length down to tens of picoseconds allows the resolution of process on the same time scale.
Emission mechanism
When highenergy particles are in rapid motion, including electrons forced to travel in a curved path by a magnetic field, 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, γ. Relativistic time contraction then bumps the frequency observed in the lab by another factor of γ, thus multiplying the GHz frequency of the resonant cavity that accelerates the electrons into the Xray range. The radiated power is given by the relativistic Larmor formula while the force on the emitting electron is given by the AbrahamLorentzDirac force. The radiation pattern can be distorted from an isotropic dipole pattern into an extremely forwardpointing cone of radiation. Synchrotron radiation is the brightest artificial source of Xrays. 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.
Formulation
Liénard–Wiechert Field
where
which is the unit vector between the observation point and the position of the charge at the retarded time, and t' 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 t' = T_{1} to t' = T_{2} 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 4acceleration 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 (γ > > 1), the angular distribution can be written approximately
The factors (1 − βcos θ) 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/dΩ vs. γθ plot) has a sharp peak around θ = 0.
Integrating over the whole solid angle we obtain the total power radiated by one electron
Note that radiated power is proportional to 1 / m^{4}, 1 / ρ^{2}, and B^{2}. Because of synchrotron radiation's high power, the surface of the vacuum chamber hit by synchrotron radiation must be cooled.
Radiation integral
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 or the modified Bessel functions).
Example 1: bending magnet
Radiation integral
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 K is modified Bessel function.
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 θ = 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 ^{[3]} (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 θ = 0, 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.
Example 2: undulator
Solution of equation of motion and undulator equation
Undulator 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 K 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
Radiation integral is
Using the periodicity of the trajectory, we can split the radiation integral into a sum over N_{u} terms.
, where
, and , , and
The radiation integral in an undulator can be written as
The sum of δ generates a series of sharp peaks in the frequency spectrum harmonics of fundamental wavelength
,and F_{n} depends on the angles of observations and K
On the axis(θ = 0, φ = 0), the radiation integral becomes
and,
, where
Note that only odd harmonics are radiated onaxis, and as K increases higher harmonic becomes stronger.
Synchrotron radiation from accelerators
Main article: synchrotron light sourceSynchrotron radiation may occur in accelerators either as a nuisance, causing undesired energy loss in particle physics 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 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 7x10^{10}. Each proton may lose 6.7keV per turn due to this phenomenon.^{[4]}
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 nonthermal powerlaw spectra, and polarization.^{[5]}
History
It was first detected in a jet emitted by M87 in 1956 by Geoffrey R. Burbidge,^{[6]} 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 and Nicolai Herlofson ^{[7]} 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 broke his relationships with I.S. Shklovsky and did not speak with him for 18 years. In the West, Thomas Gold and Sir Fred Hoyle were in dispute with H. Alfven and N. Herlofson, while K.O. Kiepenheuer and G. Hutchinson were ignored by them."^{[8]}
Supermassive black holes 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
Crab Nebula A class of astronomical sources where synchrotron emission is important is the pulsar wind nebulae, or plerions, of which the Crab nebula and its associated pulsar are archetypal. Pulsed emission gammaray radiation from the Crab has recently been observed up to ≥25 GeV,^{[9]} probably due to synchrotron emission by electrons trapped in the strong magnetic field around the pulsar. Polarization in the Crab^{[10]} at energies from 0.1 to 1.0 MeV illustrates a typical synchrotron radiation.
See also
 Synchrotron for this type of particle accelerator
 Synchrotron light source for laboratory generation and applications of synchrotron radiation
 Cyclotron Radiation
 Relativistic beaming
 Radiation reaction
 Sokolov–Ternov effect
 Bremsstrahlung
Notes
 ^ Elder, F. R.; Gurewitsch, A. M.; Langmuir, R. V.; Pollock, H. C., "Radiation from Electrons in a Synchrotron" (1947) Physical Review, vol. 71, Issue 11, pp. 829830
 ^ Handbook on Synchrotron Radiation, Volume 1a, ErnstEckhard Koch, Ed., North Holland, 1983, reprinted at "Synchrotron Radiation Turns the Big FiveO"
 ^ M.Kh.Khokonov. Cascade Processes of Energy Loss by Emission of Hard Photons // JETP, V.99, No.4, pp. 690707 \ (2004).
 ^ [1] Synchrotron Radiation Damping in the LHC 2005 Joachim Tuckmantel.
 ^ Vladimir A. Bordovitsyn, "Synchrotron Radiation in Astrophysics" (1999) Synchrotron Radiation Theory and Its Development, ISBN 9810231563
 ^ Burbidge, G. R. "On Synchrotron Radiation from Messier 87. Astrophysical Journal, vol. 124, p. 416"
 ^ Alfvén, H.; Herlofson, N. "Cosmic Radiation and Radio Stars" Physical Review (1950), vol. 78, Issue 5, pp. 616–616
 ^ Breus, T. K., "Istoriya prioritetov sinkhrotronnoj kontseptsii v astronomii %t (Historical problems of the priority questions of the synchrotron concept in astrophysics)" (2001) in IstorikoAstronomicheskie Issledovaniya, Vyp. 26, p. 88  97, 262 (2001)
 ^ "Observation of Pulsed {gamma}Rays Above 25 GeV from the Crab Pulsar with MAGIC", Science 21 November 2008: Vol. 322. no. 5905, pp. 1221–1224"
 ^ Dean et al.,"Polarized GammaRay Emission from the Crab", Science 29 August 2008: Vol. 321. no. 5893, pp. 1183–1185
External links
 Cosmic Magnetobremsstrahlung (synchrotron Radiation), by Ginzburg, V. L., Syrovatskii, S. I., ARAA, 1965
 Developments in the Theory of Synchrotron Radiation and its Reabsorption, by Ginzburg, V. L., Syrovatskii, S. I., ARAA, 1969
 Lightsources.org
 XRay Data Booklet
References
 Brau, Charles A. Modern Problems in Classical Electrodynamics. Oxford University Press, 2004. ISBN 0195146654.
 Jackson, John David. Classical Electrodynamics. John Wiley & Sons, 1999. ISBN 047130932X
Categories: Particle physics
 Synchrotron radiation
 Synchrotronrelated techniques
 Electromagnetic radiation
 Experimental particle physics
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