From the Vector to Scalar Perturbations Addition in the Stark Broadening Theory of Spectral Lines

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. The analytical solution of the problem is unachievable with famous Chandrasekhar–Von-Neumann results up to the present time. The alternative methods are connected with modeling of a real ion Coulomb field dynamics by approximate models. One of the most accurate theories of ions dynamics effect on line shapes in plasmas is the Frequency Fluctuation Model (FFM) tested by the comparison with plasma microfield numerical simulations. The goal of the present paper is to make a detailed comparison of the FFM results with analytical ones for the linear and quadratic Stark effects in different limiting cases. The main problem is connected with perturbation additions laws known to be vector for small particle velocities (static line shapes) and scalar for large velocities (the impact limit). The general solutions for line shapes known in the frame of scalar perturbation additions are used to test the FFM procedure. The difference between “scalar” and “vector” models is demonstrated both for linear and quadratic Stark effects. It is shown that correct transition from static to impact limits for linear Stark-effect needs in account of the dependence of electric field jumping frequency in FFM on the field strengths. However, the constant jumping frequency is quite satisfactory for description of the quadratic Stark-effect. The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented