Self-Absorption of Hg and Tl Emission Lines in Two-Dimensional HID Lamps: a Radiative Transfer Study

Abstract

This work investigates self-absorption effects in two-dimensional high-intensity discharge (2D HID) lamps with particular emphasis on mercury (Hg) and thallium (Tl) emission lines. Special attention is devoted to the Tl 535 nm resonance line and selected Hg transitions, both strongly affected by optical thickness and radiative trapping phenomena under high-pressure plasma conditions. A two-dimensional radiative transfer model based on the discrete ordinates method (DOM) is employed to simulate the spectral intensity distribution inside the arc tube. The model accounts for spatial variations in temperature, particle density, and absorption coefficients under local thermodynamic equilibrium (LTE) assumptions. Results show that self-absorption significantly modifies the spectral line profiles, leading to central reversal, line broadening, and intensity redistribution depending on radial and axial plasma positions. The strongest self-absorption effects are observed in cold peripheral regions where ground-state particle densities are high, whereas the hot plasma core remains comparatively optically thinner. The study further demonstrates that Hg and Tl resonance lines exhibit different sensitivities to temperature gradients and optical thickness due to their distinct spectroscopic properties. Implications for optical emission spectroscopy (OES), plasma diagnostics, and line-ratio methods are discussed. The present analysis highlights the importance of accurate multidimensional radiative transfer modeling for understanding spectral distortions and optimizing the performance and luminous efficiency of HID lamps.