Analytical Approximations in the Theory of Relativistic Thomson Scattering for High Temperature Fusion Plasma

Abstract

The light scattering spectrum from a high temperature plasma is calculated for the second order in v/c (c=light speed) and the second order approximate formula is obtained from the calculation. The blue side shift of the peak derived from the second order approximate formula agrees well with that of the full relativistic spectrum for an electron temperature of several tens of kilo electron-volts and less. The second order apparent temperature and density are deduced with an accuracy of better than 8 percent in the range up to 20 keV and 100 keV for scattering angles θ=90° and 50°, respectively, by application of the least-square procedure.

Design and development of the large helical device TV Thomson scattering

“…accurately. 7 In the initial experiments, since the typical electron temperatures were below 1.5 keV, nonrelativistic spectrum is a good approximation as well. The extra error due to neglecting relativistic effects is estimated to be less than 10%.…”

Raman calibration of the LHD YAG Thomson scattering for electron-density measurements

“…We use the Thomson spectrum that includes the second-order relativistic effect to evaluate ͐ T (T e , ) f 1 ( )d . 5 A similar equation is given for Raman signal S R : Ϫ1/2). 3 The population of the initial rotational state J in thermal equilibrium at a temperature T is given by 6,7 …”

Active Diagnostics

“…To describe Thomson scattering at fusion-relevant temperatures, Equation 3.60 needs to be used together with a relativistic Maxwell distribution function. [27] is given here. [27] is given here.…”