Emission spectrum of sprites caused by the quasi-electrostatic field above thunderstorm clouds

The synthetic spectrum of sprites caused by quasi-electrostatic field (QEF) of thunderstorm clouds is studied and calculated based on the Boltzmann equation and a single-point charge model. The reduced E-field determined with the single-point charge model is inputted to the Boltzmann model, and the electron energy distribution in the weakly ionization gas in the presence of the QEF is obtained. On the basis of these calculations, the excitation rate of the emission bands of sprites is calculated. The simulation results show that the volume emission rate of each emission band increases with the increase of the reduced E-field. The emission almost comes from several neutral N2 molecule emission bands, while the reduced E-field is lower. With the increase of the reduced E-field, the volume emission rate from two bands of \({\text{N}}_{2}^{ + }\) ion gradually increases, and the magnitude of volume emission rate from \({\text{N}}_{2}^{ + }\) ion-emission bands equals or even exceeds that of the neutral N2 molecule emission bands. The absolute values of volume emission at both N2 molecule and \({\text{N}}_{2}^{ + }\) ion-emission bands can be obtained based on the single-point charge model and the Boltzmann model. The calculated brightness can reach dozens of million Rayleighs which is consistent with the observation.