Thomson scattering is the
elastic scatteringIn scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .Electron elastic scattering:When an alpha particle...
of
electromagnetic radiationElectromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space...
by a free charged particle, as described by
classical electromagnetismClassical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
. It is just the lowenergy limit of
Compton scatteringIn physics, Compton scattering is a type of scattering that Xrays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an Xray or gamma ray photon, called the Compton effect...
: the particle kinetic energy and photon frequency are the same before and after the scattering. This limit is valid as long as the photon energy is much less than the mass energy of the particle:
.
Introduction
In the lowenergy limit, the electric field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to emit
radiationBremsstrahlung 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 a photon because energy is conserved. The term is...
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
relativisticSpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
(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, and 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 motion 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 beam can be divided up into those components lying in the plane of observation (formed by the incoming and observed beams) 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", since this is how they appear to the observer.
The diagram on the right is in the plane of observation. It shows the radial component of the incident electric field causing a component of motion of the charged particles at the scattering point which also lies in the plane of observation. It can be seen that the amplitude of the wave observed will be proportional to the cosine of χ, the angle between the incident and observed beam. The intensity, which is the square of the amplitude, will then be diminished by a factor of cos
^{2}(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
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, ε
_{r} corresponding to radially polarized light and ε
_{t} corresponding to tangentially polarized light. For unpolarized incident light, these are given by:


where n is the density of charged particles at the scattering point, I is incident flux (i.e. energy/time/area/wavelength) and is the Thomson cross sectionA cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the BeerLambert law....
for the charged particle, defined below. The total energy radiated by a volume element in time dt between wavelengths λ and λ+dλ is found by integrating the sum of the emission coefficients over all directions (solid angle):
The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by

where the first expression is in cgs units, the second in SISi, si, or SI may refer to : Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units; q is the charge per particle, m the mass of particle, and a constant, the permittivityIn electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
of free space. Integrating over the solid angle, we obtain the Thomson cross section (in cgs and SI units):

The important feature is that the cross section is independent of photon frequency. Note that the cross section is simply proportional (by a numerical factor) to the square of the classical radiusThe classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical relativistic model of the electron...
of a point particle of mass m and charge q:

Alternatively, this can be seen in terms of , the Compton wavelengthThe 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...
, and the fine structure constantIn physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part...
:

For an electron, the Thomson crosssection is numerically given by:
Examples of Thomson scattering
The cosmic microwave background is thought to be linearly polarized as a result of Thomson scattering. Probes such as WMAP and the current PlanckPlanck is a space observatory of the European Space Agency and designed to observe the anisotropies of the cosmic microwave background over the entire sky, at a high sensitivity and angular resolution...
mission attempt to measure this polarization.
The solar Kcorona is the result of the Thomson scattering of solar radiation from solar coronal electrons. NASA's STEREOSTEREO is a solar observation mission. Two nearly identical spacecraft were launched into orbits that cause them to respectively pull farther ahead of and fall gradually behind the Earth...
mission will generate threedimensional images of the electron density around the sun by measuring this Kcorona from two separate satellites.
In tokamakA tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
s and other experimental fusionFusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...
devices, the electron temperatures and densities in the plasmaIn physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
can be measured with high accuracy by detecting the effect of Thomson scattering of a highintensity laserA laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
beam.
InverseCompton scatteringIn physics, Compton scattering is a type of scattering that Xrays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an Xray or gamma ray photon, called the Compton effect...
can be viewed as Thomson scattering in the rest frame of the relativistic particle.
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