Universal FFM Hydrogen Spectral Line Shapes Applied to Ions and Electrons

Abstract

We present a method for the calculation of hydrogen spectral line shapes based on two combined approaches: Universal Model and FFM procedure. We start with the analytical functions for the intensities of the Stark components of radiative transitions between highly excited atomic states with large values of principal quantum numbers n,n’γ1, with Δn = n‐n’≪n for the specific cases of Hn−α line (Δn = 1) and Hn−β line (Δn = 2). The FFM line shape is obtained by averaging on the electric field of the Hooper’s field distribution for ion and electron perturber dynamics and by mixing the Stark components with a jumping frequency rate ve (vi) where v = N1/3u (N is electron density and u is the ion or electron thermal velocity). Finally, the total line shape is given by convolution of ion and electron line shapes. Hydrogen line shape calculations for Balmer Hα and Hβ lines are compared to experimental results in low density plasma (Ne∼1016–1017cm−3) and low electron temperature in order of 10 000K. This method relying on analytic expressions permits fast calculation of Hn−α and Hn−β lines of hydrogen and could be used in the study of the Stark broadening of radio recombination lines for high principal quantum number.