Number Density and Abundance of Atoms and Ions in the Channel Plasma of Lightning

Based on the Boltzmann distribution in local thermodynamic equilibrium, the partition functions for N I, N II, N III, and N IV and O I, O II, O III, and O IV were investigated by including highly excited energy levels. Through adding the Debye corrections into the Saha equation, the particle number density for air plasma was studied for various electron temperature (\(T_e\)) and electron density (\(n_e\)) by about 10,000–40,000 K and 5\(\times \)10\(^{15}\)–10\(^{21}\) cm\(^{-3}\). Then, the corresponding abundance for air plasma was gained. Moreover, the changing tendency of particle number density and abundance in air plasma were applied to a lightning plasma when combined with its spectral diagnosis on \(T_e\) and \(n_e\). The measured particle number density for N I, N II, N III, O I, and O II, separately, are 1.20\(\times \)10\(^{16}\), 4.08\(\times \)10\(^{17}\), 6.74\(\times \)10\(^{15}\), 4.72\(\times \)10\(^{15}\), and \(8.82\times 10^{16}\; \text {cm}^{-3}\) together with their measured abundance by about 2.31%, 78.46%, 1.29%, 0.91%, and 16.96%, respectively. Good consistency can be found in the comparison with other experiments.