Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam: analytical results and possible applications to magnetic fusion edge plasmas

Abstract

We present a theory of the Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam (REB). The theory is developed analytically by using an advanced formalism. We discuss the possible application of these analytical results to magnetic fusion edge plasmas, taking into account also the major outcome of the interaction of a REB with plasmas: the development of strong Langmuir waves.

Stark Broadening of Spectral Lines in Plasmas

“…By monitoring the dynamics of the ratio Γ σ /Γ π , it would be possible, at least in principle, to detect the development of a REB in tokamaks and to engage the mitigation of the problem. Figure 14 (which reproduces Figure 6 from [82]) shows the theoretical profiles of the entire Ly-alpha line, corresponding to the observation that is perpendicular to the REB velocity without the polarizer, at N e = 10 15 cm −3 and T e = 2 eV. The profiles were calculated using Equations (8.10)- (8.13) and presented versus the scaled detuning Δω/Γ π denoted as d. Due to the scaled detuning, the profiles are "universal" in the sense that they are independent of the beam electron density.…”

“…It is seen that as γ increases from unity, both widths significantly decrease. Figure 5 from [82]) presents the ratio Γ σ /Γ π versus the relativistic factor γ at N e = 10 15 cm −3 and T e = 2 eV. It is seen that as γ increases from unity, this ratio increases, then reaches the maximum, and then decreases.…”

“…In paper [82], the results from which we outline below, the authors used the formalism from paper [24] to treat the Stark broadening of hydrogen/deuterium spectral lines by a REB in plasmas. There are two major distinctions from paper [24]: (1) the broadening is by a beam of electrons rather than ions; (2) the electrons are relativistic.…”

“…As an example, the authors of paper [82] explicitly calculated the shape I(Δω,γ) of the spectral line Ly-alpha broadened by a REB, where Δω is the detuning from the unperturbed frequency of the spectral line. Similarly, to paper [24], after inverting the spectral operator, they obtained:…”

“…width ratio Figure 13. Ratio Γ σ /Γ π of the widths of the σand π-components of the Ly-alpha line versus the relativistic factor γ at N e = 10 15 cm −3 and T e = 2 eV [82].…”