An analytic formula for the relativistic Thomson scattering spectrum for a Maxwellian velocity distribution

A derivation of the exact scattered spectrum including depolarization effects is obtained for the LIDAR scattering of light by electrons from an incoherent relativistic plasma and an analytical formula for this spectrum is derived with an error of <0.1% for temperatures as high as 35 keV. The results for exact backscattering are compared with those expected under real measurement conditions, where the backscattered radiation is collected within a small scattering angle about the probing direction. It is shown that the exact backscattering results deviate from real measurement conditions by ∼0.09-0.6% in the temperature range 10-50 keV, which must be taken into account in LIDAR Thomson scattering systems. Note that the assumption of a Maxwellian velocity distribution has been utilized throughout this paper, believing that the straightforward derivation and subsequent analytical formulae shown may prove useful