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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]]

Latest revision as of 00:34, 9 January 2015

I do not ordinarily talk about myself. I love sharing remarkable material with other folks. I also love to discover the online market place since I think you will find a lot of to find out on the market. When I'm around the web.
|
Name: Lila Lynas
Age: 36
Country: Netherlands
City: Apeldoorn
Post code: 7311 Lg
Address: Beekstraat 81
|
My name is Lila Lynas. I life in Apeldoorn (Netherlands).
|
I’m Lila from Apeldoorn doing my final year engineering in Directing. I did my schooling, secured 73% and hope to find someone with same interests in Motor sports.
|
I like Motor sports.
I also to learn Vietnamese in my free time.
|
My name is Lila (50 years old) and my hobbies are Yo-yoing and LARPing.
|
Hello! I am Lila. I am satisfied that I can unite to the entire globe. I live in Netherlands, in the GE region. I dream to head to the various countries, to get acquainted with fascinating people.
|
I'm Lila (27) from Apeldoorn, Netherlands.
I'm learning Vietnamese literature at a local high school and I'm just about to graduate.
I have a part time job in a the office.
|
Hello!
My name is Lila and I'm a 30 years old girl from Apeldoorn.
|
Hi, everybody! My name is Lila.
It is a little about myself: I live in Netherlands, my city of Apeldoorn.
It's called often Eastern or cultural capital of GE. I've married 2 years ago.
I have two children - a son (Casimira) and the daughter (Ramonita). We all like Motor sports.
|
Hi, everybody!
I'm Vietnamese male ;=).
I really love NCIS!
|
Hello from Netherlands. I'm glad to came across you. My first name is Lila.
I live in a small city called Apeldoorn in nothern Netherlands.
I was also born in Apeldoorn 38 years ago. Married in December year 2007. I'm working at the university.
|
My name is Lila Lynas but everybody calls me Lila. I'm from Netherlands. I'm studying at the high school (3rd year) and I play the Clarinet for 4 years. Usually I choose songs from my famous films :).
I have two brothers. I like Amateur radio, watching TV (NCIS) and Sculpting.
|
I'm a 37 years old, married and work at the university (Directing).
In my free time I try to teach myself Vietnamese. I've been twicethere and look forward to returning sometime in the future. I like to read, preferably on my ipad. I like to watch Supernatural and Psych as well as docus about nature. I enjoy Motor sports.
|
I'm Lila and I live in Apeldoorn.
I'm interested in Directing, Motor sports and Vietnamese art. I like travelling and watching NCIS.
|
I'm Lila and I live with my husband and our two children in Apeldoorn, in the GE south area. My hobbies are Australian Football League, Woodworking and Basketball.
|
Hello, I'm Lila, a 30 year old from Apeldoorn, Netherlands.
My hobbies include (but are not limited to) Model Aircraft Hobbies, Australian Football League and watching NCIS.
|
Hi there! :) My name is Lila, I'm a student studying Directing from Apeldoorn, Netherlands.
|
I'm Lila and I live in a seaside city in northern Netherlands, Apeldoorn. I'm 34 and I'm will soon finish my study at Directing.
|
I am Lila from Apeldoorn. I am learning to play the Clarinet. Other hobbies are Motor sports.
|
I am Lila and was born on 24 December 1990. My hobbies are Volleyball and Exhibition Drill.
|
My name is Lila and I am studying Environmental Management and American Studies at Apeldoorn / Netherlands.
}

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