Abstract
This chapter focuses on an inversion method for ion Doppler shift of spectrum lines that was developed for plasma velocity measurements. By reducing the problem to the vectorial Radon transform, the characteristics of plasma ion velocity distribution, such as vector potential/vorticity and velocity components were computed in two-dimensional space. In case of axial symmetry plasmas the method is reduced to Abel-like inversion. Computer simulation results for 2D and 1D velocity distributions are also explained. Spectral line profiles of plasma ions have often been measured to analyze ion temperature and density, plasma flow velocities, magnetic and electric fields strength, and turbulence parameters. An important disadvantage of spectroscopic measurements is that the line-integrals of local parameters are measured along a line of sight. This complicates the interpretation of the measured Doppler shift of the signals, which contain both plasma velocity and temperature information.
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