Construction of electron distribution functions from laser scattering spectra

The Thomson scattering spectrum, for laser light scattered by a low density plasma, is determined by the Doppler shifts from the moving electrons. It is shown how the full three-dimensional distribution function may be constructed if spectra are observed in several directions. Calculations using a model loss-cone distribution show that four spectra are sufficient for a faithful reconstruction of f(v). Most of the complications that arise at relativistic electron velocities can be avoided by placing a diffraction grating in the scattered laser beam.