Thomson scattering

In physics, Thomson scattering is the scattering of electromagnetic radiation by acharged particle. The electric and magnetic components of theincident wave accelerate the particle. As it accelerates, it in turn emits
radiation and thus, the wave is scattered. Thomson scattering is an importantphenomenon 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 speedis much less than the speed of light), the main cause of the acceleration of the particle will be dueto the electric field component of the incident wave. The particle will move inthe direction of the oscillating electric field, resulting in
electromagnetic dipole radiation. The moving particle radiates most strongly in a directionperpendicular to its motion and that radiation will be polarized along thedirection 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 lesspolarized.

The electric fields of the incoming and observed beam can be divided up intothose components lying in the plane of observation (formed by the incoming andobserved beams) and those components perpendicular to that plane. Thosecomponents lying in the plane are referred to as "radial" and thoseperpendicular to the plane are "tangential", since this is how they appear tothe 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 theamplitude, will then be diminished by a factor of cos²(χ). It can be seenthat 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 definedas ε where ε dt dV dΩ dλ is the energyscattered by a volume element $dV$ in time dt into solid angle dΩbetween wavelengths λ and λ+dλ. From the point of view ofan observer, there are two emission coefficients, ε_r corresponding toradially polarized light and ε_t corresponding to tangentially polarizedlight. For unpolarized incident light, these are given by: : $epsilon\_t\; =\; frac\{pi\; sigma\; \}\{2\}~I,n$

: $epsilon\_r\; =\; frac\{pi\; sigma\; \}\{2\}~I,n,cos^2(chi)$

where n is the density of charged particlesat the scattering point, I is incident flux (i.e. energy/time/area/wavelength) andσ is the Thomson differential cross section for the charged particles (area/solid angle), which is : $sigma\; equiv\; left(frac\{q^2\}\{mc^2\}\; ight)^2=left(frac\{q^2\}\{4piepsilon\_0mc^2\}\; ight)^2$

where the first expression is in cgs units, the second in SI units; q is the charge per particle, m the mass per particle, and $epsilon\_0$ a constant, the permittivity of free space.

Note that this is the square of the classical radiusof a point particle of mass m and charge q.For example, for an electron, the differential cross section is: : $sigma\; =7.9407875ldots\; imes\; 10^\{-26\}~\; extrm\{cm\}^2/\; extrm\{sr\}$

The total energy radiated is found by integrating the sum of the emission coefficients over all directions:

:$int\_0^\{2pi\}dphi\; int\_0^pi\; dchi\; left(epsilon\_t+epsilon\_r\; ight)\; sin\; chi=\; I,sigma\_T,n$

where σ_T is the total cross section:

: $sigma\_T\; =\; frac\{8pi\}\{3\}sigma$

For an electron, this cross-section is:

: $sigma\_T\; =6.6524586ldots\; imes\; 10^\{-25\}~\; extrm\{cm\}^2$

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 future Planck mission attempt to measure this polarization.

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

In tokamaks 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.

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]

References

* Billings, Donald E., ``A Guide to the Solar Corona", Academic Press, New York 1966.