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{{Light–matter interaction}}
 
'''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 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: <math>\nu\ll mc^2/h </math>.
 
== Introduction ==
 
In the low-energy limit, the [[electric]] field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to emit [[Bremsstrahlung|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-[[special relativity|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, and the magnetic field can be neglected. The particle will move in the direction of the oscillating electric field, resulting in [[Dipole#Dipole radiation|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.
 
[[Image:Thomson scattering geometry.png|right]]
 
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<sup>2</sup>(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 <math>dV </math> 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<sub>r</sub> corresponding to radially polarized light and ε<sub>t</sub> corresponding to tangentially polarized light. For unpolarized incident light, these are given by:
 
:<math>
\epsilon_t = \frac{\pi  \sigma_t  }{2}~I\,n
</math>
 
:<math>
\epsilon_r = \frac{\pi  \sigma_t  }{2}~I\,n\,\cos^2\chi
</math>
 
where n is the density of charged particles at the scattering point, I is incident flux (i.e. energy/time/area/wavelength) and <math>\sigma_t</math> is the Thomson [[Cross section (physics)|cross section]] for the charged particle, defined below. The total energy radiated by a volume element <math>dV </math> in time dt between wavelengths λ and λ+dλ is found by integrating the sum of the emission coefficients over all directions (solid angle):
 
:<math>
\int\epsilon d\Omega = \int_0^{2\pi}d\phi \int_0^\pi d\chi \left(\epsilon_t+\epsilon_r\right) \sin \chi = I\,\sigma_t\,n
</math>
 
The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by
: <math>
\frac{d\sigma_t}{d\Omega} \equiv \left(\frac{q^2}{mc^2}\right)^2\frac{1+\cos^2\chi}{2} = \left(\frac{q^2}{4\pi\epsilon_0mc^2}\right)^2\frac{1+\cos^2\chi}{2}
</math>
where the first expression is in [[Centimeter gram second system of units|cgs units]], the second in [[SI]] units; q is the charge per particle, m the mass of particle, and <math>\epsilon_0</math> a constant, the [[permittivity]] of free space. Integrating over the solid angle, we obtain the Thomson cross section (in cgs and SI units):
 
:<math>
\sigma_t = \frac{8\pi}{3}\left(\frac{q^2}{mc^2}\right)^2=\frac{8\pi}{3}\left(\frac{q^2}{4\pi\epsilon_0mc^2}\right)^2
</math>
 
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 electron radius|classical radius]] of a point particle of mass m and charge q:
 
:<math>
\sigma_t \equiv \frac{8\pi}{3}r_e^2
</math>
 
Alternatively, this can be seen in terms of <math>\lambda_c</math>, the [[Compton wavelength]], and the [[Coupling constant|fine structure constant]]:
 
:<math>
\sigma_t  = \frac{8 \pi}{3} \left(\frac{\alpha \lambda_c}{2\pi}\right)^2
</math>
 
For an electron, the Thomson cross-section is numerically given by:
 
:<math>
\sigma_t =\frac{8 \pi}{3} \left(\frac{\alpha \hbar c}{m c^2}\right)^2 = 0.66524574 \ldots\times 10^{-24}~\textrm{cm}^2=0.66524574 \ldots~\textrm{barn}
</math>
 
== Examples of Thomson scattering ==
 
The [[cosmic microwave background]] is linearly polarized as a result of Thomson scattering, as measured by [[Degree Angular Scale Interferometer|DASI]] and more recent experiments.
 
The solar [[K-corona]] is the result of the Thomson scattering of solar radiation from solar coronal electrons. NASA's [[STEREO]] mission generates three-dimensional images of the electron density around the sun by measuring this K-corona from two separate satellites.
 
In [[tokamak]]s and other experimental [[fusion power|fusion]] devices, the electron temperatures and densities in the [[plasma (physics)|plasma]] can be [[plasma diagnostics#Thomson scattering|measured]] with high accuracy by detecting the effect of Thomson scattering of a high-intensity [[laser]] beam.
 
[[Compton scattering|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.
 
==See also==
*[[Compton scattering]]
*[[Klein-Nishina formula]]
 
==References==
*{{cite book|last=Billings|first=Donald E.|title=A guide to the solar corona|year=1966|publisher=Academic Press|location=New York|lccn=66026261}}
 
==External links==
*[http://farside.ph.utexas.edu/teaching/jk1/lectures/node85.html Lecture notes on Thomson scattering]
*[http://hutchinson.belmont.ma.us/tth/tth_example2.html  Thomson scattering notes]
 
{{CMB_experiments}}
 
[[Category:Atomic physics]]
[[Category:Scattering]]
[[Category:Plasma physics]]

Revision as of 05:36, 5 March 2014

I do not commonly mention myself. I enjoy sharing fascinating material with others. I also prefer to take a look at the online market place for the reason that I think there is certainly a great deal of to see on the market. When I'm around the world wide web.
|
My name: Sue Zink
My age: 20
Country: United Kingdom
City: Walworth
Post code: Dl2 2ur
Street: 97 Ivy Lane
|
My name is Sue Zink. I life in Walworth (United Kingdom).
|
I’m Sue from Walworth studying Architecture. I did my schooling, secured 87% and hope to find someone with same interests in Coloring.
|
Im addicted to my hobby Coloring. Sounds boring? Not at all!
I also try to learn Portuguese in my spare time.
|
My name is Sue (27 years old) and my hobbies are Woodworking and Origami.
|
Hello, dear friend! I am Sue. I smile that I can join to the entire world. I live in United Kingdom, in the south region. I dream to see the different countries, to obtain acquainted with intriguing people.
|
I'm Sue (19) from Walworth, United Kingdom.
I'm learning Portuguese literature at a local high school and I'm just about to graduate.
I have a part time job in a university.
|
Hi!
My name is Sue and I'm a 23 years old girl from Walworth.
|
Hi, everybody! My name is Sue.
It is a little about myself: I live in United Kingdom, ipad repair palatine my city of Walworth.
It's called often Northern or cultural capital of . I've married 4 years ago.
I have two children - a son (Lonna) and the daughter (Darell). We all like Coloring.
|
Hello!
I'm Portuguese male :).
I really love Coloring!
|
Hello from United Kingdom. I'm glad to came across you. My first name is Sue.
I live in a small city called Walworth in south United Kingdom.
I was also born in Walworth 37 years ago. Married in August year 2003. I'm working at the post office.
|
My name's Sue Zink but everybody calls me Sue. I'm from United Kingdom. I'm studying at the university (1st year) and I play the Viola for 9 years. Usually I choose songs from my famous films :).
I have two brothers. I love Basketball, watching TV (The Big Bang Theory) and Amateur astronomy.
|
I'm a 44 years old, married and study at the high school (Architecture).
In my spare time I teach myself Portuguese. I've been there and look forward to returning sometime near future. I love to read, preferably on my ebook reader. I really love to watch Bones and NCIS as well as docus about nature. I like Coloring.
|
I'm Sue and I live in Walworth.
I'm interested in Architecture, Coloring and Portuguese art. I like travelling and watching The Big Bang Theory.
|
I'm Sue and I live with my husband and our three children ipad repair in hanover park Walworth, in the south area. My hobbies are Herpetoculture, Jukskei and Vintage car.
|
Hello, I'm Sue, a 24 year old from Walworth, United Kingdom.
My hobbies include (but are not limited to) Amateur geology, Rugby league football and watching The Big Bang Theory.
|
Hi there! :) My name is Sue, I'm a student studying Architecture from Walworth, United Kingdom.
|
I'm Sue and I live in a seaside city in northern United Kingdom, Walworth. I'm 22 and I'm will soon finish my study at Architecture.
|
I am Sue from Walworth. I am learning to play the Viola. Other hobbies are Coloring.
|
Im Sue and was born on 6 August 1988. My hobbies are Locksport and Vehicle restoration.
|
My name is Sue and I am studying Law and Architecture, Art, and Planning at Walworth / United Kingdom.
}

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