Lorentz–Doppler profiles of hydrogen/deuterium lines for magnetic fusion: analytical solution for any angle of observation and any magnetic field strength

Abstract

We extend the analytical results for the Lorentz-Doppler profiles of highly-excited hydrogen/ deuterium spectral lines for the arbitrary strength of the magnetic field B, obtained in a paper by one of us, Oks (2015 J. Quant. Spectr. Rad. Transfer 156 24), for observations parallel or perpendicular with respect to B, to arbitrary angles of the observation ψ. We study the evolution of the effect of the suppression of the π-components (compared to the σ-components) as the angle of the observation ψ decreases from 90°, i.e., as ψ decreases from the value, at which this counterintuitive effect was discovered in the paper quoted above. We show that the suppression of the π-components (compared to the σ-components) occurs at the perpendicular or close to the perpendicular direction of observation (with respect to the magnetic field B), but disappears at lower values of the angle of the observation. Our results should be important, e.g., for spectroscopic diagnostics of edge plasmas of various magnetic fusion devices around the world. Another finding is that the width of the Lorentz-Doppler profiles is a non-monotonic function of the magnetic field for observations perpendicular to B, which is yet another counterintuitive result.

Review of Recent Advances in the Analytical Theory of Stark Broadening of Hydrogenic Spectral Lines in Plasmas: Applications to Laboratory Discharges and Astrophysical Objects

“…In paper [66], From Figures 6 and 7 it is seen that, as the angle of the observation ψ increases from 0 to 90 degrees, the π-components are suppressed, while the σ-components are not; actually, the σ-components even becomes slightly more intense as ψ increases from 0 to 90 degrees. The suppression of the πcomponents is an important counterintuitive result.…”

“…In paper [66], the authors presented five different figures the Lorentz-Doppler profiles of πcomponents and another five different figures the Lorentz-Doppler profiles of σ-components of HHSL as calculated by Equations (6.6) and (6. As an example, we reproduce below only two out of those ten figures.…”

“…It was shown that a relatively strong magnetic field causes a significant suppression of π-components when compared to σ-components for the observation at ψ = 90 degrees, which was a counterintuitive result. 1 In the subsequent paper [66], the authors obtain specific analytical results for the Lorentz-Doppler profiles of HHSL for the arbitrary strength of the magnetic field B and for an arbitrary angle of the observation ψ. In particular, it was shown in [66] that the effect of the suppression of π-components at a relatively strong magnetic field rapidly diminishes as the angle of observation ψ decreases from 90 degrees.…”

“…1 In the subsequent paper [66], the authors obtain specific analytical results for the Lorentz-Doppler profiles of HHSL for the arbitrary strength of the magnetic field B and for an arbitrary angle of the observation ψ. In particular, it was shown in [66] that the effect of the suppression of π-components at a relatively strong magnetic field rapidly diminishes as the angle of observation ψ decreases from 90 degrees. Another finding in [66] was that the width of the Lorentz-Doppler profiles is a non-monotonic function of the magnetic field for observations perpendicular to B, which was yet another counterintuitive result.…”

“…In particular, it was shown in [66] that the effect of the suppression of π-components at a relatively strong magnetic field rapidly diminishes as the angle of observation ψ decreases from 90 degrees. Another finding in [66] was that the width of the Lorentz-Doppler profiles is a non-monotonic function of the magnetic field for observations perpendicular to B, which was yet another counterintuitive result. So, the results presented below should be important for spectroscopic diagnostics of magnetic fusion plasmas [67] and for solar plasmas.…”