Thomson scattering

Thomson scattering (after Joseph John Thomson ) describes the elastic scattering of light ( photons ) on charged, free or (compared to photon energy) weakly bound particles (generally quasi-free electrons ). The Thomson scattering is the limit case of the Compton scattering for small photon energies. Both scatters describe the same phenomenon and are based on an elastic collision .

Charged particles are excited by the field of an electromagnetic wave to form coherent harmonic oscillations in the plane of the electric field. Since this oscillation is an accelerated movement, the particles simultaneously radiate energy in the form of an electromagnetic wave of the same frequency ( dipole radiation ). They say the wave is scattered.

Thomson scattering is recoil free scattering; That is, there is no momentum transfer from the photon to the electron. It only occurs as long as the energy of the incident photons is small enough, i.e. that is, the wavelength of electromagnetic radiation is much larger than an atomic radius (e.g. soft X-rays ). With shorter wavelengths, i.e. higher energies, the recoil of the electron must be taken into account ( Compton scattering ).

This model also applies to free electrons in the metal, whose resonance frequency approaches zero due to the lack of restoring forces. Scattering on bound electrons or whole atoms is called Rayleigh scattering .

In practice, Thomson scattering is used (if the densities are not too small) as a method for determining the electron density (intensity of the scattered radiation) and electron temperature (spectral distribution of the scattered radiation, assuming a Maxwell distribution of the velocity).

The classic Thomson cross section results from the oscillator model as a limit case of high frequency (compared to the natural frequency ) : ${\displaystyle \omega \gg \omega _{0}}$

${\displaystyle \sigma _{\mathrm {T} }={\frac {8\pi }{3}}r_{e}^{2}={\frac {1}{6\pi \epsilon _{0}^{2}}}{\frac {e^{4}}{{m_{e}}^{2}c^{4}}}=6{,}652\,458\,558(27)\cdot 10^{-29}\,\mathrm {m} ^{2}}$

where is the classical electron radius . ${\displaystyle r_{e}}$

A better approximation for small energies is obtained by expanding the Klein-Nishina formula :

${\displaystyle \sigma (\nu )=\sigma _{\mathrm {T} }\left(1-2\alpha +{\frac {56}{5}}\alpha ^{2}+\dots \right)}$

with the factor ${\displaystyle \alpha ={\frac {h\nu }{m_{e}c^{2}}}.}$

One application of Thomson scattering is measurements of density in plasma in fusion reactors . Several actively Q-switched Nd: YAG lasers (wavelength 1064 nm) emit parallel light beams from below into the plasma. At right angles to this, the scattered light particles are measured using monochromators using optics . This results in a shift of up to 700 nm. Due to the relatively low pulse rate of the laser, the time resolution is limited. In most cases, however, several lasers can be fired one after the other. This means that the resolution is higher in a short time interval.

Individual evidence

1. ↑ Claude Amsler: Nuclear and Particle Physics . vdf Hochschulverlag, 2007, ISBN 978-3-7281-3695-4 , limited preview in the Google book search.

See also

• Polarization factor