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Thomson scattering is the elastic scattering of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
by a free charged particle, as described by
classical electromagnetism Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical fi ...
. It is the low-energy limit of Compton scattering: the particle's
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...
and photon frequency do not change as a result of the scattering. This limit is valid as long as the photon energy is much smaller than the mass energy of the particle: \nu\ll mc^2/h , or equivalently, if the wavelength of the light is much greater than the Compton wavelength of the particle (e.g., for electrons, longer wavelengths than hard x-rays).


Description of the phenomenon

In the low-energy limit, the electric field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to emit
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, vi ...
at the same frequency as the incident wave, and thus the wave is scattered. Thomson scattering is an important phenomenon in
plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...
and was first explained by the physicist J. J. Thomson. As long as the motion of the particle is non- relativistic (i.e. its speed is much less than the speed of light), the main cause of the acceleration of the particle will be due to the electric field component of the incident wave. In a first approximation, the influence of the magnetic field can be neglected. The particle will move in the direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its acceleration and that radiation will be polarized along the direction of its motion. Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. The electric fields of the incoming and observed wave (i.e. the outgoing wave) can be divided up into those components lying in the plane of observation (formed by the incoming and observed waves) and those components perpendicular to that plane. Those components lying in the plane are referred to as "radial" and those perpendicular to the plane are "tangential". (It is difficult to make these terms seem natural, but it is standard terminology.) The diagram on the right depicts the plane of observation. It shows the radial component of the incident electric field, which causes the charged particles at the scattering point to exhibit a radial component of acceleration (i.e., a component tangent to the plane of observation). It can be shown that the amplitude of the observed wave will be proportional to the cosine of χ, the angle between the incident and observed waves. The intensity, which is the square of the amplitude, will then be diminished by a factor of cos2(χ). It can be seen that the tangential components (perpendicular to the plane of the diagram) will not be affected in this way. The scattering is best described by an emission coefficient which is defined as ε where ε dt dV dΩ dλ is the energy scattered by a volume element dV in time dt into solid angle dΩ between wavelengths λ and λ+dλ. From the point of view of an observer, there are two emission coefficients, εr corresponding to radially polarized light and εt corresponding to tangentially polarized light. For unpolarized incident light, these are given by: : \varepsilon_t = \frac \sigma_t In : \varepsilon_r = \frac\sigma_t In \cos^2\chi where n is the density of charged particles at the scattering point, I is incident flux (i.e. energy/time/area/wavelength) and \sigma_t is the Thomson cross section for the charged particle, defined below. The total energy radiated by a volume element dV in time dt between wavelengths λ and λ+dλ is found by integrating the sum of the emission coefficients over all directions (solid angle): : \int\varepsilon \, d\Omega = \int_0^ d\varphi \int_0^\pi d\chi (\varepsilon_t + \varepsilon_r) \sin \chi = I \frac n 2 \pi (2 + 2/3) = \sigma_t I n. The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by : \frac = \left(\frac\right)^2 \frac 2 expressed in SI units; q is the charge per particle, m the mass of particle, and \varepsilon_0 a constant, the
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more i ...
of free space. (To obtain an expression in cgs units, drop the factor of 4''ε''0.) Integrating over the solid angle, we obtain the Thomson cross section : \sigma_t =\frac 3 \left(\frac\right)^2 in SI units. The important feature is that the cross section is independent of photon frequency. The cross section is proportional by a simple numerical factor to the square of the classical radius of a point particle of mass m and charge q, namely : \sigma_t = \frac 3 r_e^2 Alternatively, this can be expressed in terms of \lambda_c, the Compton wavelength, and the
fine structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between e ...
: : \sigma_t = \frac 3 \left(\frac\right)^2 For an electron, the Thomson cross-section is numerically given by: : \sigma_t =\frac 3 \left(\frac\right)^2 = 6.6524587158 \ldots\times 10^ \text^2 = 66.5 \ldots \text^2 = 0.665 \ldots \text


Examples of Thomson scattering

The
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
contains a small linearly-polarized component attributed to Thomson scattering. That polarized component mapping out the so-called E-modes was first detected by DASI in 2002. The solar
K-corona A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma. The Sun's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar e ...
is the result of the Thomson scattering of solar radiation from solar coronal electrons. The ESA and NASA
SOHO Soho is an area of the City of Westminster, part of the West End of London. Originally a fashionable district for the aristocracy, it has been one of the main entertainment districts in the capital since the 19th century. The area was develo ...
mission and the NASA
STEREO Stereophonic sound, or more commonly stereo, is a method of sound reproduction that recreates a multi-directional, 3-dimensional audible perspective. This is usually achieved by using two independent audio channels through a configuration ...
mission generate three-dimensional images of the electron density around the sun by measuring this K-corona from three separate satellites. In
tokamak A tokamak (; russian: токамáк; otk, 𐱃𐰸𐰢𐰴, Toḳamaḳ) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being ...
s, corona of ICF targets and other experimental fusion devices, the electron temperatures and densities in the plasma can be
measured Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared t ...
with high accuracy by detecting the effect of Thomson scattering of a high-intensity
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...
beam. In the Sunyaev-Zeldovich effect, where the photon energy is much less than the electron rest mass, the inverse-Compton scattering can be approximated as Thomson scattering in the rest frame of the electron.
X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angle ...
is based on Thomson scattering.


See also

* Compton scattering * Kapitsa–Dirac effect * Klein–Nishina formula


References

*


External links


Thomson scattering notesThomson scattering: principle and measurements
{{CMB_experiments Atomic physics Scattering Plasma physics