# Thomson scattering

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Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequency do not change as a result of the scattering. [1] This limit is valid as long as the photon energy is much smaller than the mass energy of the particle: ${\displaystyle \nu \ll mc^{2}/h}$, or equivalently, if the wavelength of the light is much greater than the Compton wavelength of the particle.

Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the kinetic energy of a particle is conserved in the center-of-mass frame, but its direction of propagation is modified. Furthermore, while the particle's kinetic energy in the center-of-mass frame is constant, its energy in the lab frame is not. Generally, elastic scattering describes a process where the total kinetic energy of the system is conserved. During elastic scattering of high-energy subatomic particles, linear energy transfer (LET) takes place until the incident particle's energy and speed has been reduced to the same as its surroundings, at which point the particle is "stopped."

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, which are all believed to have the same charge. Another charged particle may be an atomic nucleus devoid of electrons, such as an alpha particle.

## 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 at the same frequency as the incident wave, and thus the wave is scattered. Thomson scattering is an important phenomenon in plasma physics 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.[ citation needed ] 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.

Bremsstrahlung, from bremsen "to brake" and Strahlung "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Sir Joseph John Thomson was an English physicist and Nobel Laureate in Physics, credited with the discovery and identification of the electron, the first subatomic particle to be discovered.

In physics, special relativity is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

1. the laws of physics are invariant in all inertial systems ; and
2. the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

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 ${\displaystyle dV}$ 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:

${\displaystyle \varepsilon _{t}={\frac {\pi \sigma _{t}}{2}}In}$
${\displaystyle \varepsilon _{r}={\frac {\pi \sigma _{t}}{2}}In\cos ^{2}\chi }$

where ${\displaystyle n}$ is the density of charged particles at the scattering point, ${\displaystyle I}$ is incident flux (i.e. energy/time/area/wavelength) and ${\displaystyle \sigma _{t}}$ is the Thomson cross section for the charged particle, defined below. The total energy radiated by a volume element ${\displaystyle dV}$ in time dt between wavelengths λ and λ+dλ is found by integrating the sum of the emission coefficients over all directions (solid angle):

When two particles interact, their mutual cross section is the area transverse to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as electromagnetism or gravity, their scattering cross section is generally larger than their geometric size. When a cross section is specified as a function of some final-state variable, such as particle angle or energy, it is called a differential cross section. When a cross section is integrated over all scattering angles, it is called a total cross section. Cross sections are typically denoted σ (sigma) and measured in units of area.

${\displaystyle \int \varepsilon \,d\Omega =\int _{0}^{2\pi }d\varphi \int _{0}^{\pi }d\chi (\varepsilon _{t}+\varepsilon _{r})\sin \chi =I\sigma _{t}n(2+2/3)\pi ^{2}=I\sigma _{t}n{\frac {8}{3}}\pi ^{2}.}$

The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by

${\displaystyle {\frac {d\sigma _{t}}{d\Omega }}=\left({\frac {q^{2}}{4\pi \varepsilon _{0}mc^{2}}}\right)^{2}{\frac {1+\cos ^{2}\chi }{2}}}$

expressed in SI units; q is the charge per particle, m the mass of particle, and ${\displaystyle \varepsilon _{0}}$ a constant, the permittivity of free space. (To obtain an expression in cgs units, drop the factor of 4πε0.) Integrating over the solid angle, we obtain the Thomson cross section

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

${\displaystyle \sigma _{t}={\frac {8\pi }{3}}\left({\frac {q^{2}}{4\pi \varepsilon _{0}mc^{2}}}\right)^{2}}$

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

The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energy of a homogeneous charge distribution to the electron's relativistic mass–energy. According to modern understanding, the electron is a point particle with a point charge and no spatial extent. Attempts to model the electron as a non-point particle have been described as ill-conceived and counter-pedagogic. Nevertheless, it is useful to define a length that characterizes electron interactions in atomic-scale problems. The classical electron radius is given as

A point particle is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space.. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. A point particle can also be referred in the case of a moving body in terms of physics

${\displaystyle \sigma _{t}={\frac {8\pi }{3}}r_{e}^{2}}$

Alternatively, this can be expressed in terms of ${\displaystyle \lambda _{c}}$, the Compton wavelength, and the fine structure constant:

${\displaystyle \sigma _{t}={\frac {8\pi }{3}}\left({\frac {\alpha \lambda _{c}}{2\pi }}\right)^{2}}$

For an electron, the Thomson cross-section is numerically given by:

${\displaystyle \sigma _{t}={\frac {8\pi }{3}}\left({\frac {\alpha \hbar c}{mc^{2}}}\right)^{2}=6.6524587158\ldots \times 10^{-29}{\text{ m}}^{2}=66.524587158\ldots {\text{ (fm)}}^{2}}$

[2]

## Examples of Thomson scattering

The cosmic microwave background is linearly polarized as a result of Thomson scattering, as measured by DASI and more recent experiments.

The solar K-corona is the result of the Thomson scattering of solar radiation from solar coronal electrons. The ESA and NASA SOHO mission and the NASA STEREO mission generate three-dimensional images of the electron density around the sun by measuring this K-corona from three separate satellites.

In tokamaks, corona of ICF targets and other experimental fusion devices, the electron temperatures and densities in the plasma can be measured with high accuracy by detecting the effect of Thomson scattering of a high-intensity laser beam.

Inverse-Compton scattering can be viewed as Thomson scattering in the rest frame of the relativistic particle.

X-ray crystallography is based on Thomson scattering.

## Related Research Articles

Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon the static electric (Coulomb) potential, and the minimum distance between particles is set entirely by this potential. The classical Rutherford scattering process of alpha particles against gold nuclei is an example of "elastic scattering" because neither the alpha particles nor the gold nuclei are internally excited. The Rutherford formula further neglects the recoil kinetic energy of the massive target nucleus.

Rayleigh scattering, named after the nineteenth-century British physicist Lord Rayleigh, is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation. Rayleigh scattering does not change the state of material and is, hence, a parametric process. The particles may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, and is most prominently seen in gases. Rayleigh scattering results from the electric polarizability of the particles. The oscillating electric field of a light wave acts on the charges within a particle, causing them to move at the same frequency. The particle therefore becomes a small radiating dipole whose radiation we see as scattered light. This radiation is an integral part of the photon and no excitation or deexcitation occurs.

Compton scattering, discovered by Arthur Holly Compton, is the scattering of a photon by a charged particle, usually an electron. It results in a decrease in energy of the photon, called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron. Inverse Compton scattering occurs when a charged particle transfers part of its energy to a photon.

Synchrotron radiation is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity. It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.

The Mie solution to Maxwell's equations describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the form of an infinite series of spherical multipole partial waves. It is named after Gustav Mie.

In radiometry, irradiance is the radiant flux (power) received by a surface per unit area. The SI unit of irradiance is the watt per square metre. The CGS unit erg per square centimetre per second is often used in astronomy. Irradiance is often called intensity because it has the same physical dimensions, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity.

In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of that particle.

The Newman–Penrose (NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the space-time, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward, and the formalism is well adapted to treatment of the propagation of radiation in curved spacetime. The most often-used variables in the formalism are the Weyl scalars, derived from the Weyl tensor. In particular, it can be shown that one of these scalars-- in the appropriate frame—encodes the outgoing gravitational radiation of an asymptotically flat system.

Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy. It can be parameterized in terms of either the loss angleδ or the corresponding loss tangent tan δ. Both refer to the phasor in the complex plane whose real and imaginary parts are the resistive (lossy) component of an electromagnetic field and its reactive (lossless) counterpart.

The scattering length in quantum mechanics describes low-energy scattering. It is defined as the following low-energy limit:

In the Standard Model, using quantum field theory it is conventional to use the helicity basis to simplify calculations. In this basis, the spin is quantized along the axis in the direction of motion of the particle.

When an electromagnetic wave travels through a medium in which it gets attenuated, it undergoes exponential decay as described by the Beer–Lambert law. However, there are many possible ways to characterize the wave and how quickly it is attenuated. This article describes the mathematical relationships among:

Surface plasmon polaritons (SPPs) are infrared or visible-frequency electromagnetic waves that travel along a metal–dielectric or metal–air interface. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal and electromagnetic waves in the air or dielectric ("polariton").

Plasmonic nanoparticles are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size.

In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The relation for heat transfer can be written as an integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.

## References

1. Chen, Szu-yuan; Maksimchuk, Anatoly; Umstadter, Donald (December 17, 1998). "Experimental observation of relativistic nonlinear Thomson scattering". Nature. 396 (6712): 653–655. arXiv:. Bibcode:1998Natur.396..653C. doi:10.1038/25303.
2. "National Institute of Standards and Technology" . Retrieved 3 February 2015.

Johnson W.R.; Nielsen J.; Cheng K.T. (2012). "Thomson scattering in the average-atom approximation". Physical Review. 86 (3): 036410. arXiv:. Bibcode:2012PhRvE..86c6410J. doi:10.1103/PhysRevE.86.036410. PMID   23031036.