Thomson scattering
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 in electromagnetic dipole radiation.
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 wave (i.e. the outgoing wave) can be divided up into those components lying in the plane of observation (formed by the incoming and observed waves) and those components perpendicular to that plane.
(It is difficult to make these terms seem natural, but it is standard terminology.)
The intensity, which is the square of the amplitude, will then be diminished by a factor of cos2(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, εr corresponding to radially polarized light and εt corresponding to tangentially polarized light.
is the density of charged particles at the scattering point,
is the angle between the incident and scattered photons (see figure above) and
is the Thomson cross section 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
(To obtain an expression in cgs units, drop the factor of 4πε0.)
Integrating over the solid angle, we obtain the Thomson cross section
The important feature is that the cross section is independent of light frequency.
The cross section is proportional by a simple numerical factor to the square of the classical radius of a point particle of mass m and charge q, namely[2]: 17
, the Compton wavelength, and the fine structure constant:
The cosmic microwave background contains a small linearly-polarized component attributed to Thomson scattering.
That polarized component mapping out the so-called E-modes was first detected by DASI in 2002.
The ESA and NASA SOHO mission and the NASA STEREO mission generate three-dimensional images of the electron density around the Sun by measuring this K-corona from three separate satellites.
In tokamaks, corona of ICF targets 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.
An upgraded Thomson scattering system in the Wendelstein 7-X stellarator uses Nd:YAG lasers to emit multiple pulses in quick succession.
Synchronization with plasma events is made possible by a newly added trigger system that facilitates real-time analysis of transient plasma events.
[4] In the Sunyaev–Zeldovich effect, where the photon energy is much less than the electron rest mass, the inverse-Compton scattering can be approximated as Thomson scattering in the rest frame of the electron.
[5] Models for X-ray crystallography are based on Thomson scattering.
