The Coulomb Symmetry and a Universal Representation of Rydberg Spectral Line Shapes in magnetized Plasmas

Abstract

A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two 
 fundamental problems in the
 broadening theory: the analytical description of the radiation transition array
 between excited atomic states and account of a thermal ion motion effect on the line
 shapes formation. The solution to the first problem is based on the semiclassical
 approach to dipole matrix elements calculations and the usage of the specific symmetry properises of the Coulomb field. The second one is considered in terms of the kinetic treatment of the frequency
 fluctuation model (FFM). As the result one has a universal description of line
 shapes under the action of the dynamic of ion’s microfield. The final line shape is
 obtained by the convolution of the ionic line shape with the Voigt electron-Doppler profile. The method is applicable formally for large values of principle
 quantum numbers. However, it is demonstrated the efficiency of the results even for
 well known first members of the hydrogen Balmer series Dalpha and Dbeta.
 The comparison of obtained results with accurate quantum calculations is presented. The new method may be of
 interest for investigations of spectral line shapes of hydrogen-like ions presented in
 different kinds of hot ionized environments with the presence of a magnetic field, including SoL and divertor tokamak plasmas.

The Frequency Fluctuation Model for the van der Waals Broadening

“…This model is widely used 15 for spectral line shape calculations in plasmas (see e.g. [4][5][6][7][8][9]). It was shown that the 16 FFM is equivalent to the method of the quantum kinetic equation [10].…”

“…The examination of the FFM consists in the comparsion of the CT formula ( 12) with the expression (9). In the integrand of ( 10) we will substitute the static profile (14).…”