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| Light–matter interaction |
|---|
 |
| Low-energy phenomena: |
| Photoelectric effect |
| Mid-energy phenomena: |
| Thomson scattering |
| Compton scattering |
| High-energy phenomena: |
| Pair production |
| Photodisintegration |
| Photofission |
Thomson scattering is theelastic scattering ofelectromagnetic radiation by a freecharged particle, as described byclassical electromagnetism. It is the low-energy limit ofCompton scattering: the particle'skinetic energy and photon frequency do not change as a result of the scattering.[1] This limit is valid as long as thephoton energy is much smaller than the mass energy of the particle:hν ≪mc2, or equivalently, if the wavelength of the light is much greater than theCompton wavelength of the particle (e.g., for electrons, longer wavelengths than hard x-rays).[2]
Thomson scattering describes the classical limit of electromagnetic radiation scattering from a free particle. An incident plane wave accelerates a charged particle which consequently emits radiation of the same frequency. The net effect is to scatter the incident radiation.[3]
Thomson scattering is an important phenomenon inplasma physics and was first explained by the physicistJ. 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.[2]: 15 The particle will move in the direction of the oscillating electric field, resulting inelectromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its acceleration and that radiation will bepolarized 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.
In the diagram, everything happens in the plane of the diagram. Electric fields of the incoming and outgoing wave can be divided up into perpendicular components. Those perpendicular to the plane are "tangential" and are not affected. Those components lying in the plane are referred to as "radial". The incoming and outgoing wave directions are also in the plane, and perpendicular to the electric components, as usual. (It is difficult to make these terms seem natural, but it is standard terminology.)
It can be shown that the amplitude of the outgoing wave will be proportional to the cosine ofχ, the angle between the incident and scattered outgoing waves. The intensity, which is the square of the amplitude, will then be diminished by a factor ofcos2(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 anemission coefficient which is defined asε, whereεdtdVdΩdλ is the energy scattered by a volume elementdV in timedt into solid angledΩ between wavelengthsλ andλ +dλ. From the point of view of an observer, there are two emission coefficients,εr corresponding to radially polarized light andεt corresponding to tangentially polarized light. For unpolarized incident light, these are given by:wheren is the density of charged particles at the scattering point,I is incident flux (i.e. energy/time/area/wavelength),χ is the angle between the incident and scattered photons (see figure above) andσt is the Thomsoncross section for the charged particle, defined below. The total energy radiated by a volume elementdV in timedt between wavelengthsλ andλ +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 bywhereq is the charge of the particle,m is its mass, andε0 is thepermittivity of free space. Integrating over the solid angle, we obtain the Thomson cross sectionwherer is the particle'sclassical radius,[2]: 17 is itsreduced Compton wavelength, andα is thefine structure constant.
A notable feature is that the cross section is independent of the frequency of the photon.
The value of the Thomson cross-section of the electron is given by:[4]
Thecosmic microwave background contains a small linearly polarized component attributed to Thomson scattering. That polarized component mapping out the so-calledE-modes was first detected byDASI in 2002.
The solarK-corona is the result of the Thomson scattering of solar radiation from solar coronal electrons. The ESA and NASASOHO mission and the NASASTEREO mission generate three-dimensional images of the electron density around the Sun by measuring this K-corona from three separate satellites.
Intokamaks, corona ofICF targets and other experimentalfusion devices, the electron temperatures and densities in theplasma can bemeasured with high accuracy by detecting the effect of Thomson scattering of a high-intensitylaser beam. An upgraded Thomson scattering system in theWendelstein 7-Xstellarator usesNd:YAG lasers to emit multiple pulses in quick succession. The intervals within each burst can range from 2 ms to 33.3 ms, permitting up to twelve consecutive measurements. Synchronization with plasma events is made possible by a newly added trigger system that facilitates real-time analysis of transient plasma events.[6]
In theSunyaev–Zeldovich effect, where the photon energy is much less than the electron rest mass, theinverse-Compton scattering can be approximated as Thomson scattering in the rest frame of the electron.[7]
Models forX-ray crystallography are based on Thomson scattering.
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