Exact stark analytical function for Hα line based on the FFM model related with plasma parameters

Optical Emission Spectroscopy is a widely used technique for plasma diagnosis, with particular interest in hydrogen atomic emission due to its prevalence in plasmas. However, accurately determining plasma parameters like electron density, electron temperature, and gas temperature starting from the experimental profiles remains a challenge. This paper introduces a comprehensive model for Stark broadening of the Hα line in a wide range of plasma conditions, addressing the limitations of existing analytical expressions for line shapes. The proposed model encompasses the full splitting of the transition into fifteen Lorentzian profiles and electric micro-field fluctuations surrounding the emitting atoms due to collisions with charged particles. Starting from accurate spectral data obtained from realistic computer simulations, fitting parameters of the model, have been obtained by using an optimization method based on a genetic algorithm. The set of parameters of the model are reported for a wide range of plasma conditions. The behavior of these parameters is analyzed to understand their dependence in terms of the electron density and temperature and gas density of the plasma. The model parameters here obtained constitute a useful tool in plasma diagnosis to obtaining the values of the physical parameters of the plasma starting from the experimental profiles.